Restrictions of Non Associated Plastic Flow Laws Imposed by Thermodynamics and Uniqueness

Abstract : The restrictions imposed by thermodynamics and uniqueness on non- associated elasto-plastic solids are explored. The postulates of Drucker and Illiushin are examined and it is shown that they can be violated while the second law of thermodynamics is satisfied. Some of the basic features of non- associated elasto-plastic solids are investigated, including continuity, path dependence and a rather peculiar feature in which the plastic tangent stiffness can exceed the elastic tangent stiffness. The question of uniqueness of initial value problems for non-associated elasto-plastic solids is examined; it is shown that the usual approach for proving uniqueness of associated elasto-plastic solids remains valid when the flow rule is non-associated. Finally, two types of non-associated plastic models that are widely used by the defense community in ground motion simulation studies are considered in detail, and the implication of the restrictions imposed on these models by thermodynamics are discussed. Keywords: Thermodynamics; Elastoplastic solids; Continuity; Path dependence.