基于扩展虚拟元法的线弹性断裂问题

Extended virtual element method for the linear elastic fracture problem

在断裂力学背景下,考虑应用扩展虚拟元法讨论线弹性断裂问题,该方法在多边形网格上对具有裂纹不连续和弹性裂纹尖端奇异的网格进行独立剖分.对于给定的线弹性问题,首先引入一组附加基函数构造相应的变分形式及其扩展虚拟元空间.通过引入扩展投影算子,将扩展虚拟元空间中的函数映射到线性多项式空间和富集函数上.利用相互作用积分计算应力强度因子.对含有水平裂纹的无限大板模型进行数值实验,验证了该方法的正确性和有效性.

In this paper,we apply the extended virtual element method to solve linear elastic fracture problems within the context of fracture mechanics.This method facilitates independent mesh divisions with crack discontinuities and elastic crack tip singularity on general polygonal meshes.For linear elasticity problems,we first introduce a set of additional basis functions to construct variational forms and extended virtual element spaces.Next,by introducing an extended projection operator,functions in the extended virtual element space are mapped onto linear polynomial space and enrichment functions.The interaction integral was used to calculate the stress intensity factors.We validated the accuracy and effectiveness of this method in a numerical example on an infinite plate model with horizontal cracks.