基于改进数值流形法的接触裂纹问题研究

接触裂纹问题在工程结构中较为常见。结合数值流形法在裂纹处理上的优势，分析了压剪荷载作用下的接触裂纹问题，模拟了压剪裂纹渐进扩展过程。为了减少由于裂纹尖端位置不同而产生的误差，对裂纹尖端附近一定范围内的每一个物理覆盖附加奇异覆盖函数项，并根据裂纹尖端位置和单元含奇异物理覆盖的数目进行分区积分。选取一个压剪破坏算例，分析了法向接触力对应力强度因子计算结果的影响，并模拟了其渐进破坏过程。计算结果表明，所提方法在压剪裂纹问题方面的可行性，与未细化和覆盖细化方法得到的结果相比，更能准确地描述裂纹扩展路径。法向接触力对II型应力强度因子的贡献为0，对I型应力强度因子的影响较大，相对误差随网格密度变化明显，且法向接触力对I型应力强度因子的影响要比直接施加内压时的影响大。

Study of contact cracks based on improved numerical manifold method

The problem of contact crack is common in engineering structures. Combining the advantages of numerical manifold method in crack treatment, the contact crack problem under compression and shear loads is analyzed, and the progressive propagation process of compression-shear cracks is simulated. In order to reduce errors caused by different positions of crack tips in one element, the singular cover function term is added to each physical cover near the crack tip in a certain range, and then the partitioned integration is carried out according to the position of crack tip and the number of singular physical covers in each element. A compression-shear failure example is selected to analyze the impact of normal contact force on stress intensity factor, and then the progressive failure process is simulated. The results show that the proposed method for compression-shear crack is feasible. Compared with results obtained from unrefined and refined methods, the proposed method in this paper can describe crack propagation path with much higher accuracy. The normal contact force has no contribution to mode II stress intensity factor. However, it has great influence on mode I stress intensity factor and the relative error varies with mesh density. Moreover, the effect of normal contact force on mode I stress intensity factor is larger than that of inner pressure.