Chinese Journal of Theoretical and Applied Mechanics ›› 2018, Vol. 50 ›› Issue (4): 837-846.DOI: 10.6052/0459-1879-18-039

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STUDY ON NONLINEAR ELASTIC HOMOGENIZATION WITH ITERATIVE METHOD

Hou Shujuan1,*(), Liang Huiyan1, Wang Quanzhong1, Han Xu1,2   

  1. 1College of Mechanical and Vehicle Engineering, Hunan University, Changsha 410006, China
    2College of Mechanical Engineering, Hebei University of Technology, Tianjin 300401, China;
  • Online:2018-07-18 Published:2018-08-17
  • Contact: Hou Shujuan

Abstract:

Microstructure is critical to affect or change the macroscopic mechanical properties of composites, and the desired material properties can be obtained by rationally designing the composite microstructure. As an effective design method, homogenization method is used to obtain and design the macro-mechanical properties on the basis of microstructure. However, once considering the nonlinear factors, the realization of homogenization can be very difficult. Therefore, this paper focuses on the nonlinear elastic homogenization of composite materials by theoretical deduction, and solves the problem by direct iteration method. In this study, the equation of nonlinear elastic homogenization is deduced by the asymptotic expansion homogenization method. The iterative steps of direct iteration method are given to solve the nonlinear elastic homogenization equation. According to the iterative steps and the nonlinear elastic homogenization equation, the program in MATLAB language is obtained. The porous materials with three typical constitutive relations are chosen to be the study object. The program and iterative method is verified by comparing the strain energy, maximum displacement and equivalent Poisson’s ratio with the results of detailed model. Then, the application of nonlinear elastic homogenization method is extended to three-dimensional composite materials with multi-scale periodic microstructure, a three-element rubber-based composite material. It is divided into core-scale and layer-scale and homogenized with multi-scale homogenization method. The equivalent elasticity modulus of the core-scale are obtained by linear elastic homogenization method and used as a parameter of a component in layer-scale. Then, the nonlinear elastic homogenization method is used for layer-scale. The macroscopic equivalent performance of the material is obtained and compared with experimental results. The nonlinear elastic homogenization method has certain guiding significance and reference value for the nonlinear homogenization and microstructure design of the composite material.

Key words: nonlinear elastic, homogenization, asymptotic homogenization method, iteration, multi-scale, periodic composite materials

CLC Number: