In this paper, fundamental mathematical concepts for modeling the dissipative behavior of geomaterials are recalled. These concepts are illustrated on two basic models and applied to derive a new form of the evolution law of the modified Cam-clay model. The aim is to discuss the mathematical structure of the constitutive relationships and its consequences on the structural level. It is recalled that non-differentiable potentials provide an appropriate means of modeling rate-independent behavior. The Cam-clay model is revisited and a standard version is presented. It is seen that this standard version is non-dissipative, which at the same time explains why a non-standard version is needed. The partial normality is exploited and an implicit variational formulation of the modified Cam-clay model is derived. As a result, the solution of boundary-value problems can be replaced by seeking stationary points of a functional.
Journal of Engineering Mathematics Vol. 52, no. 1, p. 147-165