Details of a Researcher - Takano, Naoki

Probabilistic prediction of mechanical behavior of additively manufactured product considering geometrical imperfections associated with building direction

Mizuki Maruno, Naoki Takano

Mechanical Engineering Journal (JSME) 8 ( 6 ) 1 - 13 2021.12

Research paper (scientific journal), Joint Work, Accepted

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Experimental study on deformability of polymeric dental aligner by digital image correlation method

Naoki Yamaguchi, Kohta Ito, Pietro Oldani, Motoya Shiogama, Moeka Sawamura, Haruhisa Nakano, Koutaro Maki and Naoki Takano

Journal of the Society of Materials Science, Japan (日本材料学会) 70 ( 1 ) 57 - 63 2021.01

Research paper (scientific journal), Joint Work, Accepted

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Influence of higher orders of Neumann expansion on accuracy of stochastic linear elastic finite element method with random physical parameters

Lucas Degeneve and Naoki Takano

Mechanical Engineering Letters (JSME) 6 20-00228 2020.10

Research paper (scientific journal), Joint Work, Accepted

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鋼材成分のばらつきを考慮した焼入れプロセスの相変態－熱伝導連成解析と温度に対する感度解析

古川達也, 高野直樹, 杉本剛, 木島秀弥, 田村茂之

日本機械学会論文集 86 ( 887 ) 2020.06

Research paper (scientific journal), Accepted

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Stochastic nonlinear multiscale computational scheme for short fiber reinforced composites to study the influence of microstructural variability on Damage Propagation

Tien-Dat Hoang, Yutaro Abe, Shinya Nakamura, Akio Miyoshi, Naoki Takano

(SN Applied Sciences) 2 ( 182 ) 1 - 16 2020.01

Research paper (scientific journal), Joint Work, Accepted

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Study on Compressive Property of Aluminum Alloy Lattice Structure Additively Manufactured by 3D Printing Technology

Naoki Takano, Hideo Takizawa, Kohta Ito, Kento Odaka, Satoru Matsunaga, Shinichi Abe

Journal of the Society of Materials Science, Japan (Society of Materials Science, Japan) 68 ( 4 ) 351 - 357 2019.04

Research paper (scientific journal), Joint Work, Accepted, ISSN 0514-5163

<p>In order to discuss the quality assurance of additively manufactured lattice structure made by aluminum alloy (AlSi10Mg) using 3D printing technology or selective laser sintering technique, compression test, micro-CT imaging and finite element analysis were carried out. The specimens were manufactured by 2 printing service companies with different expertise, which led to the choice of different process parameters such as the building direction, support structure, powder bed temperature and laser scanning speed. The largely scattered compressive peak loads were in good linear positive correlation with the weight, which is the easiest and convenient index for the quality assurance. On the other hand, the apparent density was almost the same. The reason why the weight of the products was largely scattered was investigated by micro-CT image analysis and finite element analysis. Also by comparison with the CAD data, the influence of manufacturer-dependent process parameters on the strength was discussed.</p>

First-order Perturbation-based Stochastic Homogenization Method Applied to Damage Prediction for Composite Materials

Tien-Dat Hoang and Naoki Takano

Acta Mechanica (Acta Mechanica) 230 ( 3 ) 1061 - 1076 2018.12

Research paper (scientific journal), Joint Work, Accepted, ISSN 00015970

© 2018, Springer-Verlag GmbH Austria, part of Springer Nature. In this paper, a first-order perturbation-based stochastic homogenization method was developed to predict the probabilities of not only macroscopic properties but also microscopic strain damage in multiphase composite materials, considering many random physical parameters. From the stochastic solution of microscopic strains, damage propagation was analyzed to predict where progressive damage would occur in the microstructures of composites subject to a given macroscopic strain. As an example, a short fiber-reinforced plastic, consisting of short fibers, matrix, and interphase, was used to show the influence of random physical parameters for each constituent material on the variability of the homogenized properties and microscopic strain. In another example, a coated particle-embedded composite material was stochastically analyzed to consider even slight influences of uncertainty in the mechanical properties of the coating material and show damage propagation in this coating layer. Characteristic displacements representing material heterogeneity were thoroughly investigated and extensively used with the aim of reducing

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Biomechanical Analysis of Likelihood of Optic Canal Damage in Peri-orbital Fracture

Tomohisa nagasao, Tadaaki Morotomi, Motone Kuriyama, Motoki Tamai, Yoshiaki Sakamoto and Naoki Takano

Computer Assisted Surgery (Computer Assisted Surgery) 23 ( 1 ) 1 - 7 2018.04

Research paper (scientific journal), Joint Work, Accepted

© 2018 The Author(s). Published by Informa UK Limited, trading as Taylor & Francis Group. Purpose: Detection of optic canal fractures is often difficult because of the subtleness of the fracture. If we could clarify impact on which region around the orbit is likely to accompany the fracture of the optic canal, the knowledge should be useful to make early diagnosis of optic canal fractures. The present study was conducted to elucidate this issue. Methods: Ten finite element models were produced simulating the skulls of ten humans (8 males and 2 females; 43.8 ± 10.2 y/o). The peri-orbital area of each of the ten models was divided into eight regions in a clockwise fashion per 45 degrees. These regions were defined as Superior-Medial (0–45 degrees), Medial-Superior (45–90 degrees), Medial-Inferior (90 to 135 degrees), Inferior-Medial (135 to 180 degrees), Inferior-Lateral (180–225 degrees), Lateral-Inferior (225 to 270 degrees), Lateral-Superior (270–315 degrees), and Superior-Lateral regions (315–360 degrees), respectively. Dynamic simulation of applying traumatic energy on each of these regions was conducted. Resultant fracture patterns were evaluated using finite elem

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General Formulation of the First-order Perturbation Based Stochastic Homogenization Method Using Many Random Physical Parameters for Multi-phase Composite Materials

Pin Wen, Naoki Takano and Shusuke Akimoto

Acta Mechanica (Acta Mechanica) 229 ( 5 ) 2133 - 2147 2018.01

Research paper (scientific journal), Joint Work, Accepted, ISSN 00015970

© 2018, Springer-Verlag GmbH Austria, part of Springer Nature. In the numerical prediction of the homogenized macroscopic properties of an arbitrary heterogeneous material with periodic microstructure, a general formulation of the first-order perturbation-based stochastic homogenization method is presented in a discretized form based on the finite element method in order to consider the variability or uncertainty of the mechanical properties of the material models. Many random parameters are defined for each material model and for each component of the stress–strain matrix of the constituent’s material model. The first-order terms of the characteristic displacement are thoroughly studied both theoretically and numerically, and are also used in the verification of the developed computer code. The comparison with the Monte Carlo simulation also supports the proposed formulation.

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Stochastic Prediction of Apparent Compressive Stiffness of Selective Laser Sintered Lattice Structure with Geometrical Imperfection and Uncertainty in Material Property

Naoki Takano, Hideo Takizawa, Pin Wen, Kento Odaka, Satoru Matsunaga and Shinichi Abe

International Journal of Mechanical Sciences (International Journal of Mechanical Sciences) 134 347 - 356 2017.11

Research paper (scientific journal), Joint Work, Accepted, ISSN 00207403

© 2017 Elsevier Ltd Aiming at the future applications of a lattice structure manufactured by selective laser sintering for bone scaffold in the biomedical field, by putting highlight on the possible imperfections influenced by different manufacturing strategies, a numerical prediction method was studied and compared with compressive test results. To consider the geometrical imperfections as well as the uncertainty in sintered material property, the first-order perturbation based stochastic homogenization (FPSH) method was employed. To be able to compare products made by three different printing service companies, maraging steel was used in this study, which was commonly available. Several geometrical imperfections were categorized into kink, notch and hole, and representative dimensions were parameterized and measured statistically using micro-CT images. They were also correlated to the building direction and support types. The numerical prediction revealed the reduction of stiffness in a stochastic way qualitatively. The constructed database of the geometrical imperfections and the FPSH method will be useful in the next occasion of manufacturing unexperienced product.

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Influence of Anisotropic Bone Properties on the Biomechanical Behavior of the Acetabular Cup Implant: A Multiscale Finite Element Study

Vu-Hieu Nguyen, Giuseppe Rosi, Salah Naili, Adrien Michel, Maria-Letizia Raffa, Romain Bosc, Jean-Paul Meningaud, Christine Chappard, Naoki Takano, Guillaume Haiat

Computer Methods in Biomechanics and Biomedical Engineerin (Computer Methods in Biomechanics and Biomedical Engineering) 20 ( 12 ) 1312 - 1325 2017.10

Research paper (scientific journal), Joint Work, Accepted, ISSN 10255842

© 2017 Informa UK Limited, trading as Taylor & Francis Group. Although the biomechanical behavior of the acetabular cup (AC) implant is determinant for the surgical success, it remains difficult to be assessed due to the multiscale and anisotropic nature of bone tissue. The aim of the present study was to investigate the influence of the anisotropic properties of peri-implant trabecular bone tissue on the biomechanical behavior of the AC implant at the macroscopic scale. Thirteen bovine trabecular bone samples were imaged using micro-computed tomography (μCT) with a resolution of 18 μm. The anisotropic biomechanical properties of each sample were determined at the scale of the centimeter based on a dedicated method using asymptotic homogenization. The material properties obtained with this multiscale approach were used as input data in a 3D finite element model to simulate the macroscopic mechanical behavior of the AC implant under different loading conditions. The largest stress and strain magnitudes were found around the equatorial rim and in the polar area of the AC implant. All macroscopic stiffness quantities were significantly correlated (R2 > 0.85, p < 6.5 e-6) with BV/TV (bone volume/total volume). Moreover, the maximum value of the von Mises stress field was significantly correlated with BV/TV (R2 > 0.61, p < 1.6 e-3) and was always found at the bone-implant interface. However, the mean value of the microscopic stress (at the scale of the trabeculae) decrease as a function of BV/TV for vertical and torsional loading and do not depend on BV/TV for horizontal loading. These results highlight the importance of the anisotropic properties of bone tissue.

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Parameterization, Statistical Measurement and Numerical Modeling of Fluctuated Meso/micro-structure of Plain Woven Fabric GFRP Laminate for Quantification of Gometrical Variability

Kohei Hagiwara, Shintaro Ishijima, Naoki Takano, Akio Ohtani, Asami Nakai

Mechanical Engineering Journal (JSME) 4 ( 4 ) 2017.08

Research paper (scientific journal), Joint Work, Accepted

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FRPの確率的RTM成形プロセスシミュレーションにおける裾野分布の解析

高野直樹・石島慎太郎

日本機械学会論文集 83 ( 851 ) 2017.07

Research paper (scientific journal), Joint Work, Accepted

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Stochastic Multi-scale Finite Element Analysis of the Drilling Force of Trabecular Bone during Oral Implant Surgery

Daisuke Tawara, Naoki Takano, Hideaki Kinoshita, Satoru Matsunaga and Shinichi Abe

International Journal of Applied Mechanics (International Journal of Applied Mechanics) 8 ( 6 ) 1650075 2016.08

Research paper (scientific journal), Joint Work, Accepted, ISSN 17588251

© 2016 World Scientific Publishing Europe Ltd. To avoid procedural accidents during/after oral implant surgery in a jawbone (e.g., perforation of the lingual side due to an inadequate drilling angle or scratching the mandibular canal), it is important for dentists to develop skilled drilling techniques. We have developed a stochastic multi-scale prediction of apparent elastic moduli of the jawbone with modified first-order perturbation-based stochastic homogenization in which individual differences of drilling properties relating to bone quality can be evaluated with a force-sensitive device. To establish drilling properties in various types of jawbone and the perforation case, and for drill diameters, we propose an original computational method that avoids procedural accidents by defining the drilling angle as a parameter and quantifying individual differences and the inner distribution of bone quality in several jawbones as a drilling force. Three samples demonstrated that drilling forces changed depending on the trabecular structure, with the drilling force changing little around the mandibular canal and increasing just before perforation. Drilling force also depended on the drill diameter but did not always match its size. Estimated drilling forces of the expected value and 50% and 90% probability results suggested prominent differences in drilling properties. This information enables dentists to develop a skillful surgical technique.

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Desktop Micro-CT Image-based Dynamic FEM Analysis of Stress Wave Pathways between Mandibular Trabecular Bone and Cortical Bone with Comparisons to Virtual Models with Eliminated Materials on Pathways

Haruhisa Nakano, Naoki Takano, Koutaro Maki

Journal of Biomechanical Science and Engineering (JSME) 11 ( 3 ) 1 - 11 2016.08

Research paper (scientific journal), Joint Work, Accepted, ISSN 18809863

© 2016 The Japan Society of Mechanical Engineers. To a nalyze the biomechanical behavior of human bone, micro-CT image-based static FEM analyse s considering trabecular architecture have been carried out. In the field of dental biomechanics, not only the static analysis but also dynamic analysis against impact load is required. In this paper, a desktop micro-CT was used for the right half of a human mandible with 0.103 mm resolution after dissecting. The lost information by a saw was recovered by the homogenization model. The impact load was applied to the implant in the molar part and the load transfer from the implant to the cortical bone and trabecular bone was considered. The stress wave pathways from the implant to the condyle were analyzed by comparison with virtual FEM models with eliminated materials on pathways. It was revealed that the stress wave transferred from the implant neck and end part to peri-implant trabecular bone played a significant mechanical role. It was also found that the apparent wave speed in the trabecular bone region was as fast as that in the cortical bone.

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Numerical Prediction of Scattered Initial Fracture Load of Perforated Thin Plate under Tension by Monte Carlo FEM Simulation with Stepwise Limited Sampling

Shusuke Akimoto and Naoki Takano

Mechanical Engineering Letters 2 1 - 8 2016.06

Research paper (scientific journal), Joint Work, Accepted

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Quantitative study of force sensing while drilling trabecular bone in oral implant surgery

Mohammad Aimaduddin Atiq bin Kamisan, Hideaki Kinoshita, Fumiya Nakamura, Shinya Homma, Yasutomo Yajima, Satoru Matsunaga, Shinichi Abe and Naoki Takano

Journal of Biomechanical Science and Engineering (JSME) 11 ( 3 ) 1 - 9 2016.06

Research paper (scientific journal), Joint Work, Accepted, ISSN 18809863

© 2016 The Japan Society of Mechanical Engineers. A survey done recently showed that almost 30 percent of the accidents occurred during oral implant surgery were concerned with the mandibular canal in the trabecular bone region and most of them were related to the drilling process. One of the reasons known is due to the clinicians' lack of knowledge and experience. In order to overcome the problem, through the educational approach, we proposed and developed a new system mainly for dental colleges' students, by focusing on drilling the mandibular trabecular bone. The system comes in the form of an oral implant surgery training simulator that enables student to sense the reaction force during drilling. The developed system was then evaluated by expert clinicians and dental college's students. A total of 8 clinicians and 24 students tested all three samples of drilling force database. The clinicians were asked to describe the drilling force based on a stiffness scale while the students are required to drill two samples first before drilling the third sample. They were asked to sketch the third samples based on the comparison of previous samples. Based on the evaluation done, it was found that the quantification of force sensed during drilling could be derived from the combination of drilling force and speed obtained through the relative value of comparison with the previous or accumulated experience of drilling. The results of this study also indicate that the oral implant surgery training simulator could help students learn the difference of drilling force sense dependent on the bone quality through repeated usage and practices.

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Probabilistic Multiscale Analysis of Three-phase Composite Material Considering Uncertainties in Both Physical and Geometrical Parameters at Microscale

Pin Wen, Daisuke Kurita and Naoki Takano

Acta Mechanica (Acta Mechanica) 227 ( 10 ) 2735 - 2747 2016.05

Research paper (scientific journal), Joint Work, Accepted, ISSN 00015970

© 2016, Springer-Verlag Wien. A probabilistic multiscale framework is proposed to characterize the probabilistic behaviors of macroscopic elastic properties of multiphase composite materials. The first-order perturbation-based stochastic homogenization method is extended to incorporate inherent randomness existed in multiphase constituents materials on basis of our previous work for porous material. Moreover, a generalized stochastic method is introduced to combine above with morphological nonparametric uncertainties. A numerical example for coated particulate composite material demonstrated the feasibility and effectiveness of proposed methods.

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Prediction of Apparent Properties with Uncertain Mateial Parameters Using High-order Fictitious Domain Methods and PGD Model Reduction

Gregory Legrain, Mathilde Chevreuil and Naoki Takano

International Journal for Numerical Methods in Engineering (International Journal for Numerical Methods in Engineering) 109 ( 3 ) 345 - 367 2016.04

Research paper (scientific journal), Joint Work, Accepted, ISSN 00295981

Copyright © 2016 John Wiley & Sons, Ltd. This contribution presents a numerical strategy to evaluate the effective properties of image-based microstructures in the case of random material properties. The method relies on three points: (1) a high-order fictitious domain method; (2) an accurate spectral stochastic model; and (3) an efficient model-reduction method based on the proper generalized decomposition in order to decrease the computational cost introduced by the stochastic model. A feedback procedure is proposed for an automatic estimation of the random effective properties with a given confidence. Numerical verifications highlight the convergence properties of the method for both deterministic and stochastic models. The method is finally applied to a real 3D bone microstructure where the empirical probability density function of the effective behaviour could be obtained. Copyright © 2016 John Wiley & Sons, Ltd.

