接触处理Munjiza方法在数值流形法中的应用

数值流形法（NMM）在接触处理过程包括：接触方式判断，包括点-点和点-线接触；开-闭迭代，确定块体系统的约束状态；以及接触传递，将有效的接触对传递到下一个时步。过程稍显繁琐和耗时，且与真实的物理接触状态有异。由Munjiza所提出的NBS（no binary search）接触检测算法，将单元映射到规则格子中，以链表结构将其有效地连接在一起，只在单元所在格子以及周围格子内部进行接触判断，接触检测效率大为提高，计算量仅随单元数线性增长，内存需求也很低。在计算接触力时以所定义的势为媒介，用重叠面积来衡量接触力的大小，属于分布式接触力，更接近于实际，避免了原NMM接触处理过程的繁琐。因此，将其作为一种平行的接触处理方法引入到NMM中，并以算例验证，证实了算法的可行性。

Application of Munjiza’s algorithm to contact treatment in numerical manifold method

Contact treatment of the numerical manifold method (NMM) mainly includes contact detection, including point-point and point-line contact, open-close iteration for determining the correct constrained state, and contact transfer by which effective contact couples can be transferred to the next time step. The whole process is slightly complicated and inefficient. Besides, the contact modes adopted in the NMM are quite different from the real physical contact state. The no binary search (NBS) contact detection algorithm proposed by Munjiza maps all elements into regular cells and connects the elements by the list structure effectively. The contact detections are limited within the cell and the four neighboring cells. With low requirement of random access memory, contact detection operation is just proportional to the number of the elements, and the efficiency is accordingly increased significantly. With the defined ‘potential’, contact pressure, belonging to the distribution category, is calculated by the contact overlapped area, which is closer to the real contact state, and avoids the cumbersome process involved in the NMM. As a result, it is introduced to the NMM as an alternative contact treatment method. The effectiveness is verified by the examples.