A micromorphic approach for gradient-enhanced anisotropic ductile damage

Abstract This paper deals with the numerically effective modeling of anisotropic material degradation caused by ductile damage. Although standard local anisotropic damage models are relatively well-developed nowadays, their regularization which is required in order to eliminate their mathematical ill-posedness is far from being straightforward. It bears emphasis that this regularization is not only required from a mathematical point of view, since the aforementioned ill-posedness is known to be the source for the pathological mesh dependence as far as the finite element method is concerned. Within this paper, a general local framework for capturing anisotropic material degradation caused by ductile damage is extended to a non-local model by means of a gradient-enhancement. However, in order to achieve a numerically effective implementation, the gradient-enhancement is not implemented in a direct manner, but by means of a micromorphic approximation. By doing so, the implementation of the underlying local model is almost unaffected. Particularly the inequalities resulting from the yield function can be restricted to the local integration point level. Since a naive micromorphic implementation turns out to be unsuitable for regularizing the underlying local model, a novel adaption of the yield function is proposed. It is shown that the resulting single-surface-model is indeed able to capture anisotropic material degradation caused by ductile damage and, furthermore, that the finite element implementation is mesh objective.

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