This study establishes an innovative discontinuous deformation analysis by solving the problem of frictional and cohesive contact using an implicit cone complementary formulation. In order to handle singularity associated with the vertex‐vertex contact, resistances to motion trend are firstly estimated by introducing the concepts of total and partial contact forces. Based on principle of least effort, the vertex‐vertex contact can be converted to a corresponding vertex‐edge contact properly. In addition, unnecessary vertex‐vertex contacts can be identified. The numerical scheme fully exploits geometric and dynamic conditions of the polygonal block system. As a result, determination of motion trend in the block system is penalty‐free without being affected by the time step. The advantages and application prospects of the presented dynamic framework are demonstrated by using several benchmark examples.

中文翻译：

---

基于最小努力原理的不连续变形分析处理顶点-顶点接触

本研究通过使用隐式圆锥互补公式解决摩擦和内聚接触问题，建立了创新的不连续变形分析。为了处理与顶点-顶点接触相关的奇点，首先通过引入总和部分接触力的概念来估计运动趋势的阻力。根据最小努力原则，可以将顶点-顶点接触适当地转换为相应的顶点-边缘接触。另外，可以识别不必要的顶点-顶点接触。该数值方案充分利用了多边形块系统的几何和动态条件。结果，在块系统中确定运动趋势不受惩罚，而不受时间步长的影响。