Computational Mechanics

, Volume 52, Issue 5, pp 1199–1219 | Cite as

A method of two-scale analysis with micro-macro decoupling scheme: application to hyperelastic composite materials

  • K. Terada
  • J. KatoEmail author
  • N. Hirayama
  • T. Inugai
  • K. Yamamoto
Original Paper


The aim of this study is to propose a strategy for performing nonlinear two-scale analysis for composite materials with periodic microstructures (unit cells), based on the assumption that a functional form of the macroscopic constitutive equation is available. In order to solve the two-scale boundary value problems (BVP) derived within the framework of the homogenization theory, we employ a class of the micro-macro decoupling scheme, in which a series of numerical material tests (NMTs) is conducted on the unit cell model to obtain the data used for the identification of the material parameters in the assumed constitutive model. For the NMTs with arbitrary patterns of macro-scale loading, we propose an extended system of the governing equations for the micro-scale BVP, which is equipped with the external material points or, in the FEM, control nodes. Taking an anisotropic hyperelastic constitutive model for fiber-reinforced composites as an example of the assumed macroscopic material behavior, we introduce a tensor-based method of parameter identification with the ‘measured’ data in the NMTs. Once the macro-scale material behavior is successfully fitted with the identified parameters, the macro-scale analysis can be performed, and, as may be necessary, the macro-scale deformation history at any point in the macro-structure can be applied to the unit cell to evaluate the actual micro-scale response.


Two-scale analysis Micro-macro decoupling scheme Numerical material testing Homogenization Anisotropic hyperelasticity 



The authors would like to acknowledge the Nonlinear Homogenization Research Group consisting of Tohoku University, Nitto Boseki Co., Ltd. and Quint Corporation, in particular Dr. Keizo Ishii and Mr. Makoto Tsukino (Quint Corporation ), Mr. Koji Yamamoto, Mr. Tomohiro Ishida, Mr. Akio Miyori, Mr. Fukagawa (Cybernet Systems, Co. Ltd.), and Mr. Naohiro Miyanaga (Nitto Boseki Co., Ltd.) for their contributions and discussions in developing a linear and nonlinear mutli-scale analysis code “Multiscale.Sim”, which is embedded in ANSYS\(^\mathrm{{\textregistered }}\) software.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • K. Terada
    • 1
  • J. Kato
    • 1
    Email author
  • N. Hirayama
    • 2
  • T. Inugai
    • 1
  • K. Yamamoto
    • 3
  1. 1.Department of Civil EngineeringTohoku UniversityAoba-kuJapan
  2. 2.Fukushima Research CenterNitto Boseki Co., Ltd.FukushimaJapan
  3. 3.Cybernet Systems Co.,Ltd.Chiyoda-kuJapan

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