Angle-Based Discontinuous Deformation Analysis

Due to the nonlinear nature of contacts, the real contact information is indeterminate and there is no analytical solution for discontinuous computation. In the context of two-dimensional discontinuous deformation analysis (2D DDA) for arbitrary polygon block systems, the contact indeterminacy arises from at least two aspects, namely kinematics and geometry. This study provides a specific numerical solution for 2D DDA to address the indeterminacy problem of contacts between arbitrary polygon blocks. First, local contact boundary is established by defining the solid angle of 2D blocks and the entrance solid angle between two 2D solid angles of two blocks. Second, the linearized first entrance formulas are derived to estimate the first entrance time and position. Third, an enhanced shortest exit strategy based on entrance angles is introduced to provide a unified solution of the contact points and direction of closed contacts. Some extreme and challenging examples, including oblique collision contacts, undue penetration contacts, genuine vertex–vertex contacts (including absolutely symmetric contacts), extremely abnormal block contacts (i.e., contacts between extremely short edges and/or sharp angles), multi-connected block contacts and numerous singular contacts, demonstrate the accuracy, robustness and application prospects of the proposed method in addressing difficult contact problems.