Finite strain mean-field homogenization of composite materials with hyperelastic-plastic constituents

Abstract

A finite strain mean-field homogenization (MFH) formulation is proposed for a class of composites where multiple phases of solid inclusions or cavities are embedded in a continuum matrix. Local constitutive equations of each solid phase are based on a multiplicative decomposition of the deformation gradient onto elastic and inelastic parts and hyperelastic-plastic stress-strain relations. For the special situation of hyperelastic constituents, a mixed variational formulation is presented which handles both compressible and quasi-incompressible cases within the same framework. A special emphasis is put on the proper definition of various macroscopic stress measures and tangent operators. For an extended Mori-Tanaka MFH model, numerical algorithms were developed and implemented. The MFH predictions were extensively tested against direct finite element simulations of representative volume elements or unit cells, for several heterogeneous microstructures under various loadings.