In this joint work with N. Lahellec, we discuss the effective response of composite materials made from constituents with a partially reversible and partially irreversible behavior. Attention is restricted to behaviors deriving from two potentials. A "Rate Variational Principle" is derived and used to propose approximate schemes to predict the overall response, as well as the field statistics in viscoelastic, elasto-viscoplastic or elasto-plastic composites or polycrystals. The model is applied to particle-reinforced composites and to polycrystalline ice.