Multiscale analysis of nonlinear composites via a mixed reduced order formulation

In this paper a new multiscale approach is presented for the analysis of structures made of composite material characterized by elastoplastic or viscoplastic nonlinear response. Scale separation is assumed so that the homogenization theory can be applied: at the structural scale (macroscale) the material appears as homogeneous, while at the microscale it is characterized by a heterogeneous microstructure that affects the global behavior of the structure. The resolution of the micromechanical problem is performed developing a reduced order homogenization technique based on a mixed variational formulation, named Mixed Transformation Field Analysis (MxTFA). The microscopic reduced internal variables are the stress and plastic multiplier parameters of RVE subsets, whose evolution is computed enforcing the weak form of the governing equations for every subset. Some numerical tests are performed to show the accuracy and efficiency of the proposed multiscale technique.