Inelastic constitutive relations for solids: An internal-variable theory and its application to metal plasticity

This paper is a study of the theoretical foundations of constitutive relations at finite strain for a class of solids exhibiting inelasticity as a consequence of specific structural rearrangements, on the microscale, of constituent elements of material. Metals deforming plastically through dislocation motion are of this class and form the primary application of the theory. The development is in terms of a general internal-variable thermodynamic formalism for description of the microstructural rearrangements, and it is shown how metal plasticity may be so characterized. The principal result is in the normality structure which is shown to arise in macroscopic constitutive laws when each of the local microstructural rearrangements proceeds at a rate governed by its associated thermodynamic force. This provides a theoretical framework for time-dependent inelastic behavior in terms of a “flow potential”, and reduces to statements on normality of strain increments to yield surfaces in the time-independent case. Conventional characterizations of the stress-state dependence of metallic slip are noted to be in accord with this concept of associated forces governing rates, so that the resulting normality structure may be considered directly applicable to metal plasticity.