An effective energy-conserving contact modelling strategy for spherical harmonic particles represented by surface triangular meshes with automatic simplification

Abstract

An effective discrete element modelling strategy for triangular mesh represented spherical harmonic particles is proposed. It features: (1) using a golden spiral lattice on the unit sphere to generate an initial triangular mesh with any number of vertices/triangles for a star-shaped surface; (2) applying an edge contraction mesh simplification algorithm to reduce the mesh size to any desired level; and (3) adopting an energy-conserving linear normal contact model to compute the contact geometric and force features of contacting particles. In particular, the edge contraction algorithm is applicable to any triangular mesh. It is algorithmically very simple and highly effective, and can be easily incorporated into existing discrete element frameworks. Numerical experiments are conducted to demonstrate that the simplified mesh by the edge contraction can not only have a very low geometric approximation error but also achieve expected mechanical responses. Thus this mesh simplification approach can serve as an ideal pre-processing tool to optimise a large input triangular mesh in order to significantly reduce the computational cost associated with discrete element simulations without compromising the modelling accuracy.