Abstract
It is well known, that modeling of material softening behavior can lead to ill-posed boundary value problems. This, in turn, leads to meshdependent results as far as the finite-element-method is concerned [1]. Several solution strategies in order to regularize the aforementioned problem have been proposed in the literature, cf. [2]. However, these strategies often involve high implementational effort. An approach which is very efficient froman implementational point of view is the so-called micromorphic approach by [3, 4]. This regularization technique includes gradients of internal variables implicitly into the framework, while preserving the original structure of the underlying local constitutive model. However, it is shown that a straightforward implementation of the micromorphic approach does not work for single-surface ductile damage models. By analyzing the respective equations, a modification of the micromorphic approach is proposed – first for a scalar internal variable, i.e., isotropic damage. Subsequently, the novel regularization method is extended to tensor valued damage, i.e., anisotropic material degradation.
Highlights
Defects like pores or micro-cracks can be found in any technologically relevant material, cf. Fig. 1
As far as local models are concerned, continuum damage mechanics can be considered as a well established framework. These local models which do not involve any length scale are ill-posed from a mathematical point of view
The local constitutive model is ill-posed from a mathematical point of view. This ill-posedness results in mesh dependent results as far as the finite element method is concerned
Summary
Defects like pores or micro-cracks can be found in any technologically relevant material, cf. Fig. 1. The macroscopic modeling of anisotropic damage accumulation is challenging, nowadays several promising models/frameworks are available, see [7, 8]. As far as local models are concerned, continuum damage mechanics can be considered as a well established framework These local models which do not involve any length scale are ill-posed from a mathematical point of view. An elegant framework for gradient-enhancement is the micromorphic approach by [3, 4] It implicitly incorporates gradients into the local constitutive model while preserving its original structure.
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