高阶扩展数值流形法在裂纹扩展中的应用

 为正确预测工程材料体中裂纹扩展趋势，提出改进的数值流形法。该方法在每个物理片上采用位移函数的一阶泰勒展开形式，使得物理片上的自由度均具有明确的物理意义；且在裂纹尖端附近的物理片上增加扩充位移函数，用于模拟裂纹尖端的应力奇异性，可更为准确地预测裂纹扩展方向。同时，也提出裂纹扩展过程中适用于大小变形的物理覆盖系统的更新算法。针对典型的线弹性断裂问题，给出用该方法求解的数值算例。结果表明，预测的裂纹扩展路径与已有研究结果一致，从而证实方法的有效性及正确性。

APPLICATION OF HIGHER-ORDER ENRICHED NUMERICAL MANIFOLD METHOD TO CRACK PROPAGATION

A modified numerical manifold method is proposed to predict crack growth of engineering materials. The first-order Taylor expansion of the displacement functions is adopted on physical patches，endowing the degrees of freedom of the physical patches with physical meanings. Enriched displacement functions used to capture stress singularity are adopted for the physical patches around the crack tip，which predicted more accurately the direction of crack propagation. Meanwhile a new algorithm for updating the physical cover system is proposed，which was more convenient and suitable for both small and large deformation problems. Numerical examples for typical linear elastic fracturing problems were presented. The results show that the predicted propagation paths are in accordance with the results obtained by others. The effectiveness and correctness of the method are thus confirmed.