Computational homogenization based on a weak format of micro-periodicity for RVE-problems

Computational homogenization with a priori assumed scale separation is considered, whereby the macroscale stress is obtained via averaging on Representative Volume Elements (RVE:s). A novel variational formulation of the RVE-problem, based on the assumption of weak micro-periodicity of the displacement fluctuation field, is proposed. Notably, independent FE-discretization of boundary tractions (Lagrange multipliers) allows for a parameterized transition between the conventional “strong” periodicity and Neumann boundary conditions. In this paper, the standard situation of macroscale strain control is considered. Numerical results demonstrate the convergence properties with respect to (1) the approximation of displacement and tractions and (2) the RVE-size for random realizations of the microstructure.