应用三维无单元伽辽金法追踪裂纹扩展

本文应用三维无单元伽辽金法追踪裂纹扩展。将可视准则推广到三维以处理三维不连续面对积分点影响域的影响，同时考虑不连续面刚度对整体平衡方程的贡献。利用单点位移公式计算裂纹前缘应力强度因子，假设裂纹在法平面内扩展，采用最大能量释放率判据作为三维复合型裂纹扩展判据，编制EFGM3D程序实现对线弹性体中三维准静态裂纹扩展的追踪。通过对含半币形表面裂纹的立方体算例的分析，证明本文方法和程序在裂纹扩展模拟上是合理有效的。

Crack propagation tracing by using 3-D element-free Galerkin method

Based on the moving least squares method, the 3-D element-free Galerkin method is applied to establish the discrete model for crack calculation by using only a set of nodes. The visibility criterion is extended to 3-D problems to deal with the effect of discontinuities on the influenced domain of a Gauss point. The contribution of stiffness of discontinuities to the system equilibrium equations is considered. Under the assumption that propagation occurs only in the perpendicular plane at each point in front of the crack, the G-criterion is used as the criterion of crack growth. The program EFGM3D is developed based on these theories to simulate the 3-D quasi-static crack propagation. A numerical example of a cube with a penny-shaped crack subject to tension is analyzed with EFGM3D, and the result shows that the software is effective.