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Macro/micro simultaneous validation for multiscale analysis of semi-periodically perforated plate using full-field strain measurement

T. Matsuda, T. Ito, S. Akimoto, H. Kobori, K. Goto and N. Takano

International Journal of Mechanical Sciences (Elsevier) 110 34 - 40 2016.03

Research paper (scientific journal), Joint Work, Accepted, ISSN 00207403

© 2016 Elsevier Ltd. Multiscale analysis of a semi-periodically perforated plate based on a homogenization theory is experimentally validated both macroscopically and microscopically, using a full-field strain measurement. To do this, a plate-fin-type perforated plate with a misaligned microstructure is considered as a semi-periodically perforated plate. Then, a homogenization theory that can analyze macroscopic behavior and microscopic stress and strain distributions of the perforated plate is presented. To validate the theory, a tensile test of a plate-fin-type semi-periodically perforated plate made of epoxy resin is conducted. During the test, the microscopic deformation of the specimen is observed with a digital image correlation (DIC) full-field measurement system, from which microscopic strain distribution of the specimen is calculated. It is shown that the obtained strain distribution satisfies the unit-cell periodicity except at edges of the periodic structure, and that the strain distribution is in good agreement with the result of analysis using the homogenization theory. It is also shown that the macroscopic stress-strain relationships obtained by the experiment and analysis agree well, supporting the macroscopic and microscopic validity of the multiscale analysis using the homogenization theory.

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Drilling Force and Speed for Mandibular Trabecular Bone in Oral Implant Surgery

Mohammad Aimaduddin Atiq bin Kamisan, Kenichiro Yokota, Takayuki Ueno, Hideaki Kinoshita, Shinya Homma, Yasutomo Yajima, Sinichi Abe and Naoki Takano

Biomaterials and Biomechanics in Bioengineering (TECHNO Press) 3 ( 1 ) 15 - 26 2016.03

Research paper (scientific journal), Joint Work, Accepted

Probabilistic homogenization and sensitivity analysis for robust design of coated particulate composite material considering non-parametric geometrical uncertainty at microscale

Pin Wen, Kosho Kamijo, Daichi Kurita and Naoki Takano

Transactions of JSCES (Transactions of the Japan Society for Computational Engineering and Science) 2016 ( 20160005 ) 1 - 10 2016.02

Research paper (scientific journal), Joint Work, Accepted

© 2016 by the Japan Society for Computational Engineering and Science. The aim of this study is that with consideration of geometrical fluctuation, robust design is made to assure performance of material more reliable to fabrication process. Firstly a target microstructure is defined as the optimum solution for coated particulate material. Then a slightly fluctuated computational models are generated in which some random variables are defined. Multiscale analysis is done to obtain homogenized Young’s modulus, shear modulus and an index with respect to strength. Probabilistic sensitivity for those quantities of interest against design variables is analyzed by means of response surface method. For response surface, this paper studies a case where the scattering of sampling points is clustered. The characteristics of cluster sampling points determine the response surface strategy as quadratic polynomial and least square regression method. Finally the numerical result of a specific robust design for coated particulate composite material reveals that when the mean radius of particle is bigger and mean coating thickness is smaller, the less sensitive index is. It will provide a reliable guidance and save cost in the development of wide range of composite materials.

Development of a Drilling Simulator for Dental Implant Surgery

Hideaki Kinoshita, Masahiro Nagahata, Naoki Takano, Shinji Takemoto, Satoru Matsunaga, Shinichi Abe, Masao Yoshinari and Eiji Kawada

Journal of Dental Education (Journal of Dental Education) 80 ( 1 ) 83 - 90 2016.01

Research paper (scientific journal), Joint Work, Accepted, ISSN 00220337

The aim of this study was to develop and evaluate a dental implant surgery simulator that allows learners to experience the drilling forces necessary to perform an osteotomy in the posterior mandibular bone. The simulator contains a force-sensing device that receives input and counteracts this force, which is felt as resistance by the user. The device consists of an actuator, a load cell, and a control unit. A mandibular bone model was fabricated in which the predicted forces necessary to drill the cortical and trabecular bone were determined via micro CT image-based 3D finite element analysis. The simulator was evaluated by five dentists from the Department of Implantology at Tokyo Dental College. The ability of the evaluators to distinguish the drilling resistance through different regions of the mandibular bone was investigated. Of the five dentists, four sensed the change in resistance when the drill perforated the upper cortical bone. All five dentists were able to detect when the drill made contact with lingual cortical bone and when the lingual bone was perforated. This project successfully developed a dental implant surgery simulator that allows users to experience the forces necessary to drill through types of bone encountered during osteotomy. Furthermore, the researchers were able to build a device by which excessive drilling simulates a situation in which the lingual cortical bone is perforated-A situation that could lead to negative repercussions in a clinical setting. The simulator was found to be useful to train users to recognize the differences in resistance when drilling through the mandibular bone.

The “Sea” Should Not Be Operated on in Scar Revision for “Island-Like” Scars

Tomohisa Nagasao, Yusuke Hamamoto, Motoki Tamai, Hiroo Kudo, Toshiya Ensako, Tetsukuni Kogure, Naoki Takano, Yoshio Tanaka

Medical Hypotheses 2015.04

Research paper (scientific journal), Joint Work, Accepted

Probabilistic Analysis of Mechanical Behaviour of Mandibular Trabecular Bone Using a Calibrated Stochastic Homogenization Model

Daisuke Tawara, Masahiro Nagahata, Naoki Takano, Hideaki Kinoshita and Shinichi Abe

Acta Mechanica (Springer) 226 ( 7 ) 3275 - 3287 2015

Research paper (scientific journal), Joint Work, Accepted, ISSN 00015970

© 2015, Springer-Verlag Wien. Surgical success of drilling in oral implantology depends on the sense of force on the fingers or feeling of a dental clinician, which is related to the quality of trabecular bone in the jawbone expressed by apparent mechanical characteristics. As the mechanical properties of trabecular bone depend on the bone volume fraction, microstructure, and many other factors closely related to individual differences, a probabilistic numerical procedure to assess drilling force is proposed. Using a micro-CT-based jawbone model, a first-order perturbation-based stochastic homogenization method was employed to estimate the possible scattering of apparent mechanical properties of the trabecular bone region. The complicated drilling problem was simplified to sequential linear static FEAs, to which the predicted apparent Young’s modulus and shearing moduli in the drilling direction were applied. The FEAs demonstrated that the homogenized mechanical properties showed anisotropy, which might lead to differences in the drilling forces at different drilling angles. The numerically estimated drilling forces were shown by the expected value, 50 %-probability result, and 90%-probability result and revealed that one patient among two or ten patients would probably have poor bone quality. There was a remarkable difference in the drilling forces between the expected value and the 90%-probability result.

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Scoring of Deformed Costal Cartilages Reduces Postoperative Pain after Nuss Procedure for Pectus Excavatum

Tomohisa Nagasao, Yusuke Hamamoto, Motoki Tamai, Tetsukuni Kogure, Hua Jiang, Naoki Takano and Yoshio Tanaka

Thoracic and Cardiovascular Surgeon (Thoracic and Cardiovascular Surgeon) 64 ( 1 ) 62 - 69 2015

Research paper (scientific journal), Joint Work, Accepted, ISSN 01716425

© 2016 Georg Thieme Verlag KG Stuttgart · New York. Objective The present study aims to elucidate whether or not scoring deformed cartilages reduces postoperative pain after the Nuss procedure for pectus excavatum patients. Methods A total of 46 pectus excavatum patients for whom the Nuss procedure was conducted were included in the study. The patients were categorized into two groups, depending on whether or not the supplementary maneuver of scoring deformed cartilages was performed in addition to the Nuss procedure. Patients for whom deformed costal cartilages were scored were categorized as the Scoring Group (n = 24); those who received no such scoring were categorized as the Non-Scoring Group (n = 22). After evaluating the maximum stresses occurring on the thoraces by means of dynamic simulation using finite element analyses, intergroup comparison of the maximum von-Mises stress values was performed. Furthermore, after quantifying postoperative pain as the frequency with which patients injected anesthetics through an epidural pain-control system within 2 postoperative days, the degree of pain was compared between the two groups. Results The maximum stresses occurring on the thorax were significantly greater for the Non-Scoring Group than for the Scoring Group; injection frequency was also greater for the Non-Scoring Group (average 4.9 times for 2 days) than for the Scoring Group (average 2.5 times for 2 days). Conclusion High stresses occur due to the performance of the Nuss procedure, causing postoperative pain. The stresses can be reduced by performing supplementary scoring on deformed cartilages. Accordingly, postoperative pain is reduced.

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Multiscale Stress Analysis of Trabecular Bone Around Acetabular Cup Implant by Finite Element Mesh Superposition Method

Makoto Tsukino, Naoki Takano, Adrien Michel and Guillaume Haiat

Mechanical Engineering Letters (JSME) 1 ( 15-00354 ) 1 - 8 2015

Research paper (scientific journal), Joint Work, Accepted

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Stochastic Homogenization Analysis of FIB-SEM Image-based Hierarchical Model of Sprayed Porous ZrO2

Yuma Miyauchi, Naoki Takano and Pin Wen

Mechanical Engineering Letters (JSME) 1 ( 15-00389 ) 1 - 8 2015

Research paper (scientific journal), Joint Work, Accepted

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Probabilistic prediction of homogenized property and update of prediction for spherical porous material considering microstructural uncertainties

Pin Wen, Kenichiro Yokota and Naoki Takano

Journal of Multiscale Modelling (Imperial College Press) 6 ( 4 ) 1 - 19 2015

Research paper (scientific journal), Joint Work, Accepted

The "Sea" should not be operated on in scar revision for "Island-Like" scars

Nagasao T., Hamamoto Y., Tamai M., Kudo H., Ensako T., Kogure T., Takano N., Tanaka Y.

Medical Hypotheses (Medical Hypotheses) 85 ( 2 ) 215 - 218 2015

ISSN 03069877

© 2015 Elsevier Ltd. Scars developing on body surfaces not only restrict body movement, but are also problematic from a cosmetic standpoint. Hence, revision is conducted by removing the scar and re-suturing the resultant defects. In performing scar revision, care should be taken to prevent the re-sutured wounds from developing hypertrophy again. Scars often present a pattern where hard, red parts are separated by soft parts in between. As the hard and soft parts may be analogized as islands and seas respectively, we call this the "Island-Like" scar. Two strategies can be taken to treat scars of this type. The first is to remove the entire scar-including both hard and soft parts; the second is to remove only the hard parts and leave the soft parts untouched. The authors conducted a biomechanical study using finite element analyses and found that as a body moves, greater stresses occur in the peri-wound regions with the first strategy than with the second strategy. A wound's likelihood to develop hypertrophy increases as the stresses working on it increase. Hence, it is hypothesized that the second strategy carries less risk of the operated wounds developing re-hypertrophy than the first strategy. Based on this logic, in performing scar revision for scars consisting of hard and soft parts, it is recommended only to remove only hard parts and not to operate on soft parts in between.

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Irregular Iocation of Major Pectoral Muscle Can Be A Causativ Factor of Pectus Excavatum

Tomohisa Nagasao, Yusuke Shimizu, Tadaaki Morotomi, Naoki Takano, Hua Jiang and Kazuo Kishi

Medical Hypotheses 82 ( 5 ) 512 - 517 2014.05

Research paper (scientific journal), Joint Work, Accepted

Irregular location of major pectoral muscle can be a causative factor of pectus excavatum

Nagasao T., Shimizu Y., Morotomi T., Takano N., Jiang H., Kishi K.

Medical Hypotheses (Medical Hypotheses) 82 ( 5 ) 512 - 517 2014.05

ISSN 03069877

Pectus excavatum-commonly known as funnel chest-is one of the most frequently observed congenital deformities, in which the patients' thoraces present concavity. This paper presents our original hypothesis that the abnormal positioning of the major pectoral muscle can be a potential factor in the occurrence of pectus excavatum, and evaluates the validity of the hypothesis by performing an anatomical and a biomechanical study. An anatomical study on clinical cases revealed that the major pectoral muscle tends to be positioned more superiorly in pectus excavatum patients than in normal persons. The biomechanical study, using three-dimensional finite element dynamic simulation, revealed that the major pectoral muscle functions to elevate the sternum and that the elevating effect is reduced when the muscle is located at superior regions on the thoracic wall. These findings support our hypothesis that the abnormal position of the major pectoral muscle is a potential causative factor for pectus excavatum. This hypothesis suggests that, during surgical correction of pectus excavatum with an open approach, surgeons should reposition the major pectoral muscle to its correct anatomical position to avoid recurrence. © 2014 .

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Classification and Visualization of Primary Trabecular Bone in Lumbar Vertebrae

Khairul Salleh Basaruddin, Junya Omori, Naoki Takano and Takayoshi Nakano

Advances in Biomechanics and Applications 1 ( 2 ) 111 - 126 2014.04

Research paper (scientific journal), Joint Work, Accepted

Estimation of Apparent Elastic Moduli of Trabecular Bone Considering Biological Apatite (BAp) Crystallite Orientation in Tissue Modulus

Khairul Salleh Basaruddin and Naoki Takano

Advanced Materials Research (Advanced Materials Research) 894 167-171 - 171 2014.03

Research paper (scientific journal), Joint Work, ISSN 9783038350323

This study presents a prediction of apparent elastic moduli of vertebral trabecular bone using the homogenization method. A micro-finite element (FE) model of trabecular bone was reconstructed from a sequential of cross-section micro-CT image by converting bone voxels to brick elements. Eight regions of interest (ROIs) were extracted from two lumbar vertebra bone specimens of healthy and osteoporotic. The homogenization method and finite element method was employed to analyze the microscopic trabecular bone. Bone tissue property was modeled as orthotropy material considering the biological apatite (BAp) crystallite orientation. This research focuses on the effect of morphological difference between healthy and osteoporotic bones to the apparent elastic moduli. The change of degree of anisotropy was also discussed. Comparison of the calculated Young's moduli in vertical axis with Keyak et al.'s experimental result showed good agreement and proved the reliability of the numerical model. © (2014) Trans Tech Publications, Switzerland.

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Practical Monte Carlo Simulation Method Highlighting on Tail Probability with Application to Biomechanics Analysis of Pressure Ulcer

Samuel Susanto Slamet, Kyohei Hatano, Naoki Takano and Tomohisa Nagasao

Transactions of Japan Society for Computational Engineering and Science (Transactions of the Japan Society for Computational Engineering and Science) 2014 ( 2014 ) Paper No.20140001 2014.02

Research paper (scientific journal), Joint Work, Accepted

The Monte Carlo method is a well-known method for calculating uncertainty, but it has the disadvantage of high computational cost because it usually requires 10,000 sampling points. In this paper, a practical sampling algorithm named Stepwise Limited Sampling (SLS) is proposed to obtain both accurate expected values and very accurate tail probability values in the Monte Carlo simulation. This method was then applied to a biomechanics problem concerning the risk prediction of pressure ulcers. It is known that the initial damage that leads to a fatal stage of pressure ulcer occurs in deep muscle, but its location has not been clarified. By modeling assumed damage at the bone-muscle interface in the human buttock as a cutout, and by judging whether the damage propagates or not, sets of material properties of muscle and fat in the tail probability that result in high interface shear strain were obtained as a function of body positioning during nursing. © 2014 by the Japan Society for Computational Engineering and Science.

Association between the Peri-implant Bone Structure and Stress Distribution around the Mandibular Canal: A Three-dimensional Finite Element Analysis

Hideaki Kinoshita, Ken Nakahara, Satoru Matsunaga, Akinobu Usami, Masao Yoshinari, NaokiTakano, Yoshinobu Ide and Shinichi Abe

Dental Materials Journal (Dental Materials Journal) 32 ( 4 ) 637-642 - 642 2013.08

Research paper (scientific journal), Joint Work, Accepted, ISSN 02874547

The aim of this study was to elucidate the association between the bone structure at implant insertion sites and stress distribution around the mandibular canal by means of three-dimensional finite element (3D FE) analysis. Four FE models were created with slice data using micro-computed tomography (micro-CT), and 3D FE analysis was performed. Mechanical analysis showed that the load reached the mandibular canal via the trabecular structure in all FE models. High levels of stress were generated around the mandibular canal when the distance between the mandibular canal and the implant decreased. High stress levels were also observed when cortical bone thickness and bone volume/total volume (BV/TV) were low. Our findings suggest that load is transmitted to the mandibular canal regardless of differences in the thickness of cortical bone or cancellous bone structure, but excessive load may be generated in bone with thin cortical and coarse cancellous structures.

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Consideration of Shear Modulus in Biomechanicl Analysis of Peri-implant Jaw Bone: Accuracy Verification using Image- based Multi-scale Simulation

Satoru Matsunaga, Hiroyoshi Naito, Yuichi Tamatsu, Naoki Takano, Shinichi Abe and Yoshinobu Ide

Dental Materials Journal 32 ( 3 ) 425-432 2013.08

Research paper (scientific journal), Joint Work, Accepted

Transformation of Keloids is Determinel by Stress Occurrence Patterns on Peri-keloid Regions in Response to Body Movement

Tomohisa Nagasao, Noriko Aramaki-Hattori, Yusuke Shimizu, Sumiko Yoshitatsu, Naoki Takano and Kazuo Kishi

Medical Hypotheses 81 ( 1 ) 136-141 2013.07

Research paper (scientific journal), Joint Work, Accepted

Transformation of keloids is determined by stress occurrence patterns on peri-keloid regions in response to body movement

Nagasao T., Aramaki-Hattori N., Shimizu Y., Yoshitatsu S., Takano N., Kishi K.

