This paper aims to investigate the dynamic response of a material body undergoing fracture subjected to high strain rate loading conditions such as impact or explosion. In particular, our focus is limited to softening elastic damage models using Lip-field regularization. The Lip-field approach is a new technique to introduce length scale into the softening damage models. It was first presented for the quasi-static case and then extended to a one-dimensional dynamic case. This paper extends the application of the Lip-field approach to dynamic fracture in two-dimensional cases. Lip-field approach is a variational approach, in which the potential to be minimized is a non-regularized one. A potential without regularization can result in spurious strain localization, but the Lip-field approach resolves this issue by imposing Lipschitz constraints on the damage field. Our focus is limited to utilizing an explicit staggered scheme to determine the displacement and damage fields. Numerical studies are conducted for two-dimensional cases to assess the dynamic behavior of the proposed model.

翻译：本文旨在研究材料体在冲击或爆炸等高应变率加载条件下发生断裂的动态响应。特别地，我们重点关注采用Lip场正则化的软化弹性损伤模型。Lip场方法是一种将长度尺度引入软化损伤模型的新技术。该方法最初针对准静态情况提出，随后扩展到一维动态情况。本文进一步将Lip场方法的应用扩展到二维情况下的动态断裂问题。Lip场方法是一种变分方法，其待最小化的势能是非正则化的。未经正则化的势能可能导致虚假的应变局部化，但Lip场方法通过对损伤场施加Lipschitz约束解决了这一问题。我们重点采用显式交错格式来确定位移场和损伤场。通过二维数值研究，评估了所提出模型的动态行为。