Homogenization method for heterogeneous material based on boundary element method

In this paper, formulations for homogenization method based on the boundary element method, for heterogeneous elastic materials having periodic microstructure, are presented. The formulations are developed using a novel use of the method of weighted residuals. Both the trial and test functions are expressed by asymptotic expansions with respect to the size ε of the unit cell. Two types of boundary element formulations for the analysis of unit cell, are proposed; single-region boundary element method with volume integrals and multi-region boundary element method. Convenient formulae to compute effective (homogenized) elastic constants, are presented.