Medical Hypotheses (Medical Hypotheses) 81 ( 1 ) 136 - 141 2013.07

ISSN 03069877

Keloids gradually change their shapes as they grow. We hypothesize that the change of keloid morphology reflects the incremental change of the stress patterns occurring in peri-keloid regions due to movement of the keloid-carrying body part. To examine the validity of this hypothesis, we used three-dimensional finite element analysis to calculate the stresses occurring in the peri-keloid regions of keloids on the chest in response to respiratory movement. The stresses concentrate at the peri-keloid regions close to the bilateral ends of the keloids. By reviewing this result in reference to our hypothesis, we can explain why keloids on the chest are likely to present crab or butterfly shapes. Although we know that keloids grow in response to mechanical stresses, our hypothesis differs from existing ones in that it focuses on morphological transformation. Our hypothesis is helpful for physicians in performing treatment for keloids, because they can predict what part of a keloid is likely to grow and perform preventive treatment in reference to the hypothesis. © 2013 Elsevier Ltd.

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Consideration of shear modulus in biomechanical analysis of peri-implant jaw bone: Accuracy verification using image-based multi-scale simulation

Matsunaga S., Naito H., Tamatsu Y., Takano N., Abe S., Ide Y.

Dental Materials Journal (Dental Materials Journal) 32 ( 3 ) 425 - 432 2013.05

ISSN 02874547

The aim of this study was to clarify the infuence of shear modulus on the analytical accuracy in peri-implant jaw bone simulation. A 3D fnite element (FE) model was prepared based on micro-CT data obtained from images of a jawbone containing implants. A precise model that closely reproduced the trabecular architecture, and equivalent models that gave shear modulus values taking the trabecular architecture into account, were prepared. Displacement norms during loading were calculated, and the displacement error was evaluated. The model that gave shear modulus values taking the trabecular architecture into account showed an analytical error of around 10-20% in the cancellous bone region, while in the model that used incorrect shear modulus, the analytical error exceeded 40% in certain regions. The shear modulus should be evaluated precisely in addition to the Young modulus when considering the mechanics of peri-implant trabecular bone structure.

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Relationship between Locations of Rib Defects and Loss of Respiratory Function- A Biomechanical Study

Asako Hatano, Tomohisa Nagasao, Yasunori Cho, Yusuke Shimizu, Naoki Takano, Tsuyoshi Kaneko and Kazuo Kishi

The Thoracic and Cardiovascular Surgeon (Thoracic and Cardiovascular Surgeon) 62 ( 4 ) DOI:10.1055/s-0033-1338107 - 362 2013.04

Research paper (scientific journal), Joint Work, Accepted, ISSN 01716425

Objective The present study elucidates the relationship between the locations of rib defects and loss of respiratory function. Methods Ten sets of three-dimensional finite element models were produced from computed tomography data of 10 persons and categorized as normal type models. These models were modified by removing part of the ribs, and the resultant models were categorized as defect type models. Varying the location of the defects, six types of defect model were produced from each of the 10 normal models; the defects were made on the anterior-superior, anterior-inferior, lateral-superior, lateral-inferior, posterior-superior, and posterior-inferior regions of the thorax. To simulate respiration, contracture forces were applied to nonlinear springs modeling respiratory muscles for each of the normal and defect models. Difference in volume of the thoracic cavity between inspiration and expiration phases was viewed as the indicator of respiratory function and was defined as ΔV. The values of ΔV were compared between normal type models and their corresponding defect type models. Results Among the six types of defect, the degree of functional loss was greatest with those defects on the lateral-inferior part of the thorax, where ΔV of the affected side hemithorax drops to 38 to 45% of normal values, whereas ΔV was 62 to 88% with other defect models. Conclusion Thoraces that have defects on their lateral-inferior regions present lower respiratory functioning than thoraces with other defect locations. Hence, in treating clinical cases where defects are expected to occur in this region, effort should be made to minimize the area of the defect. © 2014 Georg Thieme Verlag KG Stuttgart New York.

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Uncertainty Modeling in the Prediction of Effective Mechanical Properties Using Stochastic Homogenization Method with Application to Porous Trabecular Bone

Khairul Salleh Basaruddin,Naoki Takano , Hikaru Akiyama and Takayoshi Nakano

Materials Transactions (Materials Transactions) 54 ( 8 ) 1250-1256 - 1256 2013.04

Research paper (scientific journal), Joint Work, Accepted, ISSN 13459678

A systematic modeling of uncertainty due to image processing, material characteristics and experimental works was developed in order to propose a novel stochastic image-based multi-scale method for heterogeneous media. The effective mechanical properties with application to three porous trabecular bone models were predicted by introducing the correction factor (β) to represent the miscellaneous errors or unknown factors. Finally, the probability density was obtained for the effective mechanical properties, which could evaluate the reliability of scattered experimental results. It has been concluded that variation in effective properties of heterogeneous media can be predicted even when only limited measured values are available by using the present extrapolation technique based on verified simulation results. © 2013 The Japan Institute of Metals and Materials.

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Stochastic Multi-scale Prediction on the Apparent Elastic Moduli of Trabecular Bone Considering Uncertainties of Biological Apatite (BAp) Crystallite Orientation and Image-based Modelling

Khairul Salleh Basaruddin, Naoki Takano and Takayoshi Nakano

Computer Methods in Biomechanics and Biomedical Engineerig (Computer Methods in Biomechanics and Biomedical Engineering) 18 ( 2 ) DOI:10.1080/10255842.2013.785537 - 174 2013.04

Research paper (scientific journal), Joint Work, Accepted, ISSN 10255842

© 2013 Taylor & Francis. An assessment of the mechanical properties of trabecular bone is important in determining the fracture risk of human bones. Many uncertainty factors contribute to the dispersion of the estimated mechanical properties of trabecular bone. This study was undertaken in order to propose a computational scheme that will be able to predict the effective apparent elastic moduli of trabecular bone considering the uncertainties that are primarily caused by image-based modelling and trabecular stiffness orientation. The effect of image-based modelling which focused on the connectivity was also investigated. A stochastic multi-scale method using a first-order perturbation-based and asymptotic homogenisation theory was applied to formulate the stochastically apparent elastic properties of trabecular bone. The effective apparent elastic modulus was predicted with the introduction of a coefficient factor to represent the variation of bone characteristics due to inter-individual differences. The mean value of the predicted effective apparent Young's modulus in principal axis was found at approximately 460 MPa for respective 15.24% of bone volume fraction, and this is in good agreement with other experimental results. The proposed method may provide a reference for the reliable evaluation of the prediction of the apparent elastic properties of trabecular bone.

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Stochastic modeling and analysis of porous media using first-order perturbation-based homogenization method

Basaruddin K., Takano N.

ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers (ECCOMAS 2012 - European Congress on Computational Methods in Applied Sciences and Engineering, e-Book Full Papers) 621 - 630 2012.12

ISSN 9783950353709

A stochastic analysis of multi-scale problem in porous media was introduced in this paper to determine the variation of macroscopic homogenized properties considering uncertainties at microscopic level. By assuming the small fluctuation that arises in microscopic properties was distributed in Gaussian normal distribution, the macroscopic homogenized properties has been formulated in stochastic manner using first-order perturbation-based. The merit of this method lies in the ability to consider other uncertainties instead of microscopic properties due to random microstructure variations. Hence, the proposed stochastic homogenization method was established by adding two demonstrative problems that commonly occur in engineering materials. First, the fluctuation of Young's modulus in adhesive of two-phase materials was considered to demonstrate a simple numerical model that can predict the dispersion of macroscopic properties. Next, the variation in microscopic properties was combined with misalignment of stacked plate microstructure to investigate the effects on macroscopic properties of corrugated-core. The results showed that the misaligned position in some distances increased the macroscopic properties but by taking the probability function on misalignment reduced that. It proved that the significance of this study in design and fabrication of porous media considering random variation of microstructure.

Biomechanics Analysis of Pressure Ulcer Using Damaged Interface Model between Bone and Muscle in the Human Buttock

Samuel Susanto Slemet, Naoki Takano, Yoshiyuki Tanabe, Asako HATANOatano and Tomohisa Nagasao

Journal of Computational Science and Technology 6 ( 2 ) 70-80 2012.06

Research paper (scientific journal), Joint Work

Monte Carlo Simulation of Dynamic Problem Using Model Order Reduction Technique Highlighting on Tail Probability

Naoki Takano, Mitsuteru Asai and Kohta Okamoto

Journal of Computational Science and Technology 6 ( 3 ) 169-181 2012

Research paper (scientific journal), Joint Work

Morphology Analysis of Vertebral Trabecular Bone under Dynamic Loading based on Multi-scale Theory

Khairul Salleh Basaruddin, Naoki Takano, Yuto Yoshiwara and Takayoshi Nakano

Medical and Biological Engineering and Computing (Medical and Biological Engineering and Computing) 50 ( 10 ) 1091-1103 - 1103 2012

Research paper (scientific journal), Joint Work, ISSN 01400118

Trabecular bone has a complicated porous microstructure and consists of interconnected plates and rods known as trabeculae. The microarchitecture of the trabeculae contributes to load distribution capacity and, particularly, the optimal bone strength. Many previous studies have shown that morphological parameters are used to characterize the microarchitecture of trabecular bone, but little is known about the mechanical role of trabecular morphology in the context of load-bearing behavior. Therefore, this study proposes a new segmentation method for examining the morphology of trabecular structure foci of load-bearing capability. A micro-finite element model of trabecular bone was obtained from the fourth lumbar vertebra on the basis of a three-dimensionally reconstructed micro-computed tomography (CT) image. We used an asymptotic homogenization method to determine microscopic stress by applying three unidirectional compressive loads in the vertical, anteroposterior, and right-left axes of two trabecular bone volumes. We then classified the complicated trabecular microstructure into three segments: primary and secondary trabeculae and trabeculae of no contribution. Next, a dynamic analysis was conducted by applying a force impulse load. The result indicated that 1/3 of the trabecular volume functions as primary trabecula. The morphology of the trabecular network could be visualized successfully highlighting the percolation of the stress wave in the primary trabecular segment. Further, we found that the role of the plate-like structures was that of a hub in the trabecular network system. © International Federation for Medical and Biological Engineering 2012.

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Calibration of Wet Etching Parameters for Sacrifice Layer of MEMS

Naoki Takano, Kenichi Sato, Toshiyuki Toriyama, Toru Yamasaki and Seiichi Uesugi

Journal of Computational Science and Technology 5 ( 3 ) 106-119 2011.10

Research paper (scientific journal), Joint Work

Numerical Study on the Morphology and Mechanical Role of Healthy and Osteoporotic Vertebral Trabecular Bone

Yuto Yoshiwara, Miguel Clanche, Khairul Salleh Basaruddin, Naoki Takano and Takayoshi Nakano

Journal of Biomechanical Science and Engineering (Journal of Biomechanical Science and Engineering) 6 ( 4 ) 270-285 - 285 2011.09

Research paper (scientific journal), Joint Work, ISSN 18809863

This study presents a numerical methodology to clarify the morphology of complex trabecular network architecture in human lumbar vertebra by means of the new post-processing technique for calculated microscopic stress by the homogenization method. Micro-CT image-based modeling technique is used and careful but intuitive and easy-to-use method for microstructure model, in other words region of interest (ROI), is also presented. The macroscopic homogenized properties that include not only the Young's moduli but also shear moduli could explain the difference of morphology between healthy and osteoporotic bones. This paper focuses on the change of degree of anisotropy. Then, the microscopic stress under three basis load cases was analyzed. In this analysis, the homogenization method has a merit in the computational cost. The trabeculae are classified into eight groups from the viewpoint of load bearing function against three loading conditions in the proposed post-processing of numerical results. It contributes to the understanding of the mechanical role of trabecular bone in vertebra. The primary trabecular bone that has been supposed to support the self-weight and secondary bone that connects the primary bone are successfully visualized. The discussion on the mechanical role of plate-like trabecular bone in the load path network system is also highlighted. © 2011 by JSME.

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Formation of Polymer Microneedle Arrays Using Soft Lithography

Yoshimichi Ami, Hiroto Tachikawa, Naoki.Takano and Norihisa Miki

Journal of Micro/Nanolithography,MEMS,and MOEMS (Journal of Micro/Nanolithography, MEMS, and MOEMS) 10 ( 1 ) 011503/1-6 2011.03

Research paper (scientific journal), Joint Work, Accepted, ISSN 19325150

We demonstrate the fabrication of polymer microneedle arrays using soft lithography. A photomask was designed to use Fresnel diffraction of UV light to create sharp, tapered hollows in SU-8, a negative photoresist, after development. Polymer microneedles were formed using these SU-8 structures as a mold. These polymer needles may be applicable as flexible electrodes in brain-machine interfaces because they are more likely to survive movement of the skin than conventional brittle silicon needles. Similar needles, made from medicinal substances, could be used for transdermal drug administration. For these applications, the needles must be long, sharp, and stiff enough to penetrate the stratum corneum (∼20 m in thickness) and reach the viable epidermis (200-300 m in thickness), but must not reach the dermis, which contains sensitive nerve endings. We successfully manufactured 2020 microneedle arrays of polydimethylsiloxane with a needle length of 200 m. We experimentally verified that these manufactured electrodes successfully penetrated the stratum corneum of a cultured skin. © 2011 Society of Photo-Optical Instrumentation Engineers (SPIE).

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Biomechanics of Jaw Bone Considering Structural Properties of Trabecular Bone

Satoru Matsunaga, Naoki Takano, Yuichi Tamatsu, Shinichi Abe and Yoshinobu Ide

Journal of Oral Biosciences (Journal of Oral Biosciences) 53 ( 2 ) 143/147 - 147 2011

Research paper (scientific journal), Joint Work, ISSN 13490079

Mechanical stress is an important factor in bone homeostasis, which is impossible to visualize and therefore difficult to evaluate. Biomechanical analysis based on the three-dimensional finite element method (3D FEM) has become more accurate, and it is now possible to analyze load transfer pathways taking into consideration the trabecular structures. It has even become feasible to develop treatment plans based on mechanical factors using image data acquired from the patient. This review describes the usefulness and prospects of biomechanical analysis of the jaw bones, specifically finite element analysis (FEA) based upon the consideration of internal microstructures.

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Biomechanical Role of Peri-Implant Cancellous Bone Architecture

Satoru Matsunaga ,Yoshitaka Shirakura, Takashi Ohashi, Ken Nakahara, Yuichi Tamatsu, Naoki Takano and Yoshinobu Ide

The International Journal of Prosthodontics (International Journal of Prosthodontics) 23 ( 4 ) 333-338 - 338 2010.07

Research paper (scientific journal), Joint Work, Accepted, ISSN 08932174

Purpose: The aim of this study was to investigate the biomechanical role of trabecular bone around dental implants in the mandible. Materials and Methods: The model in this study was made using micro-computed tomography data taken from a cadaver in whom endosseous implants had been in place for 15 years prior to death. Morphologic analysis and three-dimensional (3D) finite element analysis were performed to calculate the peri-implant loading path of the model in which the trabecular structure was accurately simulated. Results: As seen through multiscale analysis using the homogenization method, the trabecular bone architecture around implants was isotropic for the most part. Also, 3D finite element analysis showed that compressive stresses oblique to the implant axis were transmitted to the lower constrained surface; tensile stresses oblique to the implant axis were transmitted to the upper constrained surface, and they intersected each other with vertical loading. The highest stress in cancellous bone was observed on perpendicular loading, and stress produced in trabeculae decreased approaching horizontal loading. Conclusion: Cancellous bone architecture around the implant was generally isotropic. 3D finite element analysis showed that cancellous bone trabeculae around implants dispersed stress by forming load transfer paths. The results suggest that trabecular bone plays a major role in supporting functional pressure exerted via the implant. © 2010 by Quintessence Publishing Co Inc.

