On upscaling of discrete element models: similarity principles

Purpose The main purpose of this paper is to derive a set of similarity principles for discrete element modelling so that a numerical model can exactly reproduce the physical phenomenon concerned. Design/methodology/approach The objective is achieved by introducing the concepts of particle “strain” and “stress” so that some equivalence between the physical system and the numerical model can be established. Findings Three similarity principles, namely geometric, mechanical and dynamic, under which the numerical model can exactly reproduce the mechanical behaviour of a physical model are proposed. In particular, the concept of the scale invariant interaction law is further introduced. The scalability of a number of most commonly used interaction laws in the discrete element modelling is examined. Research limitations/implications This is a preliminary research for a very important and challenging topic. More research, particularly in the understanding of the convergent properties of discrete element models, is needed. Originality/value The paper provides some important theoretical guidances to computational modelling of particle systems using discrete element techniques.