AbstractThis paper is devoted to the homogenization for a class of rate‐independent systems described by the energetic formulation. The associated nonlinear partial differential system has periodically oscillating coefficients, but has the form of a standard evolutionary variational inequality. Thus, the model applies to standard linearized elastoplasticity with hardening. Using the recently developed methods of two‐scale convergence, periodic unfolding and the new introduced one, periodic folding, we show that the homogenized problem can be represented as a two‐scale limit which is again an energetic formulation, but now involving the macroscopic variable in the physical domain as well as the microscopic variable in the periodicity cell. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)