A reduced simulation applied to viscoelastic fatigue of polymers using a time multi-scale approach based on partition of Unity method

Abstract The simulation of viscoelastic time-evolution problems described by a large number of internal variables and with a large spectrum of relaxation times requires high computational resources for their resolution. Furthermore, the internal variables evolution is described by a set of linear differential equations which involves many time scales. In this context, the use of a space-time PGD approximation is proposed here to boost their resolution, where the temporal functions are constructed following a multi-scale strategy along with the partition of unity method, in order to catch each dynamic efficiently. The feasibility and the robustness of the method are discussed in the case of a polymer in a non-equilibrium state under cyclic loading.