Linearization and Computation for Large-Strain Viscoelasticity

TL;DR

This paper introduces a novel approach for large-strain viscoelasticity that uses local minimizers of simple-material models, avoiding complex higher-order gradient computations while maintaining accuracy.

Contribution

The paper proposes a new method based on local minimizers to address well-posedness issues in large-strain viscoelasticity without resorting to complex higher-gradient models.

Findings

Good agreement between the proposed model and original complex models.

Efficient computational scheme for large-strain viscoelasticity.

Avoids numerical complications of higher-order gradient models.

Abstract

Time-discrete numerical minimization schemes for simple viscoelastic materials in the large strain Kelvin-Voigt rheology are not well-posed due to non-quasiconvexity of the dissipation functional. A possible solution is to resort into non-simple material models with higher-order gradients of deformations. This makes, however, numerical computations much more involved. Here we propose another approach relying on local minimizers of the simple-material model. Computational tests are provided showing a very good agreement between our model and the original one.