Elastic–plastic shear deformation of frictional granular materials

Abstract

AbstractA theory describing plastic deformation of granular (purely frictional) materials is presented. The theory is developed from postulates for energy dissipation and for the mode of plastic deformation. The postulates are based on some restrictions for the properties of granular materials and on a frictional analogy. A distinction is made between the description of plastic behaviour of a locally homogeneous and a locally non‐homogeneous material. An interpretation of the deformation process is presented which implies that the theory accounts for the changes in the density of some local non‐homogeneities underlying a plastic hardening effect. Based on this interpretation, an analogy between elastic–plastic behaviour of granular materials and frictional, sliding of two solid bodies is assumed. In the general case, the presented constitutive equations describe two hardening (softening) effects and are capable of describing both initial and advanced plastic deformations. A special, simplest form of the constitutive equations is examined in detail and a yield condition and a stress–strain relationship are derived. An example of elastic–plastic stress–strain–strength behaviour is presented for the cuboidal loading conditions.