On the Volume Changes of Granular Materials and Their Consequences for Plasticity Theory

Abstract

After many years of study, granular materials still present problems to the mathematical modeller. It is agreed that their behaviour is broadly in line with the theory of plasticity: there is often a well defined yield point and the resistance to deformation is approximately rate independent. It is a relatively simple matter to write down plausible yield functions (ψ) in terms of the components of stress (σ ij ) such that when ψ < 0 no deformation takes place while when ψ = 0 some plastic deformation can occur. The difficult problem, however, is to decide how the strain increment is apportioned between the various components (ė ij ) by defining a flow rule. Unfortunately it has not been easy to find a consistent way of formulating such flow rules so as to ensure that the corresponding energy dissipation is always positive [1,2]. This paper reviews some of the current procedures for linking the flow rule with the yield, plastic potential or dissipation functions.