Constrained, thermomechanical, rigid-plastic models of granular materials

Non-associated flow rules used to describe the plastic behaviour of geomaterials are normally expressed in terms of a plastic potential. It is shown that this is an overly restrictive assumption, and in general two such potentials are needed. In addition, internal kinematic constraints are shown to be a source of non-associated behaviour. The well known Reynold’s dilatancy phenomenon can be modelled by the use of such a constraint, which does not dissipate any energy. The resulting theory predicts that both the strength and the dilatation of a material are the sum of two terms, one arising solely from the grain rearrangement, the other is a result of frictional dissipation. It also predicts the development of anisotropy, with the internal reaction stress playing the role of a fabric tensor. Other examples of non-dissipative plane deformations are discussed, including the double shearing model of Spencer.