Multiscale analysis of elasto-plastic composite material

A numerical method is proposed for elasto-plastic analysis of composite material. Homogenization method using asymptotic expansion is employed to establish the relations between Micro-scale and Meso-scale, while the elasto-plastic responses are solved by a proposed method based on Parametric Variational Principles. An implicit algorithm is employed, but the numerical results are not very accurate because the Parametric Variational Principles just include the first-order approximation of yielding functions in solving linear complementary problems with Lemek algorithm. Therefore, modified Parametric Variation Principles are proposed to solve non-linear complementary problems with second-order approximation of yielding functions. The result is enough accurate when both the two constituted materials satisfy the von-Mises criterion.