マルチスケール応力解析によるヒト椎体海綿骨の力学的評価

TAKANO Naoki

日本骨形態計測学会雑誌 20 ( 1 ) S100-S107 2010.05

Research paper (scientific journal), Joint Work, Accepted

Effect of Tension and Curvature of Skin on Insertion Characteristics of Microneedle Array

Hiroto Tachikawa, Naoki Takano, Kazuaki Nishiyabu Norisisa Miki and Yoshimichi Ami

Journal of Solid Mechanics and Materials Engineering 4 ( 3 ) 470-480 2010.03

Research paper (scientific journal), Joint Work, Accepted

Structural Strength Prediction for Porous Titanium Based on Micro-stress Concentration by Micro-CT Image-based Multiscale Simulation

Naoki Takano, Ken Fukasawa and Kazuaki Nishiyabu

International Jouranal of Mechanical Sciences (International Journal of Mechanical Sciences) 52 ( 52 ) 229-235 - 235 2010.01

Research paper (scientific journal), Joint Work, ISSN 00207403

For the design of porous titanium component, differently from its use as functional materials, structural strength prediction algorithm is proposed based on the micro-stress concentration analyzed by the multiscale simulation. The modeling of real microstructure is carried out by the image-based technique with X-ray micro-CT. The multiscale computational method consists of asymptotic homogenization and finite element mesh superposition (FEMS) techniques. A criterion is proposed to predict the nonlinearity initiation point in the load and displacement curve by means of micro-stress distribution expressed by histogram. Only the constituent's yield strength is referred regardless of the microscopic morphology. The originality of this paper lies in the validation of the homogenization process, the modeling guideline of micro-mesh superposition onto macro-mesh in FEMS, and the strength prediction algorithm. L-shaped components with different pore diameter were discussed in both experiment and simulation. © 2009 Elsevier Ltd. All rights reserved.

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Biomechanical Role of Peri-implant Trabecular Structures during Vertical Loading

Takashi Ohashi, Satoru Matsunaga ,Ken Nakahara, Shinichi Abe, Yoshinobu Ida, Yuichi Yamatsu and Naoki Takano

Clinical Oral Investigation (Clinical Oral Investigations) 14 ( 5 ) 507-513 - 513 2009.08

Research paper (scientific journal), Joint Work, ISSN 14326981

The aim of this study was to identify the load transfer paths in cortical bone and trabecular structure of cancellous bone in the jawbones for loads from endosseous implants. Maxillae were resected from beagle dogs 6 months after implant surgery and imaged using micro-computed tomography (micro-CT). A three-dimensional structure was produced based on the CT data and peri-implant trabecular structure was observed. Load transfer paths were analyzed from the results of three-dimensional finite element analysis. Furthermore, buffer actions in bone trabeculae when strain increased during stress analysis and when loads were applied were observed. Peri-implant bone trabeculae were seen extending into the upper and lower cortical bone from the fixture. The direction of bone trabecular alignment corresponded with the load transfer paths. In addition, analysis with increased strain confirmed that trabecular structures could serve as load buffers. These results suggest that bone trabeculae supporting load transfer from implants undergo remodeling. © 2009 Springer-Verlag.

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Creative Design with Multi-objective Topology Optimization

Chen Jian Ken Lee, Naoki Takano

Transactions of Japan Society for Computational Engineering and Science, Vol.2009 Paper No.20090011 2009.07

Research paper (scientific journal), Joint Work

Reduction of Finite Element Mesh and Model Order for Fast Dynamic Analysis of Global/Local Problem

Atsushi Sando, Naoki Takano, Mitsuteru Asai, Toshiyuki Toriyama, Shoji Kido and Jan.G.Korvonk

Jurnal of Solid Mechanics and Materials Engineering (JSME) 3 ( 3 ) 572-583 2009.03

Research paper (scientific journal), Joint Work

Insertion Testing of Polyethylene Glycol Microneedle Array into Cultured Human Skin with Biaxial Tension

Naoki Takano, Hiroto Tachiawa, Takaya Miyano, and Kazuaki Nishiyabu

Journal of Solid Mechanics and Materials Engineering (JSME) 3 ( 3 ) 604-612 2009.03

Research paper (scientific journal), Joint Work

Removing Void Elements for Structural Level Set Topology Optimizaiton

Chen Jian Ken Lee, Zhiqian Zhang, Naoki Takano

Journal of Computational Science and Technology (JSME) 3 ( 1 ) 385-395 2009

Research paper (scientific journal), Joint Work, Accepted

Adjoint Variable Method for Multi-objective Sizing and Shape Optimization

C. J. K. Lee, W. Furuya, M. Tanaka and N. Takano

Journal of Computational Science and Technology (JSME) 2009

Research paper (scientific journal), Joint Work, Accepted

Three-dimensional morphology analysis and finite element modeling of nano particle dispersed materials

Takano N., Asai M., Kouda T., Hashimoto K.

Zairyo/Journal of the Society of Materials Science, Japan (Zairyo/Journal of the Society of Materials Science, Japan) 57 ( 5 ) 423 - 429 2008.05

ISSN 05145163

This paper presents a three-dimensional morphology analysis technique by means of TEM tomography and finite element modeling of nano particle dispersed composite materials. The target material system in this paper is natural rubber reinforced by carbon black (CB) nano-particles. The average diameter of CB ranges from 30 to 122nm. The main feature of this paper is that the interphase named sticky hard layer between CB and free rubber is considered in detail. The Young's modulus was estimated by pulse nuclear magnetic resonance (NMR), and the thickness was obtained by measuring the volume content and moreover considering the agglomeration of CB nano-particles. The Young's modulus of the sticky hard layer was 5 to 30 times larger than that of free rubber. The relative thickness of the sticky hard layer divided by the CB diameter was found to be very influential on the overall properties of the composites, because its percolation forms the load carrying path in the composites as demonstrated by finite element analysis. These results have been supposed to be the major reason to explain the nano-particle size effect on the overall properties, which have never been understood by the classical rule of mixture. © 2008 The Society of Materials Science.

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Assessment of bone quality. Biomechanics simulation for bone quality evaluation

Takano N., Nakano T.

Clinical calcium (Clinical calcium) 18 ( 3 ) 347 - 353 2008.03

ISSN 09175857

The outline of the novel multiscale biomechanics simulation is described, which bridges nanoscale, microscale and macroscale by considering both the three-dimensional network architecture of trabecular bone captured by means of micro-CT and the biological apatite crystallite orientation. The article covers the fundamentals of the stress analysis and the muliscale computational method including some important topics in the engineering field. And finally, the simulation of trabecular bone of human vertebra is presented.

Two-dimensional quantitative analysis of preferential alignment of biological apatite c-axis for isolated human trabecular bone using microbeam X-ray diffractometer with a transmission optical system

Miyabe S., Nakano T., Ishimoto T., Takano N., Adachi T., Iwaki H., Kobayashi A., Takaoka K., Umakoshi Y.

Nippon Kinzoku Gakkaishi/Journal of the Japan Institute of Metals (Nippon Kinzoku Gakkaishi/Journal of the Japan Institute of Metals) 72 ( 1 ) 57 - 62 2008.01

ISSN 00214876

Two-dimensional quantitative analysis of microbeam X-ray diffraction (XRD) was performed using a transmission optical system to examine biological apatite (BAp) orientation in an isolated trabecula of a human fourth lumber vertebral body. The incident X-ray beam is 20 μm in diameter, which is small enough for the isolated trabecula despite a slight beam divergence of 0.2°. Integrated intensities of (002) and (310) are obtained separately by different incident angles and detector positions. Distribution of the preferential orientation of the BAp c-axis is finally calculated quantitatively as an integrated intensity ratio of (002) / (310) in a plane containing the trabecular direction. Preferential alignment of the BAp c-axis was finally determined to be perfectly parallel to the fiber direction in a rod-shaped trabecula, since accurate one-dimensional alignment is different from the alignment in the femoral cortical bone as a long bone that shows the local maximum of preferential alignment perpendicular to the longitudinal bone axis. For example, the integrated intensity ratio of (002) / (310) has a maximum value of 16 along the trabecular fiber and a minimum value of 0.09 in the perpendicular direction. Using this method, the anisotropy of BAp orientation in the trabecular bone can be quantitatively evaluated in the plane including the trabecular fiber. Thus, we successfully obtained a methodology that two-dimensionally analyzes the distribution of the BAp c-axis along all axes within a plane in a bone specimen. © 2008 The Japan Institute of Metals.

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骨質を考慮した椎体海綿骨の高分解能ミクロ応力解析

TAKANO Naoki

日本臨床バイオメカニクス学会誌 20 7-14 2008

Research paper (scientific journal), Joint Work, Accepted

透過型光学系を有する微小領域X線回折法によるヒト海綿骨内生体アパタイト結晶配向性の２次元定量解析

TAKANO Naoki

日本金属学会誌 72 ( 1 ) 57-62 2008

Research paper (scientific journal), Joint Work, Accepted

ナノ粒子分散材の3次元モルフォロジー分析と有限要素モデリング

TAKANO Naoki

材料 57 ( 5 ) 423-429 2008

Research paper (scientific journal), Joint Work, Accepted

Hydrolytic microneedles as transdermal drug delivery system

Miyano T., Miyachi T., Okanishi T., Todo H., Sugibayashi K., Uemura T., Takano N., Konishi S.

TRANSDUCERS and EUROSENSORS '07 - 4th International Conference on Solid-State Sensors, Actuators and Microsystems (TRANSDUCERS and EUROSENSORS '07 - 4th International Conference on Solid-State Sensors, Actuators and Microsystems) 355 - 358 2007.12

ISSN 9781424408429

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Proposal of a new bimorph piezoelectric actuator for blood extraction pump in health monitoring system

Uetsuji Y., Nagakura H., Kawahara S., Hwang F., Tsuchiya K., Yamamoto H., Takano N., Nakamachi E.

Zairyo/Journal of the Society of Materials Science, Japan (Zairyo/Journal of the Society of Materials Science, Japan) 56 ( 5 ) 477 - 482 2007.05

ISSN 05145163

Health monitoring system equipped with blood extraction pump is one of the important problems for new medical technology to support the advanced age society. In this paper, a new piezoelectric actuator for blood extraction pump was proposed to increase volumetric change in pump. We devised the geometry of piezoelectric actuator with some slits that allows the stretching and contracting deformation in in-plane direction to create large deflection in out-of-plane direction. Focusing on a disc-type bimorph plate with some slits, the deformations under static electric load have been analyzed by finite element method with consideration of two geometric parameters, length l and width w of slits. The computational results indicated that the deformation of bimorph actuator changes from complex mode to single mode according to increase of slit length, and that single mode presents remarkable increase of deflection under surrounding-fixed condition. And then, a bimorph actuator with 4 slits l = 2.0, w = 0.5mm has been manufactured as an experiment. As a result, a developed actuator was proved to increase the deflection under dynamic electric load compared with a conventional bimorph actuator without slits. © 2007 The Society of Materials Science.

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Two-dimensional quantitative analysis of preferential alignment of BAp c-axis for isolated human trabecular bone using microbeam X-ray diffractometer with a transmission optical system

Miyabe S., Nakano T., Ishimoto T., Takano N., Adachi T., Iwaki H., Kobayashi A., Takaoka K., Umakoshi Y.

Materials Transactions (Materials Transactions) 48 ( 3 ) 343 - 347 2007.03

ISSN 13459678

Two-dimensional quantitative analysis of microbeam X-ray diffraction (XRD) was performed using a transmission optical system to examine biological apatite (BAp) orientation in an isolated trabecula of a human fourth lumber vertebral body. The incident X-ray beam is 20 μm in diameter, which is small enough for the isolated trabecula despite a slight beam divergence of 0.2°. Integrated intensities of (002) and (310) are obtained separately by different incident angles and detector positions. Distribution of the preferential orientation of the BAp c-axis is finally calculated quantitatively as an integrated intensity ratio of (002)/(310) in a plane containing the trabecular direction. Preferential alignment of the BAp c-axis was finally determined to be perfectly parallel to the fiber direction in a rod-shaped trabecula, since accurate one-dimensional alignment is different from the alignment in the femoral cortical bone as a long bone that shows the local maximum of preferential alignment perpendicular to the longitudinal bone axis. For example, the integrated intensity ratio of (002)/(310) has a maximum value of 16 along the trabecular fiber and a minimum value of 0.09 in the perpendicular direction. Using this method, the anisotropy of BAp orientation in the trabecular bone can be quantitatively evaluated in the plane including the trabecular fiber. Thus, we successfully obtained a methodology that two-dimensionally analyzes the distribution of the BAp c-axis along all axes within a plane in a bone specimen. © 2007 The Japan Institute of Metals.

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An Iterative Solver Applied to Strongly Coupled Piezoelectric Problems of Porous Pb(Zr,Ti)O3 with Nondestructive Modelling of Microstructure

Mitsuteru Asai, Naoki Takano, Yasutomo Uetsuji and Kunihiko Taki

Modelling and Simulation in Materials Science and Engineering 15 ( 6 ) 597-617 2007

Research paper (scientific journal), Joint Work, Accepted

Two-Dimensional Quantitative Analysis of Preferential Alignment of BAp c-axis for Isolated Human Trabecular Bone using Microbeam X-ray Diffractometer with Transmission Optical System

Sayaka Miyabe, Takayoshi Nakano, Takuya Ishimoto, Naoki Takano, Taiji Adachi, Hiroyoshi Iwaki, Akio Kobayashi, Kunio Takaoka and Yukichi Umakoshi

Materials Transactions 48 ( 3 ) 343-347 2007

Research paper (scientific journal), Joint Work, Accepted

HMS採血ポンプ用新型バイモルフ圧電アクチュエータの提案

TAKANO Naoki

材料 56 ( 5 ) 477-482 2007

Research paper (scientific journal), Joint Work, Accepted

Multi-scale stress analysis of trabecular bone considering trabeculae morphology and biological apatite crystallite orientation

Kawagai M., Takano N., Nakano T., Asai M.

Zairyo/Journal of the Society of Materials Science, Japan (Zairyo/Journal of the Society of Materials Science, Japan) 55 ( 9 ) 874 - 880 2006.09

ISSN 05145163

This paper presents the multi-scale stress analysis of trabecular bone by the homogenization method bridging nano-micro-macro scales. Three-dimensional microstructure of trabeculae is obtained by the X-ray CT and the image-based modeling technique. Biological apatite (BAp) crystallite orientation is considered in the microstructure model by means of the anisotropic mechanical properties. The c-axis of BAp is set up as the maximum principal stress direction under the long term macroscopic stress condition. These properties are automatically assigned to each voxel element. To determine appropriately the microstructure model, the trabeculae morphology is analyzed and quantified as the trabecular density distribution. The proposed method is applied to pig's femur. It was revealed by the morphology analysis and homogenized macroscopic properties that the trabecular bone has plate-like characteristics. The predicted anisotropic level of the macroscopic properties was quantitatively coincident with the measured value by the X-ray diffraction analysis.

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均質化法による多孔質圧電材料のイメージベース・マルチスケール解析

TAKANO Naoki

材料 55 ( 12 ) 1111-1116 2006

Research paper (scientific journal), Joint Work, Accepted

Image-based Multi-scale Modelling Strategy for Complex and Heterogeneous Porous Microstructures by Mesh Superposition Method

Mitsuhiro Kawagai, Atsushi Sando and Naoki Takano

Modelling and Simulation in Materials Science and Engineering (Modelling and Simulation in Materials Science and Engineering) 14 ( 1 ) 53-69 - 69 2006

Research paper (scientific journal), Joint Work, Accepted, ISSN 09650393

This study is focused on the multi-scale modelling strategy for complex and heterogeneous microstructures of real materials by automatic image-based modelling and finite element mesh superposition method. The synergetic application of the conventional asymptotic homogenization method and the authors' mesh superposition method has been proposed to obtain the microscopic responses under high gradient of macroscopic fields at the macroscopic crack tip and/or interface, for instance. For complex and random microstructures, automatic image-based voxel meshing by means of x-ray CT is commonly required; however, it cannot always adapt to the mathematical theory of microscopic modelling in the mesh superposition method. Therefore, a modelling technique for mesh refinement is proposed in this paper using additional elements for insulation in consideration of the theoretical background of the mesh superposition method. In this paper, we provide the modelling procedure and its theoretical consideration of mesh refinement for flexible modelling of real materials. To demonstrate the technique, a numerical example of a porous ceramic component with random microstructure and macroscopic crack is illustrated. © 2006 IOP Publishing Ltd.

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生体硬組織の高分解能イメージベース・マルチスケールモデリング

TAKANO Naoki

日本計算工学会論文集 Paper No.20060017 2006

Research paper (scientific journal), Joint Work, Accepted

海綿骨の骨梁モルフォロジーと生体アパタイト結晶配向性を考慮したマルチスケール応力解析

TAKANO Naoki

材料 55 ( 9 ) 874-880 2006

Research paper (scientific journal), Single Work, Accepted

Finite Element Analysis of Fiber-reinforced Fixed Partial Dentures

Takashi Nakamura, Tatsuo Ohyama, Tomonori Waki, Soichiro Kinuta, Kazumichi Wakabayashi, Naoki Takano and Hirofumi Yatani

Dental Materials Journal (Dental Materials Journal) 24 ( 2 ) 275-279 - 279 2005

Research paper (scientific journal), Joint Work, Accepted, ISSN 02874547

Two-dimensional finite element models were created for a three-unit posterior fixed partial denture. An experimental resin-impregnated glass fiber was used as the fiber-reinforced composite (FRC) for the framework. The FRC was evaluated using varying combinations of position and thickness, alongside with two types of veneering composite. A load of 50 N simulating bite force was applied at the pontic in a vertical direction. Tensile stress was examined using a finite element analysis program. Model without FRC showed tensile stress concentrations within the veneering composite on the cervical side of the pontic - from the connector area to the bottom of the pontic. Model with FRC at the top of the pontic had almost the same stress distribution as the model without FRC. Models with 0.4-0.8 mm thick FRC positioned at the bottom of the pontic showed maximum tensile stresses reduced by 4-19% within the veneering composite.

