Prediction of the mechanical behavior of nonlinear heterogeneous systems by multi-level finite element modeling

An accurate homogenization method that accounts for large deformations and viscoelastic material behavior on microscopic and macroscopic levels is presented. This method is based on the classical homogenization theory, assuming local spatial periodicity of the microstructure. Consequently, the microstructure is identified by a representative volume element (RVE) with conformity of opposite boundaries at any stage of the deformation process. The local macroscopic stress is obtained by applying the local macroscopic deformation (represented by the deformation tensor) on a unique RVE through imposing appropriate boundary conditions and averaging the resulting RVE stress field. If the assumption of local periodicity of the morphology is valid, this homogenization procedure supplies a consistent objective relationship between the local macroscopic deformation and the microstructural deformation. The homogenization method was implemented in a multi-level finite element program with meshes on macroscopic level (mesh of entire structure) and microscopic level (meshes of RVEs). The performance was successfully verified by the comparison of the deformation of a perforated macroscopic sheet to the response of a homogenized sheet.