Application of the multiscale FEM to the modeling of nonlinear multiphase materials

This contribution is concerned with the modeling of composite materials and, particularly, with the application of the multiscale finite element method for that purpose. The method is a result of combining homogenization theory with the finite element method and is based on the idea of splitting the simulation of a heterogeneous body into two tasks: the first one is the modeling of the actual body and the second one the modeling of the representative volume element, the material sample whose analysis replaces the missing effective constitutive law. The connection of these two simulation levels is achieved by introducing the Hill macrohomogeneity condition which requires the equality of the macropower and the volume average of the micropower. The method has the advantage to be applicable for simulation of materials with very different microstructure types. This is illustrated by the examples concerned with effective behavior of two- and three-phase composite materials.