Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment
Dynamic crack propagation based on loss of hyperbolicity and a new discontinuous enrichment
复制标题
DOI：
10.1002/nme.941
复制
发表时间：
2003-11
影响因子：
2.9
通讯作者：
T. Belytschko;Hao Chen;Jingxiao Xu;G. Zi
中科院分区：
文献类型：
--
作者：
T. Belytschko;Hao Chen;Jingxiao Xu;G. Zi
本文提出了一种从连续介质转换为控制偏微分方程失去双曲性的离散不连续介质的方法。该方法仅限于速率无关的材料，因此跃迁发生在一组测量零上。采用扩展有限元法（XFEM）处理离散不连续点，任意不连续点可以在模型中合并而不需要重新网格划分。双曲度的损失由双曲度指示器跟踪，该指示器可以确定给定材料模型的裂纹速度和裂纹方向。提出了一种新的计算方法，用于计算不连续在单元内结束的情况；它便于在动态环境中对元件内发生的裂纹尖端进行建模。将该方法应用于包括裂纹分支在内的几种动态裂纹扩展问题。版权所有©2003 John Wiley & Sons， Ltd
A methodology is developed for switching from a continuum to a discrete discontinuity where the governing partial differential equation loses hyperbolicity. The approach is limited to rate‐independent materials, so that the transition occurs on a set of measure zero. The discrete discontinuity is treated by the extended finite element method (XFEM) whereby arbitrary discontinuities can be incorporated in the model without remeshing. Loss of hyperbolicity is tracked by a hyperbolicity indicator that enables both the crack speed and crack direction to be determined for a given material model. A new method was developed for the case when the discontinuity ends within an element; it facilitates the modelling of crack tips that occur within an element in a dynamic setting. The method is applied to several dynamic crack growth problems including the branching of cracks. Copyright © 2003 John Wiley & Sons, Ltd.