On upscaling of discrete element models: similarity principles

TLDR

More research, particularly in the understanding of the convergent properties of discrete element models, is needed. The paper aims to derive similarity principles for discrete element modelling that enable a numerical model to exactly reproduce the physical phenomenon. This is achieved by introducing particle strain and stress concepts to establish equivalence between physical and numerical systems, and by examining the scalability of commonly used interaction laws. The authors propose three similarity principles—geometric, mechanical, and dynamic—that allow exact reproduction of mechanical behaviour, introduce a scale‑invariant interaction law, and provide theoretical guidance for particle system modelling. This preliminary research addresses a very important and challenging topic.

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.