On upscaling of discrete element models: similarity principles

Abstract

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.