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

TL;DR

This paper introduces a multi-scale space-time PGD approach using Partition of Unity to efficiently simulate viscoelastic fatigue in polymers with complex internal variables and multiple relaxation times.

Contribution

It presents a novel multi-scale space-time PGD method combined with Partition of Unity for simulating viscoelastic polymers more efficiently.

Findings

Method effectively captures dynamic behavior of polymers under cyclic loading.

Approach reduces computational resources needed for complex viscoelastic simulations.

Demonstrates robustness and feasibility in non-equilibrium polymer states.

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.