A viscoplastic theory with thermodynamic considerations

A thermodynamic foundation using the concept of internal state variables is given for a general theory of viscoplasticity for initially isotropic materials. Three, fundamental, internal, state variables are admitted; they are: a tensorial back stress for kinematic effects, and scalar drag and yield strengths for isotropic effects. All three are considered to evolve phenomenologically according to competitive processes between strain hardening, deformation induced dynamic recovery, and thermally induced static recovery. Within this phenomenological framework, a thermodynamically admissible set of evolution equations is proposed. The theory allows each of the three internal variables to be composed as a sum of independently evolving constituents. The evolution of internal state can also include terms that vary linearly with the external variable rates, whose presence affects the energy dissipation properties of a material.