Chapter

Mathematics and Mechanics of Granular Materials

pp 147-165

Formulation of non-standard dissipative behavior of geomaterials

  • Mohammed HjiajAffiliated withDepartment of Civil, Surveying and Environmental Engineering, The University of Newcastle Email author 
  • , Wenxiong HuangAffiliated withDepartment of Civil, Surveying and Environmental Engineering, The University of Newcastle
  • , Kristian KrabbenhøftAffiliated withDepartment of Civil, Surveying and Environmental Engineering, The University of Newcastle
  • , Scott W. SloanAffiliated withDepartment of Civil, Surveying and Environmental Engineering, The University of Newcastle

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Abstract

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.

Key words

convex analysis Fenchel transform internal variables modified Cam-clay model variational inequality