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.

中文翻译：

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大变形时梯度增强损伤模型的高效鲁棒数值处理

材料中损伤过程的建模构成了不适定的数学问题，其表现为依赖于网格的有限元结果。离散方程组的椭圆度损失可以通过正则化方案来抵消，该方案经常使用应变能密度的梯度增强。在这一贡献中，我们提出了在[1]中提出的将有效数值处理扩展到经受大变形的材料的方法。伴随模型推导，我们提出了一种在材料严重受损的情况下元素腐蚀的技术。两个数值示例证明了我们方法的效率和鲁棒性。