Numerical homogenization of periodic composite materials with non-linear material components

In this paper a numerically developed homogenized constitutive relation for the global behaviour of periodic composite materials with elasto-plastic components is derived. The algorithm presented is general and can be applied to any kind of non-linear material behaviour respecting the complementarity rule. The method, di!erent from those presented in the literature, is currently restricted to small strains, plane problems and monotonic proportional loading conditions