Efficient and robust numerical treatment of a gradient-enhanced damage model at large deformations

TL;DR

This paper extends an efficient numerical method for gradient-enhanced damage models to large deformations, introducing element erosion techniques and demonstrating robustness through numerical examples.

Contribution

It presents a novel extension of an existing numerical treatment to large deformation scenarios with damage, including a new element erosion technique.

Findings

Method is efficient and robust for large deformation damage modeling.

Element erosion effectively handles severely damaged materials.

Numerical examples validate the approach's performance.

Abstract

The modeling of damage processes in materials constitutes an ill-posed mathematical problem which manifests in mesh-dependent finite element results. The loss of ellipticity of the discrete system of equations is counteracted by regularization schemes of which the gradient enhancement of the strain energy density is often used. In this contribution, we present an extension of the efficient numerical treatment, which has been proposed in [1], to materials that are subjected to large deformations. Along with the model derivation, we present a technique for element erosion in the case of severely damaged materials. Efficiency and robustness of our approach is demonstrated by two numerical examples.