Energy-conserving contact interaction models for arbitrarily shaped discrete elements

This work aims to establish a unified theoretical framework for normal contact of arbitrarily shaped discrete elements in discrete element modelling solely based on the energy-conservation principle for elastic contact. It will show that the normal force must be a potential field vector associated with a potential. With the construction of an appropriate potential function, a complete normal contact model, including the magnitude and direction of the normal force and the normal contact line, can be unambiguously derived for a pair of any shaped bodies. The model in its final form is simple and has a clear geometric perspective for 2D bodies. It can also recover some well-known models for bodies with simple geometric shapes.