The Minkowski overlap and the energy‐conserving contact model for discrete element modeling of convex nonspherical particles

Abstract

AbstractA unified contact overlap, termed the Minkowski overlap, between any two shapes is proposed in this article. This overlap is based on the concept of the Minkowski difference of two shapes, and particularly on the equivalence between the contact state of the two shapes and the location of the origin relative to their Minkowski difference. The Minkowski contact features of a contact, including the overlap, normal direction, and contact points, are also defined for convex shapes. In particular, an important property of the Minkowski overlap is introduced which lays the solid theoretical foundation for proposing a Minkowski overlap based energy‐conserving contact model in the current work. The energy‐conserving property for cases where the contact normal direction and point may be subject to discrete changes is also rigorously proved. For convex particles, the computational procedures combining both GJK and EPA algorithms are outlined, and uniqueness and ambiguity issues associated with some special cases are clarified and resolved. The elastic energy conservation of the proposed contact model for convex shapes in elastic impact is further verified using two numerical examples, and two more examples involving more convex particles with different sizes and shapes are also conducted to demonstrate the robustness and applicability of the proposed Minkowski overlap contact model and the computational procedures.