A sphere-triangle contact model with complex boundary face problems

Abstract This paper proposes a sphere-triangle contact model for three-dimensional sphere discontinuous deformation analysis to simulate complex boundary face problems often encountered in engineering. First, the detection of sphere-triangle contact and the calculation of corresponding sphere-triangle contact submatrices for building a sphere-triangle contact model are described. Then, the correctness of the proposed model is preliminarily verified by simulating the sphere-plane/edge/vertex contact, sphere-triangle friction problem and a complex boundary face problem. Furthermore, a rigorous open-close iteration is proposed to guarantee the correctness of setting penalty springs for sphere-triangle contacts, to ensure computational stability of three-dimensional sphere discontinuous deformation analysis. Meanwhile, two imperceptible fatal errors (i.e., direction deflection error and oscillation error) hidden in the sphere-triangle contact model are estimated, which reveals that a larger sphere or a higher collision velocity at a sphere-triangle contact leads to larger errors. In addition, an algorithm for excluding invalid contacts is proposed to avoid these fatal errors, enhancing the robustness of the proposed contact model. Finally, a landslide simulation with 80,974 spheres, 76,382 triangles and 150,000 calculation steps is conducted, further validating the proposed model in large-scale simulations. This work indicates the feasibility of the proposed model for simulating complex boundary face problems.