比例边界有限元模拟裂纹和夹杂动力相互作用

Simulation of dynamic interactions between a crack and inclusions with scaled boundary finite element method

基于三角形背景网格,任意结构可用n(n≥3)边多边形比例边界有限元(Polygon Scaled Boundary Finite Elements,PSBFE)自动离散。相对以往基于比例边界有限元(SBFEM)的应用,该多边形单元不但继承SBFEM半解析求解裂纹尖端奇异性的特性,而且在模拟复杂结构的网格生成和裂纹扩展上具有更高的通用性。首次用该单元模拟了动荷载下复合材料裂纹和夹杂相互作用。动荷载稳定裂纹情况下,PSBFE计算结果同现有文献吻合良好,在此基础上,结合基于拓扑的局部网格重剖分方法,模拟了动荷载下夹杂和扩展裂纹相互作用。结果表明,硬质夹杂和软质夹杂对结构的动力应力强度因子分别起到抑制和放大的作用。夹杂尺寸,夹杂大小也会在一定范围内影响动力应力强度因子,尺寸越大距离裂纹越近的夹杂影响越大。

Any structural domain can be discretized automatically with a mesh of arbitrary n-sided（ n≥3） polygon scaled boundary finite elements（ PSBFE） based on Delaunay triangulation background mesh. Compared with previous literatures based on SBFEM,PSBFE retains the characteristics of SBFEM’s accurately representing orders of singularities at crack tips it is more general and flexible in modeling complicated structures and their crack propagation. Here,PSBFE was for the first time applied to simulate the dynamic interactions between a crack and inclusions in composite material.The numerical results of stationary cracks under dynamic load were consistent with available data in literatures. Next,a local remeshing scheme was employed to simulate the dynamic crack propagation. The numerical results demonstrated that stiff and soft inclusions have the restraining and amplification effects on the dynamic stress intensity factor of a structure;the sizes and positions of inclusions also affect the dynamic stress intensity factor,the larger the size and the closer the inclusion,the more the effects.