Model of Sphere-to-Edge Contact for Spherical Discontinuous Deformation Analysis

Spherical element-based discontinuous deformation analysis (SDDA) usually uses simple types of contact such as sphere-sphere and sphere-plane contact for detection. However, in practical engineering simulations, there is also found sphere-edge contact in the context of interactions between spheres and fixed boundaries. This incompleteness of contact types in the original SDDA restricts its application to problems involving complex boundary shapes. To fill this gap, this paper presents a sphere-edge contact model to extend the application of SDDA to complex boundary shapes such as edges, corners, and finite and infinite planes. The contact formulation is deduced and the algorithm is implemented in SDDA source code developed by the authors. Four numerical examples are simulated for verification. The results show that the proposed model is correct and effective.