A multiscale finite element technique for nonlinear multi-phase materials

This paper presents a multiscale finite element homogenization technique (MFEH) for modelling nonlinear deformation of multi-phase materials. A novel condensation technique to relate force variations acting on the representative volume element (RVE) – involving antiperiodicity of traction forces at RVE corners – and displacement variations on boundary-nodes is proposed. The formulation to accommodate the condensation technique and overall tangent modulus is presented in detail. In this context, the effective homogenised tangent modulus is computed as a function of microstructure stiffness matrix which, in turn, depends upon the material properties and geometrical distribution of the micro-constituents. Numerical tests concerning plastic materials with different voids distributions are presented to show the robustness of the proposed MFEH.