Thermodynamics of Elastic-Plastic Materials as a Theory with Internal State Variables

We develop an analytical framework for the theory of plasticity in which the constitutive equations are single valued and which at the same time represents the proper physical concepts. A Coleman-Gurtintype thermodynamics which utilizes internal state variables is used for the study of an elastic-plastic substance. Quantities which are related to the dislocation motion and the dislocation arrangement in the material, play the role of the internal state variables in this thermodynamics. Rate-independent plasticity is studied as a limiting case of the present theory. We illustrate the theory with a special case: a one-dimensional, homogeneous, cyclic deformation of a rate-independent elastic-plastic body which exhibits a Bauschinger effect.