Efficient numerical treatment of a gradient damage model for materials undergoing large deformations

Abstract

In this contribution we present a gradient damage formulation (cf. [1]) for hyperelastic materials undergoing large deformations, which is based on the small strain formulation of [2]. Through discretizing the gradient extended damage field with the neighbored element method the damage update can be performed at the element level. Although local update iterations remain present, the global system of equations goes without any additional degrees of freedom compared to purely elastic computations. Furthermore, in the case of severely damaged material, an element erosion based stabilization technique is considered. Computing efficiency and numerical robustness is demonstrated in several numerical examples.