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

arXiv: https://arxiv.org/abs/2408.05143 · HTML: https://mlsanity.com/paper/2408.05143/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Aug 2024.

## Built on by (most cited first, 1 of 1)

- [Application of Reduced-Order Models for Temporal Multiscale Representations in the Prediction of Dynamical Systems](https://mlsanity.com/paper/2510.18925/) (2025)

## Abstract (arXiv)

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.