ON THE THERMODYNAMICS OF ELASTIC-PLASTIC MATERIALS WITH TEMPERATURE-DEPENDENT MODULI AND YIELD STRESSES

The subject of this article is the thermodynamics of perfect elastic-plastic materials undergoing unidimensional, but not necessarily isothermal, deformations. The first and second laws of thermodynamics are employed in a form in which only the following quantities appear: the temperature θ, the elastic strain λe, the plastic strain λp, the elastic modulus μ(gq), the yield strain α(gq), the heat capacity κθ(λe, λp,θ), the latent elastic heat Λe(λe, λp, θ), and the latent plastic heat Λp(λe, λp, θ). Relations among the response functions μ, α, κθ, Λe, and Λp are derived, and it is shown that a set of these relations gives a necessary and sufficient condition for compliance with the laws of thermodynamics. Some observations are made about the existence and uniqueness of energy and entropy as functions of state. © 1979 Springer-Verlag.