An energy-conserving contact theory for discrete element modelling of arbitrarily shaped particles: Contact volume based model and computational issues

Abstract The contact volume based energy-conserving contact model is presented in the current paper as a specialised version of the general energy-conserving contact model established in the first paper of this series (Feng, 2020). It is based on the assumption that the contact energy potential is taken to be a function of the contact volume between two contacting bodies with arbitrary (convex and concave) shapes in both 2D and 3D cases. By choosing such a contact energy function, the full normal contact features can be determined without the need to introduce any additional assumptions/parameters. By further exploiting the geometric properties of the contact surfaces concerned, more effective integration schemes are developed to reduce the evaluation costs involved. When a linear contact energy function of the contact volume is adopted, a linear contact model is derived in which only the intersection between two contact shapes is needed, thereby substantially improving both efficiency and applicability of the proposed contact model. A comparison of this linear energy-conserving contact model with some existing models for discs and spheres further reveals the nature of the proposed model, and provides insights into how to appropriately choose the stiffness parameter included in the energy function. For general non-spherical shapes, mesh representations are required. The corresponding computational aspects are described when shapes are discretised into volumetric meshes, while new developments are presented and recommended for shapes that are represented by surface triangular meshes. Owing to its additive property of the contact geometric features involved, the proposed contact model can be conducted locally in parallel using GPU or GPGPU computing without occurring much communication overhead for shapes represented as either a volumetric or surface triangular mesh. A set of examples considering the elastic impact of two shapes are presented to verify the energy-conserving property of the proposed model for a wide range of concave shapes and contact scenarios, followed by examples involving large numbers of arbitrarily shaped particles to demonstrate the robustness and applicability for more complex and realistic problems.