基于MLS的数值流形法模拟多裂纹扩展

A MLS-based numerical manifold method for multiple cracks propagation

含多裂纹的脆性材料在伺服加载下的响应分析对结构进行性能评估具有重要意义。得益于数学覆盖和物理覆盖这两套覆盖系统,数值流形法能够很自然地模拟多裂纹的萌生与扩展。为了更好地模拟二维裂纹的交叉、汇合,采用基于移动最小二乘插值(MLS)的数值流形法(NMM)进行模拟,并对包含裂尖的物理片进行自由度扩充来模拟裂尖的奇异性,裂纹扩展中裂尖可以停留在背景网格的内部。针对多裂纹扩展中的一些数值问题,给出了相应的解决方案,并提出一个简单、能近似满足断裂韧度的多裂纹扩展算法。对几个典型多裂纹算例进行了裂纹扩展分析,结果表明所提算法是有效且鲁棒的。

The full response of a brittle structure containing multiple cracks under the servo loading condition is of vital importance in the evaluation of properties of the structure. Due to the mathematical covers and physical covers,numerical manifold method is able to simulate the initiation and growth of multiple cracks in a natural way. In order to handle the junction of cracks more straightly,the MLS-based numerical manifold method was used,and the physical patches containing crack tips were enriched to describe the singularity. During the crack growth,crack tips can be located anywhere in the background meshes. Several numerical issues encountered in the simulation were discussed and solved. Besides,a simple algorithm for multiple crack propagation was presented to satisfy the fracture toughness closely. Several numerical examples are illustrated to demonstrate the efficiency and robustness of the proposed method in the simulation of multiple crack propagation.