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Stress Analysis of Endodontically Treated Anterior Teeth Restored with Different Types of Post Material

Takashi Nakamura, Tatsuo Ohyama, Tomonori Waki, Soichiro Kinuta, Kazumichi Wakabayashik Yoshihiko Mutobe, Naoki Takano and Hirofumi Yatani

Dental Materials Journal (Dental Materials Journal) 25 ( 1 ) 145-150 - 150 2005

Research paper (scientific journal), Joint Work, Accepted, ISSN 02874547

Finite element analysis was performed to evaluate stress distribution in maxillary central incisors treated endodontically and restored with a post and an all-ceramic crown. Tensile stress at tooth root was analyzed using two-dimensional finite element models with different post diameters and lengths. One post length was 1/3 of the root (short), while the other was 2/3 of the root (long); one post diameter was 1/3 of the root (narrow), while the other was 2/3 of the root (wide). The following combinations were used for posts and cores: gold alloy cast post and core, commercial stainless steel post and resin core, and fiber post and resin core. Results showed that the fiber post produced less stress on the root dentin around the post tip than did the metal posts. This finding thus suggested that to reduce the stresses that cause root fracture, a long, thin fiber post should be used.

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Macro-micro stress analysis of porous ceramics by homogenization method

Ikeda Y., Nagano Y., Kawamoto H., Takano N.

Ceramic Engineering and Science Proceedings (Ceramic Engineering and Science Proceedings) 25 ( 3 ) 177 - 182 2004.12

ISSN 01966219

The 3-D image modeling of the porous alumina was obtained by X-ray CT, and microscopic volume elements were obtained from it. Porous alumina including spherical pores 60μm and 20μm in diameter with porosities 7.05% and 1.76% were studied by homogenization method, which calculated homogenized elastic constants for the microscopic volumes. These constants were applied to simulate 4-point bending tests and to analyze macroscopic stress distributions coupled with FEM calculation. Microscopic stress distributions were analyzed using the FEM result. The maximum microscopic stress concentration near a spherical pore were about 2 times higher than the average stress one.

3D modeling of porous ceramics by high-resolution X-ray CT for stress analyses

Ikeda Y., Nagano Y., Kawamoto H., Takano N.

Key Engineering Materials (Key Engineering Materials) 270-273 ( I ) 28 - 34 2004.11

ISSN 10139826

Porous ceramic materials are in widespread use and continue to be developed as the key materials for many industrial fields. The mechanical properties of these porous materials are very sensitive to their 3-dimensional structures. It is very important to analyze such materials taking into account their 3-dimensional morphology of the pore structure. An image-based modeling method using high resolution 3-dimensional computed tomography (CT) was developed, which makes it possible to reconstruct the complicated porous structures of porous ceramics nondestructively. From the 3-dimensional CT data, binary-processed images can be obtained and a voxel mesh computational analysis was carried out with a homogenization method, from which macroscopic and microscopic stress distribution for porous ceramics were possible to be calculated and visualized. From the 3-D CT image, a local microscopic model of the porous alumina was analyzed using voxel mesh method of mathematical homogenization method. Using the data the microscopic local stress distribution of the model was obtained.

Digital image-based analysis of morphology for porous materials

Takano N., Tsujimura K.

Nippon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A (Nippon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A) 70 ( 6 ) 787 - 793 2004.06

ISSN 03875008

The porous material is one of the promising functional materials, and its macroscopic properties are strongly dependent on the microscopic morphology. To study the correlation between the microscopic heterogeneity and the macroscopic properties, a novel digital image-based analysis methodology is proposed in this paper, which consists of high resolution X-ray CT, digital image-based modeling, multi-scale stress analysis and geometrical morphology analysis. The proposed morphology analysis enables us to predict the microscopic stress concentration for spherical porous ceramics considering the heterogeneous dispersion of spherical pores and the macroscopic loading condition. The heterogeneity can be analyzed geometrically for very huge data with approximately 58 million voxel elements quickly. The morphology analysis is helpful for the multi-scale modeling and microscopic stress evaluation. The microscopic stress distribution is also discussed in association with the random heterogeneity for ceramics with open pores and with high porosity ratios.

Microscopic stress analysis at crack tip in heterogeneous media by multi-scale method

Takano N., Okuno Y.

ISSN 03875008

In the development of various advanced materials by controlling their heterogeneous microstructures, there is a growing need for the multi-scale analysis. There have been many studies on the correlation between the heterogeneous microstructure and the macroscopic properties mainly using the asymptotic homogenization method with the help of the finite element method. Although the consideration of fracture origin in components such as interface crack is important in the multi-scale stress analysis, it was impossible to calculate the microscopic stress under high gradient of macroscopic strain/stress field at the crack tip. Furthermore, the representative dimension of the fracture origin lies between the microscopic scale and the macroscopic one. Hence, this paper proposes a novel three-scale computational method that employs both the homogenization method and the enhanced mesh superposition method to study the correlation among microstructure, component and fracture origin simultaneously. An equation solver for large-scale 3 D analysis by the mesh superposition method is also presented. A demonstrative 3 D example of porous thin film with interface crack, whose finite element model has approximately 78 thousand solid elements, is shown.

マルチスケール法による不均質体中のき裂先端におけるミクロ応力解析

TAKANO Naoki

日本機械学会論文集A編 70 ( 692 ) 525-531 2004

Research paper (scientific journal), Joint Work, Accepted

多孔体モルフォロジーのディジタルイメージベース・アナリシス

TAKANO Naoki

日本機械学会論文集A編 70 ( 694 ) 787-793 2004

Research paper (scientific journal), Joint Work, Accepted

Three-scale Finite Element Analysis of Heterogeneous Media by Asymptotic Homogenization and Mesh Superposition Methods

Naoki Takano and Yoshihiro Okuno

International Journal of Solids and Structure (International Journal of Solids and Structures) 41 ( 15 ) 4121-4135 - 4135 2004

Research paper (scientific journal), Joint Work, Accepted, ISSN 00207683

This paper studies a three-scale computational method that simultaneously considers the microstructure of heterogeneous materials, the macroscopic component, and the fracture origin such as interface or crack. The synergetic application of the asymptotic homogenization and mesh superposition methods to problems with strong scale mixing is emphasized. The scale gap between the microstructure and the component is very large, but the fracture origin is at the middle scale between them. The overall behavior is analyzed by means of the homogenization of the heterogeneity expressed by the unit cell model, while the fracture origin is modeled directly with the microscopic heterogeneity by another microscopic mesh. The microscopic mesh is superposed onto the macroscopic mesh. This mesh superposition method can analyze the non-periodic microscopic stress at the crack tip under a non-uniform macroscopic strain field with high gradient. Hence, the present three-scale method can accurately focus on the behaviors at arbitrary scale differently from the conventional hierarchical model. A demonstrative example of porous thin film on a substrate with an interface crack was solved and the microscopic stress was analyzed at the crack tip considering the random dispersion of pores and the high gradient of macroscopic strain field. To solve the large-scale 3D problem with approximately 80,000 solid elements, a renumbering technique and the out-of-core skyline solver was employed. © 2004 Elsevier Ltd. All rights reserved.

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Study on Large Deformation Characteristics of Knitted Fabric Reinforced Thermoplastic Composites at Forming Temperature by Digital Image-based Strain Measurement Technique

Naoki Takano, Masaru Zako, Reiko Fujitsu and Kazuaki Nishiyabu

Composites Science and Technology (Composites Science and Technology) 64 ( 13-14 ) 2153-2163 - 2163 2004

Joint Work, Accepted, ISSN 02663538

The continuous fiber reinforced thermoplastic composites, such as textile composites, have many attractive properties and functions and they are used widely nowadays in industrial applications. The important point in the design and manufacturing is that the composites as well as the reinforcing textiles undergo large deformation during thermoforming, which is much influential on the overall properties. Hence, the large deformation characteristics must be investigated at thermoforming temperature. For this sake, the digital image-based measurement technique of large strain distribution is developed. It is applicable to arbitrary complex shaped components with the help of 3D-CAD. As the large strain definition, Biot's strain is adopted that is calculated by the polar decomposition of the deformation gradient tensor based on continuum mechanics. The developed strain measurement technique is applied to the deep-drawing of aramid rib-knitted fabric reinforced polypropylene composites. The comparison between rib and plain-knitted fabrics reinforced composites is studied and many differences are found. The large deformation characteristics are also investigated from microscopic point of view under uniaxial tension at thermoforming temperature. © 2004 Elsevier Ltd. All rights reserved.

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Multi-Scale Finite Element Analysis for Joint Members of Heterogeneous Dissimilar Materials with Interface Crack

Takano N., Zako M., Okuno Y.

Zairyo/Journal of the Society of Materials Science, Japan (Zairyo/Journal of the Society of Materials Science, Japan) 52 ( 8 ) 952 - 957 2003.08

ISSN 05145163

In the last decade, a multi-scale computational method using the asymptotic homogenization method with the help of the finite element method has been intensively studied and applied to various advanced materials such as fiber reinforced composite materials and porous materials. It enables us to analyze the overall behaviors of structures considering the microscopic heterogeneity, where there is a large gap between the macro-scale and the micro-scale within the framework of continuum mechanics. However, no literature can be found that studied the joint or laminated members of heterogeneous dissimilar materials with interface crack. Due to the non-periodic condition at the interface and the existence of crack, the homogenized material modeling is of no use. Hence, an enhanced finite element mesh superposition method is employed to solve the two-scale problem. Two independent meshes, i. e., the global mesh and the local mesh, are used. The global mesh represents the joint or laminated members from the macroscopic viewpoint using the homogenized model. The local mesh is used to consider the heterogeneous microstructure of the material as well as the crack and superimposed onto the global mesh. The formulation, numerical accuracy and effectiveness of the proposed multi-scale method are presented in this paper.

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テキスタイル複合材料成形品における大ひずみ分布のデジタルイメージベース計測

TAKANO Naoki

日本複合材料学会誌 29 ( 1 ) 17-23 2003

Research paper (scientific journal), Joint Work, Accepted

Microstructure-based Stress Analysis and Evaluation for Porous Ceramics by Homogenization Method with Digital Image-based Modeling

Naoki Takano, Masaru Zako, Futoshi Kubo and Keiichi Kimura

International Journal of Solids and Structures (International Journal of Solids and Structures) 40 ( 5 ) 1225-1242 - 1242 2003

Research paper (scientific journal), Joint Work, Accepted, ISSN 00207683

Multi-scale analysis using the asymptotic homogenization method is becoming a matter of concern for microstructural design and analysis of advanced heterogeneous materials. One of the problems is the lack of the experimental verification of the multi-scale analysis. Hence, it is applied to the porous alumina with needle-like pores to compare the predicted homogenized properties with the experimental result. The complex and random microstructure was modeled three-dimensionally with the help of the digital image-based modeling technique. An appropriate size of the unit microstructure model was investigated. The predicted elastic properties agreed quite well with the measured values. Next, a four-point bending test was simulated and finally the microscopic stress distribution was predicted. However, it was very hard to evaluate the calculated microscopic stress quantitatively. Therefore, a numerical algorithm to help understanding the three-dimensional and complex stress distribution in the random porous microstructure is proposed. An original histogram display of the stress distribution is shown to be effective to evaluate the stress concentration in the porous materials. © 2002 Elsevier Science Ltd. All rights reserved.

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Multi-scale Finite Element Analysis of Porous Materials and Components by Asymptotic Homogenization Theory and Enhanced Mesh Superposition Method

Naoki Takano, Masaru Zako and Yoshihiro Okuno

Modelling and Simulation in Materials Science and Engineering (Modelling and Simulation in Materials Science and Engineering) 11 ( 2 ) 137-156 - 156 2003

Research paper (scientific journal), Joint Work, Accepted, ISSN 09650393

To analyse the macroscopic and microscopic behaviours of heterogeneous materials and components, a multi-scale computational method is studied. Although asymptotic homogenization theory has been the main tool during the last decade to solve various multi-scale problems, the assumption of the periodicity of the microscopic unit cell and the incapability of considering the scale effect have resulted in the limitations to this theory's applications. These problems should be overcome because advanced materials are often used as joint or laminated components and the interface crack problem must be analysed. For this sake, a novel multi-scale finite element method is proposed that uses the enhanced mesh superposition method together with the asymptotic homogenization theory. The finite element mesh superposition method uses the global mesh and the local mesh that is superimposed arbitrarily onto the global mesh. The enhanced method allows the adoption of different constitutive laws for the two meshes. The advantage of the homogenization theory to predict the homogenized material model accurately based on the complex microstructure is still utilized. The homogenized material model is used for the global mesh, whilst the microscopic heterogeneity and the crack are considered in the local mesh with the material properties of the constituents. The formulation, modeling strategy, implementation and numerical accuracy of the proposed method is described. A porous ceramic is studied in the numerical example.

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界面き裂を有する不均質接合体のマルチスケール有限要素解析

TAKANO Naoki

材料 52 ( 8 ) 952-957 2003

Research paper (scientific journal), Joint Work, Accepted

Three-dimensional Microstructural Modeling and Homogenization of Porous Alumina with Needle-like Pores

Naoki Takano, Keiichi Kimura, Masaru Zako and Futoshi Kubo

JSME International Journal Series A (Nippon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A) 46 ( 4 ) 519-526 - 1169 2003

Research paper (scientific journal), Joint Work, Accepted, ISSN 03875008

In the development of functional ceramics, the study on the relation between the macroscopic properties and the microstructures has been a critical issue. However, it has not been made clear by many experimental works. On the other hand, this paper takes the computational mechanics approach using the homogenization method. To model the very complex microstructure architecture three-dimensionally, the image-based modeling technique is employed. A porous alumina with needle-like random pores with 3.1% porosity ratio is studied in this paper. The effect of the location of extracting the unit cell and its size on the homogenized elastic constants is investigated. Then, the predicted values were compared with the measured ones. As a result, a unit cell region expressed by one million voxel elements with 2 μm resolution provides very accurate prediction regardless of the location of the unit cell in the random microstructures. The error between the numerical prediction and the measurement is only 1%.

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Multi-scale Analysis and Microscopic Stress Evaluation for Ceramics Considering The Random Microstructures

Naoki Takano, Keiichi Kimura, Masaru Zako and Futoshi Kubo

JSME International Journal Series A (Nippon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A) 46 ( 4 ) 527-535 - 1053 2003

Research paper (scientific journal), Joint Work, Accepted, ISSN 03875008

A multi scale computational method using the homogenization method is applied to the stress analysis of ceramics considering the random and complex microstructure three-dimensionally. The main purpose of this paper is to propose a numerical method to understand quantitatively the microscopic stress distribution in the random microstructure especially for porous ceramics. The voxel mesh is used to model the microstructure automatically with the help of the image-based modeling technique. In the analysis of porous alumina with needle-like random pores, the distance from the nearest pore is measured for all the voxel elements, which is plotted with the histogram of the microscopic stress distribution. This is of great help to study the relation between the stress concentration and the pore geometry and dispersion.

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Image-based modeling and elastic analysis of porous ceramics by the homogenization method

Keiichi K., Naoki T., Futoshi K., Syusui O., Hiroshi K., Masaru Z.

Journal of the Ceramic Society of Japan (Journal of the Ceramic Society of Japan) 110 ( 1282 ) 567 - 575 2002.06

ISSN 09145400

A three-dimensional elastic analysis system for porous ceramics has been built. In this system, three-dimensional morphology of pores is modeled using voxel (volume pixel) elements from digital images. Elastic analysis with this image-based finite element model is performed by the homogenization method. In order to investigate this analysis system, the elastic properties and behavior of porous Al2O3with spherical pores on the order of 1% by volume were computed. Young's moduli obtained by the homogenization method were consistent with both experimental and theoretical values. Using computed moduli of elasticity, the state of local stress concentration around the pores in a bending test was calculated together with the global stress in the sample. It was found that the dependence of the bending strength upon porosity can be described by taking into account local stresses around the pores. The combination of image-based modeling and homogenization method is a useful way to analyze the mechanical behavior of porous ceramics especially with inhomogeneous morphology.

Numerical analysis of permeability tensor for sheared woven fabrics

Takano N., Zako M., Okazaki T.

ISSN 03875008

Permeability tensor is a key parameter for Resin Transfer Molding (RTM) of fiber reinforced plastics as well as for its simulation. For sheared textile composites such as woven and knitted fabric composites after preforming or draping, the permeability tensor includes non-diagonal components, which can not be measured easily. This paper describes a numerical evaluation of permeability from both macro- and microscopic standspoints for sheared plain woven fabrics. The asymptotic homogenization theory for solid-fluid mixture is employed to characterize the micro-macro coupling effects. The nature of the macroscopic permeability tensor is discussed first. The microscopic flow field is next evaluated in detail by various ways. The differences of the microscopic flow field was recognized between the undeformed and sheared fabrics. The effects of the macroscopic pressure gradient is also discussed.

