Elastic Potentials and the Structure of Inelastic Constitutive Laws

Abseact. The existence of a work potential. governing materlal response when elastic behav~or occurs. is shown to prov~de a concise framework for the structure of inelastic constitutive laws. The discussion includes the identification of differential invariants In conjugate stress and straln variables, an examination and reformulat~on of postulates leading to "normal~t) rules". and a study of the transmission of constitutive properties from subelements to overall behavior of heterogeneous sjstems. Also. internal variable representations of inelast~citj are examined uithin this framework. 1. Introduction. We consider elastic/plastic materials of a general kind. either time-independent or time-dependent. which have the property that their purely rlastic response admits a work potential. We show how this property can form the basis of a concise framework for the structure of their inelastic constitutive laws. The formalism is well suited to discussing macroscopic properties of materials which are heterogeneous on the microscale. This approach is motivated by the work of Kestin and Rice [I] and Rice [2] on internal state-variable models for plasticity. The postulated existence of thermo-dynamic potrntials was there shown to lead to an explicit relation between inelastic strain-increments and changes in the variables. A class of kinetic rate laws for the variables was thereby identified which implies a normality structure in the macro-scopic constitutive equations. By contrast we proceed here without specific reference to internal variables, though we subsequently introduce them as one possible way to represent the history dependence of inelastic deformation. We show further how invariance theorems in the general class established by Hill [3] can be derived concisely in the event that elastic potentials exist. The invariance in question refers not only to the whole family of conjugate measures of stress and strain, but also to the transmissibility of constitutive properties between microscopic and macroscopic levels.