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

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.