せん断変形した織布の樹脂透過テンソルの数値解析

TAKANO Naoki

日本機械学会論文集A編 68 ( 668 ) 529-536 2002

Research paper (scientific journal), Joint Work, Accepted

セラミックス多孔体のイメージベースモデリングと均質化法による弾性解析

TAKANO Naoki

日本セラミックス協会学術論文誌 110 ( 1282 ) 567-575 2002

Research paper (scientific journal), Joint Work, Accepted

セラミックスのランダムなミクロ構造を考慮したマルチスケール解析とミクロ応力評価

TAKANO Naoki

日本機械学会論文集A編 68 ( 671 ) 1046-1053 2002

Research paper (scientific journal), Joint Work, Accepted

Microstructure-based Evaluation of the Influence of Woven Architecture on Permeability by Asymptotic Homogenization Theory

Naoki Takano, Masaru Zako, Toru Okazaki and Kenjiro Terada

Composites Science and Technology (Composites Science and Technology) 62 ( 10-11 ) 1347-1356 - 1356 2002

Research paper (scientific journal), Joint Work, Accepted, ISSN 02663538

A microstructure-based computational approach is taken to predict the permeability tensor of woven fabric composites, which is a key parameter in resin transfer moulding (RTM) simulation of polymer-matrix composites. An asymptotic homogenization theory is employed to evaluate the permeability from both macro- and microscopic standpoints with the help of the finite-element method (FEM). This theory allows us to study the relation between microscopic woven architecture and macroscopic permeability based on the method of two-scale asymptotic expansions. While the fluid velocity is introduced for Stokes flow microscopically, the macroscopic one is for seepage flow with the Darcy's law. The latter can be characterized for arbitrary configurations of unit microstructures that are analyzed for the former under the assumption of the periodicity. After discussing the validity of this approach, we present a typical numerical example to discuss the permeability characteristics of plain weave fabrics undergoing shear deformation in the preforming in comparison with the underformed one. Another notable feature of the proposed method is that the correlation between the macroscopic behaviors and the microscopic ones can be analyzed, which is important to analyze and/or design the RTM process. Hence, it is also demonstrated that the microscopic velocity field evaluated with macroscopic pressure gradient provides important information about the flow in RTM processes. © 2002 Elsevier Science Ltd. All rights reserved.

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針状気孔を有するアルミナ多孔体の３次元ミクロ構造モデリングと均質化

TAKANO Naoki

日本機械学会論文集A編 68 ( 672 ) 1163-1169 2002

Research paper (scientific journal), Joint Work, Accepted

Microstructure-based deep-drawing simulation of knitted fabric reinforced thermoplastic by homogenization theory

Takano N., Ohnishi Y., Zako M., Nishiyabu K.

International Journal of Solids and Structures (International Journal of Solids and Structures) 38 ( 36-37 ) 6333 - 6356 2001.08

ISSN 00207683

Process simulation of fiber reinforced composite materials is an important research theme for the development of low-cost and advanced functional composite materials. This paper aims at the simulation of deep-drawing process of knitted fiber reinforced thermoplastics and its verification. The feature of the simulation is that the large deformation of the knitted microstructures can be traced everywhere in the deep-drawn product. The homogenization theory is applied to analyze the micro-macro coupled behaviors of the knitted fabric composite material. By employing a simplified nonlinear computational algorithm, the deep-drawing simulation was carried out on a personal computer. The predicted largely deformed microstructures were compared with the experimental results. The numerical results and experimental ones agreed quite well. This deep-drawing simulation requires us to prepare only the mechanical properties of the constituents, while it provides us all the necessary quantities such as the deformation, strain, stress and stiffness from both microscopic and macroscopic standpoints. © 2001 Elsevier Science Ltd. All rights reserved.

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Deep-drawing simulation of knitted fabric reinforced thermoplastics by homogenization theory and experimental verification

Takano N., Ohnishi Y., Nishiyabu K., Zako M.

Zairyo/Journal of the Society of Materials Science, Japan (Zairyo/Journal of the Society of Materials Science, Japan) 50 ( 5 ) 461 - 467 2001.05

ISSN 05145163

A novel computational method for deep-drawing simulation of composite materials has been proposed with taking a three-dimensional continuum mechanics approach. The most notable feature is the consideration of micro-macro coupling effects by the mathematical homogenization theory. The homogenized properties and the constitutive law are evaluated carefully using the three-dimensional microstructure model under the large deformation and biaxial loading conditions. In this paper, the knit reinforcement of aramid fiber is studied, which has very complex microstructure architecture. The polypropylene is used as the matrix. The newly developed deep-drawing simulation provides us the macroscopic deformation, strain, stress and stiffness distribution as well as the largely deformed microstructures in the deep-drawn product. The high-speed computing technique which has been developed in the previous report enables us to carry out the micro-macro coupled nonlinear analysis easily on the personal computer. The experimental work has also been conducted, and the largely deformed microstructures are compared between experiment and simulation. A good coincident was obtained, which implies the validity and reliability of the proposed computational method.

Three-dimensional evaluation of permeability of fiber reinforced composite materials based on their microstructures

Takano N., Terada K., Zako M.

Zairyo/Journal of the Society of Materials Science, Japan (Zairyo/Journal of the Society of Materials Science, Japan) 50 ( 5 ) 488 - 494 2001.05

ISSN 05145163

This paper proposes a novel computational method for the evaluation of the permeability of fiber reinforced composite materials with complex microstructures. The homogenization theory for solid-fluid mixture is employed to characterize the micro-macro coupling effects. A characteristic function associated with the flow velocity is derived, whose average is defined as the permeability tensor. The derived relation between the macroscopic velocity and pressure gradient coincides with the conventional Darcy's law. Therefore, the proposed method enables us to predict the permeability tensor numerically without any experimental work. Furthermore, the characteristic function provides useful information to understand the correlation between the microscopic architecture and the macroscopic permeability tensor. Once the permeability tensor is given, we can use a conventional process simulator under the realistic process conditions. The macroscopic pressure gradient is obtained, which leads to the analysis of the actual microscopic flow field in the microstructure. The proposed microstructure-based evaluation can be used as the pre/post-processing of the conventional macroscopic process simulation. Three-dimensional modeling and analysis are shown for textile composites with the help of finite element method.

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重合メッシュ法による不均質体のミクロ応力解析

TAKANO Naoki

日本機械学会論文集A編 67 ( 656 ) 603-610 2001

Research paper (scientific journal), Joint Work, Accepted

均質化法による編物強化熱可塑性プラスチックの深絞り成形解析とその検証

TAKANO Naoki

材料 50 ( 5 ) 461-467 2001

Research paper (scientific journal), Joint Work, Accepted

繊維強化複合材料のミクロ構造に基づく樹脂透過性の３次元評価

TAKANO Naoki

材料 50 ( 5 ) 488-494 2001

Research paper (scientific journal), Joint Work

Computational Method for Homogenizatoin of Heterogeneous Materials with Voxel Element Modeling of Their Microstructures

Naoki Takano, Masaru Zako, Futoshi Kubo and Keiichi Kimura

Materials Science Research International 2 66-71 2001

Research paper (scientific journal), Joint Work, Accepted

Finite Element Mesh Superposition Method Applied to Local Stress Analysis of Interphase of Composite Joints

Naoki Takano, Masaru Zako, Toru Okazaki and Futoshi Kubo

Materials Science Research International 2 219-224 2001

Research paper (scientific journal), Joint Work, Accepted

Microstructure-based Deep-drawing Simulation of Knitted Fabric Reinforced Thermoplastics by Homogenization Theory

Naoki Takano, Yoshihiro Ohnishi, Masaru Zako and Kazuaki Nishiyabu

International Journal of Solids and Structures 38 ( 36-37 ) 6333-6356 2001

Research paper (scientific journal), Joint Work, Accepted

Efficient Modeling of Microscopic Heterogeneity and Local Crack in Composite Materials by Finite Element Mesh Superposition Method

Naoki Takano, Masaru Zako, Toru Okazaki

JSME International Journal Series A (JSME International Journal, Series A: Solid Mechanics and Material Engineering) 44 ( 4 ) 602-609 - 609 2001

Research paper (scientific journal), Joint Work, Accepted, ISSN 13447912

The finite element mesh superposition method is applied to the two-dimensional crack problem of composite materials. The microscopic heterogeneity involved in the composite materials is modeled by the fixed grid model. On this global mesh, a local mesh that considers the local crack is superimposed without taking care of the matching of nodes and elements of both meshes. The use of the fixed grid model for the global mesh can reduce the time and efforts for the mesh generation to express the complex heterogeneous microstructures. Also it makes the computation and the implementation of the finite element mesh superposition method very easy. The accuracy was verified by comparing with the theory and the calculation by the conventional fine mesh.

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Microscopic stress analysis of heterogeneous media by finite element mesh superposition method

Takano N., Zako M.

Nihon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A (Nihon Kikai Gakkai Ronbunshu, A Hen/Transactions of the Japan Society of Mechanical Engineers, Part A) 67 ( 656 ) 603 - 610 2001

ISSN 03875008

Multiscale Modeling for heterogeneous media such as fiber or particulate reinforced composite materials and porous materials is one of the recent topics in computational mechanics and materials science. Homogenization technique has been, studied and used for the micro-macro bridging under the conditions of periodicity of the microstructures and of uniformity of macroscopic field. However, these two conditions make the evaluation of microscopic stresses using the homogenized model useless in the real applications, because the stresses with high gradient at the interface, edge or surface as well as the stress concentration due to voids etc. must be calculated. To solve this problem, in this paper, the finite element mesh superposition method is employed to calculate the microscopic stresses directly for local heterogeneity without the periodicity under non-uniform macroscopic strain field. Through two numerical examples, the efficiency of the modeling and the effectiveness of the microscopic stress evaluation are discussed.

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Formulation of homogenization method applied to large deformation problem for composite materials

Takano N., Ohnishi Y., Zako M., Nishiyabu K.

International Journal of Solids and Structures (International Journal of Solids and Structures) 37 ( 44 ) 6517 - 6535 2000.11

ISSN 00207683

In order to analyze the mechanical behaviors of composite materials under large deformation, the formulation of the homogenization method is described. In this formulation, assuming that the microstructures in a local region of the global structure are deformed uniformly and that consequently the microscopic periodicity remains in the local region under large deformation, the microscopic deformation is precisely defined by the perturbed displacement and product of macroscopic displacement gradient and microscopic coordinates. Finally, microscopic and macroscopic equations are obtained. The above mentioned assumption of the periodicity of microstructures is experimentally validated. The computer program is also developed according to this formulation, and the large deformation is analyzed for the unidirectional fiber reinforced composite material and the knitted fabric composite material.

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傾斜ミクロ構造設計による材料機能化

TAKANO Naoki

日本複合材料学会誌 26 ( 1 ) 9-16 2000

Research paper (scientific journal), Joint Work, Accepted

局所的不均質部を有する構造体のグローバル／ローカルモデリング

TAKANO Naoki

日本機械学会論文集A編 66 ( 642 ) 220-227 2000

Research paper (scientific journal), Joint Work, Accepted

The Formulation of Homogenization Method Applied to Large Deformation Problem for Composite Materials

Naoki Takano, Yoshihiro Ohnishi, Masaru Zako and Kazuaki Nishiyabu

International Journal of Solids and Structures 37 ( 44 ) 6517-6535 2000

Research paper (scientific journal), Joint Work, Accepted

均質化法によるテキスタイル複合材料の樹脂浸透係数の評価

TAKANO Naoki

日本複合材料学会誌 26 ( 5 ) 171-178 2000

Research paper (scientific journal), Joint Work, Accepted

Integrated Design of Graded Microstructures of Heterogeneous Materials

Naoki Takano and Masaru Zako

Archive of Applied Mechanics (Archive of Applied Mechanics) 70 ( 8-9 ) 585-596 - 596 2000

Research paper (scientific journal), Joint Work, Accepted, ISSN 09391533

This paper proposes a novel, integrated, computational design methodology of graded microstructures of heterogeneous materials for the emergence of macroscopic function. In the first step of the design procedure, some discrete microstructures among a large number of graded microstructures are determined by the genetic algorithm as the optimization method. In this determination procedure, the homogenized modeling is adopted considering the micro-macro coupling by the homogenization method. This method enables us to study complex microstructures. Homogenized properties such as elastic properties, coefficient of thermal expansion and thermal conductivity can be calculated rigorously based on continuum mechanics. Calculated homogenized properties are stored in the micro-macro correlative database. The genetic algorithm can select the best geometrical arrangement of multiple microstructures from the pre-calculated database to construct the graded microstructure architecture. By using the database, the microscopic and macroscopic analyses are separated from each other, which reduces considerably the computational cost for the micro-macro coupled design. In the second step, continuously graded microstructures are designed using a feature-based 3D-CAD system by interpolating the discretized graded microstructures. In addition, a solid model is produced by the stereolithography technique to help in understanding the computationally designed complex microstructures. Brief descriptions of the formulation of the homogenization method for heat conduction and thermal stress problems are shown. A design problem for a plate with graded microstructures in its thickness direction is shown. The objective function for this example is the control of the wrap of the plate under the condition of temperature distribution. © Springer-Verlag 2000.

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Multi-scale Computational Method for Elastic Bodies with Global and Local Heterogeneity

Naoki Takano, Masaru Zako and Manabu Ishizono

Journal of Computer-Aided Materials Design (Journal of Computer-Aided Materials Design) 7 ( 2 ) 111-132 - 132 2000

Research paper (scientific journal), Joint Work, Accepted, ISSN 09281045

A multi-scale computational method using the homogenization theory and the finite element mesh superposition technique is presented for the stress analysis of composite materials and structures from both micro- and macroscopic standpoints. The proposed method is based on the continuum mechanics, and the micro-macro coupling effects are considered for a variety of composites with very complex microstructures. To bridge the gap of the length scale between the microscale and the macroscale, the homogenized material model is basically used. The classical homogenized model can be applied to be case that the microstructures are periodically arrayed in the structure and that the macroscopic strain field is uniform within the microscopic unit cell domain. When these two conditions are satisfied, the homogenization theory provides the most reliable homogenized properties rigorously to the continuum mechanics. This theory can also calculate the microscopic stresses as well as the macroscopic stresses, which is the most attractive advantage of this theory over other homogenizing techniques such as the rule of mixture. The most notable feature of this paper is utilize the finite element mesh superposition technique along with the homogenization theory in order to analyze cases where non-periodic local heterogeneity exists and the macroscopic field is non-uniform. The accuracy of the analysis using the finite element mesh superposition technique is verified through a simple example. Then, two numerical examples of knitted fabric composite materials and particulate reinforced composite material are shown. In the latter example, a shell-solid connection is also adopted for the cost-effective multi-scale modeling and analysis.

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Global/local modelling of structures with local heterogeneity

Takano N., Zako M., Ishizono M.

ISSN 03875008

For the numerical simulation of mechanical behaviors of structures with local heterogeneity, a global/local modelling technique using the finite element mesh superposition technique and shellsolid connection is proposed. Not only the global deformation but also three-dimensional stresses nearby the local heterogeneity can be analyzed precisely with less efforts than conventional methods. The finite element mesh superposition technique makes it possible to overlay local fine solid mesh which considers the local heterogeneity on global rough solid mesh which neglects the local heterogeneity. A plate structure that contains dissimilar material in a local portion is analyzed by the proposed modelling technique. The results agreed well with those calculated using the conventional three-dimensional fine mesh model.

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Hierarchical modelling and local stress analysis of composite materials and structures

Takano N., Kashiwagi Y., Ohnishi Y., Zako M.

ISSN 03875008

In the numerical simulation of mechanical behaviors of composite materials and structures, a novel hierarchical modelling technique is proposed. Not only the global deformation but also the mesoscopic stresses are analyzed precisely with less human efforts than conventional methods. Four level hierarchy is defined for the textile composites, and the homogenization method and finite element mesh superposition technique are adopted. The latter technique makes it possible to overlay arbitrary local fine mesh on the global rough mesh. A panel with a rib made of knitted fabric composite material is analyzed by the proposed method. Three-dimensional modelling of the mesostructure of knitted fabric composite material is also shown. The validity of the proposed method was examined, and the mesoscopic stresses are calculated easily.

複合材料構造物の階層モデリングと局所的応力解析手法

TAKANO Naoki

日本機械学会論文集A編 65 ( 631 ) 498-505 1999

Research paper (scientific journal), Joint Work, Accepted

Hierarchical Modelling of Textile Composite Materials and Structures by the Homogenization Method

Naoki Takano, Yasutomo Uetsuji, Yukio Kashiwagi and Masaru Zako

Modelling and Simulation in Materials Science and Engineering (Modelling and Simulation in Materials Science and Engineering) 7 ( 2 ) 207-231 - 231 1999

Research paper (scientific journal), Joint Work, Accepted, ISSN 09650393

For the simulation of mechanical behaviours of textile composite materials and structures, a novel hierarchical modelling technique is proposed. Not only the global deformation but also the stresses at multiscales are analyzed precisely. Four-level hierarchy is defined for the textile composites such as woven and knitted fabric composites. The stresses at the mesostructure, which is a periodic unit cell of textile composite materials consisting of fibre bundles and matrix, can be evaluated accurately by the homogenization method and finite-element mesh superposition technique. The latter technique makes it possible to overlay arbitrary local fine mesh on the global rough mesh. Anisotropic damage mechanics is also utilized for strength evaluation at the mesoscale. Three-dimensional modelling of the mesostructure of woven and knitted fabric composite materials is shown. Localization analysis has been carried out within practical computational time and cost by the proposed hierarchical modelling.

