Deformation of Ideal Granular Materials

Abstract

The formulation of the equations which govern the deformation and flow of granular materials is an outstanding problem in continuum mechanics. This article concentrates on one model for the mechanical behaviour of granular materials, termed the “double-shearing model”, in which deformation is assumed to occur by simultaneous shearing on the two families of characteristic curves of the stress equations. We review the formulation of the equations of the double-shearing model for plane deformations, and describe the known exact solutions of these equations. Further developments of the plane strain theory are then given in which the velocity equations are expressed in a new form from which some general results are derived. In the last part of the article the theory is extended to include problems in three dimensions. The three-dimensional theory is applied to some special cases of nonplanar deformations, and in particular we formulate a new theory of axially symmetric deformations of granular materials, and apply this theory to the solution of some boundary value problems.