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Intelligent Material Systems Using Epoxy Particles to Repair Microcracks and Delamination Damage in GFRP

Masaru Zako and Naoki Takano

Journal of Intelligent Material Systems and Structures (Journal of Intelligent Material Systems and Structures) 10 ( 10 ) 836-841 - 841 1999

Research paper (scientific journal), Joint Work, Accepted, ISSN 1045389X

The objective of this study is to propose an intelligent material system that can perform a self-repairing operation against initial damage that might occur in GFRP laminates. Specifically, we highlight the development of a novel actuator to be used in such self-repairing operations. There has been much research on sensor systems to detect damage and some actuators to control the shape of the structure or to control the vibration. However, no literature can be found on the actuator aiming at the self-repair of damage. For this purpose, a small grain particle-type adhesive is embedded in a glass/epoxy composite (GFRP) laminate. The diameter of the particle is approximately 50 μm. Hence, in the developed intelligent material system, coldsetting epoxy resin is used as the matrix, uni-directionally arranged glass fiber is used as the reinforcement, and a thermosetting epoxy particle is used as a repairing actuator. The volume fraction of the particles in the matrix was approximately 40%. The embedded particles can repair the damage, when melted by heat. Basic characteristics of the particles were investigated first, and we confirmed that the embedded particles in the matrix can melt by heat and flow to repair the crack. We also confirmed that the embedded particles do not deteriorate the stiffness of the GFRP laminate. Then we investigated the efficiency of the repairing operation against initial damage such as microscopic matrix cracks and delamination, by conducting two typical tests, i.e., static three-point bending of [0/90] laminate and tensile fatigue of [0/90]slaminate. Damage was observed by CCD camera. As a result, the decrease in the stiffness due to initial damage has been recovered and consequently increased, the residual fatigue life.

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カップリング効果を考慮した曲げ試験法

TAKANO Naoki

強化プラスチックス 45 ( 3 ) 84-87 1999

Research paper (scientific journal), Joint Work, Accepted

On an intelligent structure of concrete reinforced by CFRP

Zako M., Takano N., Fujioka H.

Zairyo/Journal of the Society of Materials Science, Japan (Zairyo/Journal of the Society of Materials Science, Japan) 47 ( 11 ) 1183 - 1187 1998.11

ISSN 05145163

An intelligent structure of concrete reinforced by CFRP which can detect and repair the delamination of CFRP from the surface of concrete has been proposed and the performance has been evaluated in this paper. In order to investigate the effect of repair, three-point bending test has been performed on the test piece. When the optical fiber sensor detects the delamination during the test, the processor judges the damage to be repaired. The embedded Ni-Cr wire is heated to release the epoxy resin in the capsule, it spreads into the delamination to adhere the damage. The result of three-point bending test after repair showed better performance than that of a specimen of non-repaired. In case the repair was delayed, however, reasonable repairing cannot be expected. Therefore, delamination must be detected and repaired in the early stage of fracture. As a result, it was recognized that the delamination of CFRP on mortar concrete can be repaired with the proposed system.

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On sensor and actuator for intelligent structure of concrete reinforced by CFRP

Zako M., Takano N., Fujioka H.

Zairyo/Journal of the Society of Materials Science, Japan (Zairyo/Journal of the Society of Materials Science, Japan) 47 ( 11 ) 1178 - 1182 1998.11

ISSN 05145163

When CFRP lamina is applied for the reinforcement of concrete structures, the lamina has a possibility to delaminate from the surface of concrete. The delamination must be detected and be repaired as soon as possible for the reliability of structures. In pursuit of this, an intelligent structure was proposed in this paper. Both sensor and actuator are required to detect and to repair the delamination, respectively. As the intelligent structure, optical fiber was used to detect the delamination of CFRP as a sensor. Epoxy resin adhesive in a capsule was used to repair the delamination as an actuator. In the first paper, characteristics of both sensor and actuator were investigated. The brightness of transmitted light in the optical fiber was decreased at bended point caused by delamination of CFRP. On the other hand, the capsuled epoxy resin has been spreaded widely into delaminated interface. As a result, it was recognized that the proposed sensor and actuator can be used to detect and repair the delamination of CFRP.

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Design procedure for laminated composites based on genetic algorithm with function approximation

Zako M., Takano N., Takeda N.

Zairyo/Journal of the Society of Materials Science, Japan (Zairyo/Journal of the Society of Materials Science, Japan) 47 ( 5 ) 446 - 451 1998.05

ISSN 05145163

In this paper, a design procedure for laminated composite structures based on GA (Genetic Algorithms) with function approximations is proposed. Design variables considered to enhance the rigidity of the laminated composite structure are the number of laminae, the fiber orientations and the stacking sequence. The fiber orientations are chosen from some prepared angles. In the proposed procedure, the rigidity of laminated composites is approximated by means of weighing coefficients and transformed elastic constants at the prepared angles. The proposed approximate function can be thought of response surfaces, because the weighing coefficients are adjusted with pairs of input and output data. The effective approximation is generated using auxiliary information about the principal stress distribution. The approximate function is used as the objective function of GA and can be evaluated without finite element analysis. As a result, the proposed procedure can reduce computational cost remarkably. In this paper, the detail of our developed design procedure and data sampling scheme are described.

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Development of design margin decision system considering fatigue limit

Zako M., Takano N., Hanaki S.

Zairyo/Journal of the Society of Materials Science, Japan (Zairyo/Journal of the Society of Materials Science, Japan) 47 ( 1 ) 90 - 94 1998.01

ISSN 05145163

The experimental results of fatigue at low stress levels around the fatigue limit have large scatter. For the design of structures and machines, it is important to evaluate the scatter and to decide the design margin. In this paper, the statistical method to decide the fatigue limit is proposed. In the proposed method, the fatigue limit is decided with considering the distribution of fatigue strength. Because each fatigue data is transformed into normalized fatigue strength, this method has the advantage point that the distribution of fatigue strength and the fatigue limit can be found by relatively small samples. Using the proposed method, the computer system to decide the design margin for fatigue is developed. In this system, the S-N curve with fatigue limit and the distribution of fatigue strength are obtained at first. Then the design margin with a given probability of failure and a confidence level is calculated. The developed system is applied to some experimental results for fatigue test. As a result, the S-N curve with the design margin has obtained easily. It is recognized that the obtained S-N curve is decided after consideration of scatter.

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CFRP貼付補強によるコンクリートのインテリジェント化

TAKANO Naoki

材料 47 ( 11 ) 1183-1187 1998

Research paper (scientific journal), Joint Work, Accepted

CFRP貼付補強コンクリートのインテリジェント化のためのセンサ・アクチュエータに関する研究

TAKANO Naoki

材料 47 ( 11 ) 1178-1182 1998

Research paper (scientific journal), Joint Work, Accepted

耐久限度を考慮した疲労設計基準決定システムの構築

TAKANO Naoki

材料 47 ( 1 ) 90-94 1998

Research paper (scientific journal), Joint Work, Accepted

関数近似法を用いた遺伝的アルゴリズムによる積層複合材料の設計手法

TAKANO Naoki

材料 47 ( 5 ) 446-451 1998

Research paper (scientific journal), Joint Work, Accepted

ミクロ構造を考慮した複合材料の深絞り成形解析－解析手法の提案－

TAKANO Naoki

材料 47 ( 6 ) 593-598 1998

Research paper (scientific journal), Joint Work, Accepted

Design of Microstructures for the Emergence of Macroscopic Function by Homogenization Method and Genetic Algorithms

Naoki Takano, Masaru Zako, Masaya Nakagawa and Norio Takeda

Materials Science Research International (Materials Science Research International) 4 ( 3 ) 153-158 - 158 1998

Research paper (scientific journal), Joint Work, Accepted, ISSN 13411683

In this paper, a design procedure of the microstructure of composite materials is proposed for the emergence of desired macroscopic function. The homogenization method is used for the expression of the correlativity between micro- and macroscopic properties, and genetic algorithms (GA) is used to solve the optimization problem. Using the micro-macro correlative database of material properties constructed by the homogenization method, the design problem is separated into micro- and macroscopic sub-problems. Thus, the proposed procedure is quite efficient and extendable to various design problems of new advanced materials such as functionally gradient materials. As an example, a plate of graded micro-porous materials, that is free of warp and/or twist under the environment with temperature gradient from the upper to lower surfaces, is shown.

Computational analysis of deep-drawing for composite materials considering the microstructure -proposition of analytical method

Takano N., Zako M., Ohnishi Y.

Zairyo/Journal of the Society of Materials Science, Japan (Zairyo/Journal of the Society of Materials Science, Japan) 47 ( 6 ) 593 - 598 1998

ISSN 05145163

In order to simulate the deep-draw forming process for composite materials with complex microstructure, a novel computational method that takes the microscopic large deformation into consideration is proposed. The microstructure of composite materials affects the deep-draw forming process. The proposed method decouples this complicated problem into macro- and microscopic problems by means of homogenized nonlinear material properties, which contributes much to the computational cost effectiveness. First, using the large deformation analysis and homogenization, the homogenized nonlinear properties considering the microstructural geometrical nonlinearity are obtained by microscopic analyses. Secondly, the deep-draw forming analysis is carried out macroscopically with precalculated material database. This material database consists of 21 independent parameters given by microscopic analyses, and is referred with respect to three macroscopic strain parameters. An example of deep-draw forming simulation for a formed core is shown.

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I : Numerical analysis and design - Development of new methods like homogenization method to composite materials

Takano N., Zako M.

Zairyo/Journal of the Society of Materials Science, Japan (Zairyo/Journal of the Society of Materials Science, Japan) 46 ( 1 ) 97 - 102 1997.12

ISSN 05145163

Design method for three-dimensional reinforcement partially considering the correlation between layout and cross-sectional shape

Zako M., Takano N., Sakata S.

ISSN 03875008

In this paper, we describe a methodology for three-dimensional structural design for reinforcement that determines both layout and cross-sectional shape. Considering the difference in scale between the design variables for the layout design and those for the design of a cross-sectional shape, we separate the design problem into two sub-problems. One can be called a macroscopic design problem, and the other a microscopic one. The proposed design method takes the correlation between the sub-problems partially into account by using a new parameter to construct a feedback loop. The effectiveness of this method has been proved through simple numerical examples.

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Mesoscopic strength evaluation of woven fabric composite materials by homogenization method and anisotropic damage mechanics

Takano N., Zako M., Uetsuji Y., Kashiwagi Y.

ISSN 03875008

In this paper, a woven structure consisting of fiber bundles is defined as a mesostructure and we evaluate the strength of woven fabric composite materials mesoscopically by the homogenization method and anisotropic damage mechanics. A numerical simulation system for virtual strength test has been developed to predict the initial mesoscopic fracture, the fractured location in both macro-and mesostructure and the fracture mode. The mesoscopic fracture mode is shown schematically, which greatly aids in the understanding of the mesomechanics of woven fabric composite materials. This system is effective for material and structure design and proves the necessity of considering the interaction between macro-and mesostructures. Furthermore, the formulation and a numerical example for mesoscopic fracture propagation considering the fracture mode are shown.

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複合材料の設計と評価の最前線　１．数値解析・設計－均質化法等新しい手法の複合材料への展開

TAKANO Naoki

材料 46 ( 1 ) 97-102 1997

Research paper (scientific journal), Joint Work, Accepted

均質化法と異方損傷力学を用いた織物複合材料のメゾ強度評価

TAKANO Naoki

日本機械学会論文集A編 63 ( 608 ) 808-814 1997

Research paper (scientific journal), Joint Work, Accepted

Cost Effective Design Procedure for Laminated Composite Structure Based on GA

Masaru Zako, Naoki Takano, Norio Takeda and Tetsuya Tsujikami

Science and Engineering of Composite Materials (Science and Engineering of Composite Materials) 6 ( 2 ) 131-140 - 140 1997

Research paper (scientific journal), Joint Work, Accepted, ISSN 0334181X

We present a design procedure for symmetrically laminated composite structure with GA (Genetic Algorithm) and finite element analysis. Design variables to enhance the rigidity of the laminated composite structure are the number of laminae, the fiber orientation and the stacking sequence. Here, the fiber orientation is selected among some prepared angles from a manufacturing viewpoint. In a conventional design procedure based on GA, an objective function is calculated by costly finite element analysis. Consequently, it is quite time consuming and unpractical. In this paper, to minimize the displacement at a point in the structure, we define an approximated rigidity function of the laminated composites by means of weighing coefficients and transformed elastic moduli in the prepared angles. The weighing coefficients are initially determined using the distribution of principal stress in the structure under an applied load. Then, we can guess that reinforcements should be oriented according to the weighing coefficients with which the rigidity function takes maximum. To find the global optimum solution, the weighing coefficients are adjusted with as small a number of finite element analyses as possible. As a conclusion, the proposed procedure can reduce the computational cost remarkably compared to the conventional one, and can be applied practically to arbitrary shaped structures.

部材のレイアウトと断面形状の相関を部分的に考慮した三次元補強設計法

TAKANO Naoki

日本機械学会論文集A編 63 ( 613 ) 2070-2076 1997

Research paper (scientific journal), Joint Work, Accepted

Efficient application of GA to design of fiber reinforced composites

Zako M., Takano N., Tsujikami T., Takeda N.

Zairyo/Journal of the Society of Materials Science, Japan (Zairyo/Journal of the Society of Materials Science, Japan) 45 ( 12 ) 1316 - 1321 1996.12

ISSN 05145163

In this paper, a cost effective design procedure for laminated composite structure using GA (Genetic Algorithms) is proposed. Design variables considered to enhance the rigidity of the laminated composite structure are the number of laminae, the fiber orientation and the stacking sequence. The fiber orientations are chosen among some prepared angles. In the proposed design procedure, a rigidity function is defined to determine which angle to reinforce by means of weighing coefficients and transformed elastic constants in the prepared angles. The weighing coefficients are defined to represent the distribution of principal stress in the structure. Then, the orientation of reinforcements can be found according to the weighing coefficients such that the defined rigidity function takes maximum. Futhermore, to find a global optimum solution, the weighing coefficients are adjusted. In this paper, the detail of our developed procedure and some applications are shown.

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Development of expert system for three-dimensional analysis of composites

Zako M., Tsujikami T., Takano N., Uemura M., Ichikawa M., Hirata T.

ISSN 03875008

There are, at present, too many design parameters for composite structures such as reinforcing fiber architecture, fiber orientation, and volume fraction, among others. Therefore, the material data base system, which can calculate three-dimensional mechanical properties of lamina and laminate using the classical stacking theory, has been developed. The advantage of this system is that it is able to calculate mechanical properties easily and visually by using graphical user interface. As an application of the developed system, a wastewater treatment tank made of GFRP under internal water pressure has been analyzed. The computational results show good agreement with the experimental ones. It is revealed that the proposed system is very useful for three-dimensional structural analysis of composite materials.

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Numerical prediction of strength of notched UD laminates by analyzing the propagation of intra- and inter-laminar damage

Zako M., Takano N., Tsumura T.

Materials Science Research International (Materials Science Research International) 2 ( 2 ) 117 - 122 1996.06

ISSN 13411683

To predict the strength of notched unidirectional (UD) fiber reinforced laminates, computational modeling method is shown as well as its verification. Both intra-laminar damage such as fiber breaking, matrix cracking and fiber-matrix interface debonding and inter-laminar damage such as delamination occur and propagate up to the final breaking. In the proposed numerical method, the occurrence of the intra-laminar damage is judged by Hoffman's failure criterion and its propagating behavior is theoretically formulated by anisotropic damage mechanics. The delamination is numerically treated by introducing inter-laminar element (IE) in the finite element analysis. Applying the proposed method to CFRP laminates with a hole under tensile load, the damage mode in each lamina and the notched strength have been predicted. By comparison with the experimental results, the validity and the reliability of our simulation have been recognized.

Development of virtual production system for tape winding structures (1st Report, tape winding simulation and strength evaluation)

Zako M., Takano N., Tujikami T., Hirata T.

ISSN 03875008

The strength of tape-wound structures depends on many factors such as winding angle and path. Because winding path cannot be obtained explicitly before production, it is very difficult to evaluate the strength. Therefore, a computer system for the design and analysis of wound structures has been developed. This system consists of calculating the winding path and generating a finite-element model to predict the strength. This paper focuses on the algorithm of winding simulation and the modeling method of complicatedly wound tape layers. As an example, design and FEM analysis are carried out for CFRP-tape-wound pipe. It is found that the developed system is very useful for design and safety evaluations of winding structures.

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Homogenization analysis method for composites considering geometrical nonlinearity and fracture of microstructure

Takano N., Zako M., Heguri H., Kikuchi N.

ISSN 03875008

For the design and production of new advanced composite materials and structures, the need for numerical simulations of their mechanical behaviors is increasing. There are two requirements for the simulation. First, microstructural architectures must be considered. The homogenization analysis method, which is an applied mathematical method developed from late 1970's to early 1980's, seems to be the most appropriate method for modelling microstructures in current literature. The second requirement is the solution of nonlinear problems. Therefore, we have developed a nonlinear homogenization method where both geometrical nonlinearity due to large deformation of microstructures and material nonlinearity due to microscopic fractures are considered. The new formulation of the nonlinear homogenization method is based on a stepwise linear algorithm with initial stresses. Two examples, i.e., biomechanical problem and fracture behavior of woven fabric composite material, were solved.

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Three-dimensional microstructural design of woven fabric composite materials by homogenization method (2nd report, detailed analysis of microscopic behavior under bending load)

Takano N., Zako M., Sakata S.

ISSN 03875008

For design and development of advanced textile composite materials, evaluation of their bending strength is essential. However, as far as we know, there has been no literature on the numerical simulation predicting the bending strength of textile composites. In this paper, we show a methodology for calculation of the bending strength for woven fabric composite materials by the homogenization method. Both the location and the cause of microscopic fracture in a fiber bundle and resin are discussed in detail. The effect of the pitch of woven fabrics on the bending characteristics is also noted.

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Macro-micro uncoupled analysis procedure for nonlinear structural mechanics of composites - RVE approach to microstructural geometrically nonlinear problem

Takano N., Zako M., Ohnishi Y.

Zairyo/Journal of the Society of Materials Science, Japan (Zairyo/Journal of the Society of Materials Science, Japan) 45 ( 2 ) 163 - 168 1996.02

ISSN 05145163

The purpose of this study is to develop a practical analysis procedure for nonlinear structural mechanics of composites. Especially, to solve such a nonlinear mechanical problem arising from the microstructural nonlinear behavior, the new homogenization procedure named macro-micro uncoupled method is proposed. First, the homogenized macroscopic material properties are calculated by precise microscopic nonlinear analysis. Then, macroscopic analysis can be performed easily by only referring to the pre-calculated nonlinear material properties. In this paper, RVE approach is taken for the microscopic nonlinear analysis, and the proposed macro-micro uncoupled method is applied to a microstructural large deformation problem of porous media.

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繊維強化複合材料の剛性設計のためのGAの効率的適用

TAKANO Naoki

材料 45 ( 12 ) 1316-1321 1996

Research paper (scientific journal), Joint Work, Accepted

複合材料の非線形構造力学解析のためのマクロ－マイクロ非連成化手法－マイクロ構造における幾何学的非線形問題へのRVEアプローチ－

TAKANO Naoki

材料 45 ( 2 ) 163-168 1996

Research paper (scientific journal), Joint Work, Accepted

複合材料のマイクロ構造における幾何学的非線形性と破壊を考慮した均質化解析手法

TAKANO Naoki

日本機械学会論文集A編 62 ( 595 ) 859-864 1996

Research paper (scientific journal), Joint Work, Accepted

均質化法による織物複合材料の三次元マイクロ構造設計（第２報，曲げ負荷時のマイクロスコピックな挙動の詳細解析

TAKANO Naoki

日本機械学会論文集A編 62 ( 595 ) 884-889 1996

Research paper (scientific journal), Joint Work, Accepted

Macro-Micro Uncoupled Homogenization Procedure for Microscopic Nonlinear Behavior Analysis of Composites

Naoki Takano, Masaru Zako and Yoshihiro Ohnishi

Materials Science Research International (Materials Science Research International) 2 ( 2 ) 81-86 - 86 1996

Research paper (conference, symposium, etc.), Joint Work, Accepted, ISSN 13411683

For easy and practical simulation of microscopic nonlinear mechanical behavior of composite materials, new homogenization analysis procedure named macro-micro uncoupled method is proposed. In this procedure, microscopic simulation of material strength test is carried out first, then nonlinear homogenized material properties are obtained. Both the homogenization method and RVE (Representative Volume Element) approach are shown for this microscopic simulation. Macroscopic nonlinear behavior of a structure made of composite materials can be analyzed by only referring the pre-calculated homogenized material nonlinearity. As an example, microscopic fracture propagation for textile composite materials and microscopic large deformation for porous elastic materials are analyzed.

Numerical Prediction of Strength of UD Notched Laminates by Analyzing the Propagation of Intra- and Inter-laminar Damage

Masaru Zako, Naoki Takano and Takuya Tsumura

Materials Science Research International 2 ( 2 ) 117-122 1996

Research paper (scientific journal), Joint Work, Accepted

ワインディング構造物の仮想試作システム構築（第１報，テープワインディングならびにその強度）

TAKANO Naoki

日本機械学会論文集A編 62 ( 598 ) 1450-1455 1996

Research paper (scientific journal), Joint Work, Accepted

複合材料用三次元構造解析支援システムの構築

TAKANO Naoki

日本機械学会論文集A編 62 ( 598 ) 1501-1505 1996

Research paper (scientific journal), Joint Work, Accepted

Three-dimensional microstructural design of woven fabric composite material by homogenization method

Takano N., Zako M.

American Society of Mechanical Engineers, Pressure Vessels and Piping Division (Publication) PVP (American Society of Mechanical Engineers, Pressure Vessels and Piping Division (Publication) PVP) 302 141 - 146 1995.12

ISSN 0277027X

The strength of woven fabric composite materials depends on the microstructural geometry. However, the conventional methods for mechanical analysis, which have been widely used so far, are insufficient because they cannot take into account for the three-dimensional microstructure. In this study, three-dimensional homogenization method is shown to be effective for the evaluations of the material constants, microscopic stresses and the strength. It has been found that the transverse stresses in the direction of lamination play an important role for the fracture of both fiber bundle and resin. Also, the effect of the mismatched lay-up on the strength has been investigated. It has well been predicted that the mismatched lay-up causes the reduction of the strength and the difference of crack initiation in the resin. These simulations give us a new concept of the microstructural design of the composite materials.

微視破壊を考慮した均質化法による織物複合材料の非線形解析

TAKANO Naoki

材料 44 ( 505 ) 1231-1237 1995

Research paper (scientific journal), Joint Work, Accepted

Fixed Grid に基づく均質化法による複合材料のマイクロスコピック・シミュレーション技法の提案

TAKANO Naoki

日本機械学会論文集A編 61 ( 583 ) 589-594 1995

Research paper (scientific journal), Joint Work, Accepted

均質化法による織物複合材料の三次元マイクロ構造設計（第１報，強度に及ぼす織物積層方向位置ずれの影響）

TAKANO Naoki

日本機械学会論文集A編 61 ( 585 ) 1038-1043 1995

Research paper (scientific journal), Joint Work, Accepted

Stress Analysis of Sandwich Plate by the Homogenization Method

Naoki Takano, Masaru Zako and Noboru Kikuchi

Materials Science Research International (Journal of the Society of Materials Science, Japan) 1 ( 2 ) 82-88 - 88 1995

Research paper (scientific journal), Single Work, Accepted, ISSN 05145163

The effectiveness of the homogenization method for analysis of composite materials has been shown since it was firstly introduced in 1970's. As this method is applicable to periodic problems only, however, some engineering problems remain unsolved. For instance, we could not apply it to honey-comb sandwich plates and panels with reinforcing ribs because these structures are not periodic in the thickness direction. In this paper, the application of the homogenization method to those composite structures is discussed. As a practical example, stress analysis of single-layered corrugated core sandwich plate is presented. A method to homogenize the complicated geometry to a simple solid model, to get the homogenized material constants, and to calculate the microscopic stress is proposed. © 1995, The Society of Materials Science, Japan. All rights reserved.

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均質化法による単層波状コアサンドイッチ板の解析－面内のみ周期性を有する複合構造への均質化法の適用について－

TAKANO Naoki

材料 44 ( 502 ) 905-910 1995

Research paper (scientific journal), Joint Work, Accepted

損傷力学に基づく複合材料用三次元有限要素法の開発

TAKANO Naoki

材料 44 ( 502 ) 921-926 1995

Research paper (scientific journal), Joint Work, Accepted

信頼性に基づく先端材料用設計寿命評価システム

TAKANO Naoki

日本機械学会論文集A編 61 ( 589 ) 1909-1913 1995

Research paper (scientific journal), Joint Work, Accepted

Analysis of Single-Layered Corrugated Core Sandwich Plate by Homogenization Method — On the Application of Homogenization Method to Composite Structures with Only Planar Periodicity —

Takano N., Zako M.

Journal of the Society of Materials Science, Japan (Journal of the Society of Materials Science, Japan) 44 ( 502 ) 905 - 910 1995

ISSN 05145163

The effectiveness of the homogenization method for the analysis of composite materials has been shown since it was firstly introduced in the 1970's. As this method is applicable to periodic problems only, however, some important engineering problems remain unsolved. Those problems are, for instance, honey-comb sandwich plates and panels with reinforcing ribs, which are not periodic in the thickness direction. In this paper, the application of the homogenization method to those problems is discussed. As a pratical example, stress analysis of single-layered corrugated core sandwich plates is presented. A method to homogenize its complicated geometry to a simple solid model, to get the homogenized material constants, and to calculate the microscopic stress is proposed. © 1995, The Society of Materials Science, Japan. All rights reserved.

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Three Dimensional Microstructural Design of Woven Fabric Composite Materials by the Homogenization Method (1st Report, Effect of Mismatched LayUp of Woven Fabrics on the Strength)

Takano N., Zako M., Sakata S.

ISSN 03875008

The strength of woven fabric composite materials depends on their microstructural geometry. However, the conventional methods for mechanical analysis, which have been widely used to date, are insufficient because they cannot take into account the three-dimensional microstructure. In this study, the three-dimensional homogenization method is shown to be effective for determination of the material constants, microscopic stresses and strength. It has been found that the transverse stress in the lamination direction plays an important role in the fracture of both the fiber bundle and the resin. Also, the effect of the mismatched lay-up on the strength has been investigated. It was predicted that the mismatched lay-up causes a reduction in strength and a difference of crack initiation in the resin. These simulations provide a new concept for the microstructural design of composite materials. © 1995, The Japan Society of Mechanical Engineers. All rights reserved.

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Nonlinear Analysis of Woven Fabric Composite Materials by Homogenization Method Considering Microscopic Fracture

Takano N., Zako M.

Journal of the Society of Materials Science, Japan (Journal of the Society of Materials Science, Japan) 44 ( 505 ) 1231 - 1237 1995

ISSN 05145163

Textile composites are becoming more and more important in engineering field. Need for computational simulations of their mechanical behaviors is also growing. In this study, a nonlinear homogenization method has been developed for the analysis of fracture behaviors of woven fabric composite materials. First, the mechanical behaviors of flat plates made from woven fabric composite materials were analyzed under various loading conditions, and then the reduction of modulus of elasticity by microscopic fracture was calculated precisely. Next, the nonlinear fracture analysis of a plate with an open hole was carried out. It is revealed that the knee points and notched strength are able to be predicted. © 1995, The Society of Materials Science, Japan. All rights reserved.

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Microscopic Simulation Technique for Composite Meterials Using the Homogenization Method Based on Fixed Grid

Takano N., Zako M.

ISSN 03875008

Recently, the homogenization method is becoming a matter of interest as a new analysis method of composite materials. This method aims at stricter modeling and more precise simulation for any kind of reinforcement. Discretization of complicated microstructures of such reinforcement, however, becomes the bottleneck in the analysis procedure. Therefore, a new simulation technique based on a fixed grid is proposed in this paper. Fundamental investigation of the accuracy of the homogenization method based on a fixed grid for unidirectional FRP is presented. The obtained elastic constants show good agreement with the solution of the Halpin-Tsai equation. Microscopic stress distribution has also been evaluated well compared with conventional smooth finite-element discretization. © 1995, The Japan Society of Mechanical Engineers. All rights reserved.

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Development of Three-Dimensional Finite Element Method for Composite Materials Based on Damage Mechanics

Zako M., Tsujikami T., Takano N.

Journal of the Society of Materials Science, Japan (Journal of the Society of Materials Science, Japan) 44 ( 502 ) 921 - 926 1995

ISSN 05145163

A computer program of the three-dimensional finite element method for composite materials based on damage mechanics has been developed. There are many kinds of fracture pattern in composite materials. Especially, the progression of fracture caused by out-of-plane and shearing deformation is very complex. The effect of these fracture patterns on the mechanical behavior must be considered for the design and analysis of fracture behavior of composites. The consideration of damage mechanics has been introduced into the proposed program in order to treat above mentioned behaviors. A numerical procedure with new concept for the constitutive equation with damaged elements is introduced in this paper. As an example, the mechanical behavior of laminate under three point bending was analyzed by the developed computer program. The computational results concerning the fracture pattern agreed well with the experiments. Consequently, it can be recognized that our proposed program is very useful for structural design and analysis of mechanical behavior for composite structures. © 1995, The Society of Materials Science, Japan. All rights reserved.

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Development of Design Margin Decision System for Advanced Materials Based on Reliability

Zako M., Takano N., Ichikawa M., Hanaki S.

Transactions of the Japan Society of Mechanical Engineers Series A (Transactions of the Japan Society of Mechanical Engineers Series A) 61 ( 589 ) 1909 - 1913 1995

ISSN 03875008

The design concept based on reliability is effective for advanced materials, because advanced materials such as fiber-reinforced composites have variable mechanical properties. In addition, as the failure mode in the low cycle fatigue region differs from that in the high cycle fatigue region, it is difficult to predict the fatigue life of advanced materials. So far, we have developed a design margin decision system based on reliability by evaluating fatigue life. In this study, the system is improved for application to advanced materials and a method to divide whole sets of data into the above two regions and to calculate the design margin in each region is presented. From numerical examples for CF/PEEK laminates and epoxy resin, it is revealed that a more reasonable S-N curve and design margin are obtained by the proposed system. © 1995, The Japan Society of Mechanical Engineers. All rights reserved.

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Application of Steering Technique to Structural Analysis by Finite Element Method

Naoki Takano

Jsme News (The Japan Society of Mechanical Engineers) 4 ( 2 ) 7-8 1993

Research paper (scientific journal), Single Work, Accepted

Stress singularities at the interface crack and the corner of edge-bonded dissimilar materials

Miyoshi T., Shiratori M., Okuda H., Takano N.

American Society of Mechanical Engineers, EEP (American Society of Mechanical Engineers, EEP) 1 551 - 557 1992.12

ISSN 0791807665

From a structural point of view, the electronic devices and/or components can be classified as the multi-layered structures composed of dissimilar materials. Therefore, the stress singularities caused by the mismatch of the elastic constants and the thermal expansion coefficients has to be taken into consideration when carrying out the finite element stress analysis. In this paper, the stress singularities encountered at the corner of the bonded edge and/or the interface crack tip in dissimilar materials are theoretically described. Furthermore, it is demonstrated that the finite element method can properly explain the theoretical stress singularities i.e. the order of the singularity and the stress distributions. The intensity of the singular stress field, which is measured by the stress intensity factor, is also analyzed.

Finite element analysis by transputer

Miyoshi T., Takano N.

ISSN 0277027X

This paper describes a speed up of finite element analysis by a parallel computer using transputer. As a solver suited for parallel computers, skyline method by Cholesky decomposition in inner product form is presented. This algorithm uses row wise Cholesky decomposition and its parallelism can be extracted easily. In the three dimensional structural analysis, concurrent processing of three rows and columns is shown to be effective. Using this solver, elastic-plastic analyses have been carried out and the computational speed by 4 transputers was about 10 to 20 times faster than by EWS. Furthermore, this solver is one of the direct methods, independent of the number of processors or the architecture of parallel computers and a promising speed up by both vector and parallel processing is possible.

Large scale structural analysis by a supercomputer

Miyoshi T., Takano N., Shiratori M.

ISSN 0277027X

The authors have developed finite element codes FEM3D/S and FEM3D/I for three dimensional large scale structural analysis. Their solvers are based upon parallel skyline method and the ICCG method, respectively, and they are specially designed for the high speed and large scale supercomputing. A bench mark test shows that the developed codes are effective among the different kinds of supercomputers. Further, the authors have developed a system integrated with these codes and pre and post processors, which run on an engineering work station. Examples of the three dimensional elastic-plastic analysis show that the developed system is effective for the large scale structural analysis.

LARGE SCALE STRUCTURAL ANALYSIS BY A SUPERCOMPUTER.

Miyoshi T., Yoshida Y., Takano N.

Journal of the Faculty of Engineering, the University of Tokyo, Series A (Journal of the Faculty of Engineering, the University of Tokyo, Series A) ( 25 ) 22 - 23 1987.12

ISSN 05637945

スーパコンピュータによる大規模構造解析（ICCG法による有限要素解析）

TAKANO Naoki

日本機械学会論文集A編 53 ( 492 ) 1607-1613 1987

Research paper (scientific journal), Joint Work, Accepted

Large Scale Structural Analysis by a Supercomputer (Application of the ICCG Method to Finite Element Analysis)

Miyoshi T., Takano N., Yoshida Y.

Transactions of the Japan Society of Mechanical Engineers Series A (Transactions of the Japan Society of Mechanical Engineers Series A) 53 ( 492 ) 1607 - 1613 1987

ISSN 03875008

Recently, with the rapid progress of computer technology, there is a growing need for large scale non-linear finite element analyses. However, These calculations take a lot of time and have large storage requirements. The authors have applied the ICCG method, which is one of the iterative solutions, to the three dimensional finite element analysis by supercomputer. Using the ICCG method, large problems with over 10 000 nodes have been solved in a short computational time and with good accuracy. © 1987, The Japan Society of Mechanical Engineers. All rights reserved.

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