A thermodynamical theory of plastic spin and internal stress with dislocation density tensor

A thermodynamical theory of elastoplasticily including kinematic hardening and dislocation density tensor is developed. The theory is self-consistent and is based on two fundamental principles of thermodynamics, i.e., the pri nciple of increase of entropy and maximal entropy production rate. The ther modynamically consistent governing equations of plastic spin and back stres s are rigorously derived. An expression for the plastic spin tensor is obta ined from the constitutive equation of dislocation drift rate tensor and an expression for the back stress tensor is given as a balance equation expre ssing an equilibrium between internal stress and microstress conjugate to t he dislocation density tensor. Moreover, it is shown that, in order to obta in a thermodynamically consistent theory for kinematic hardening, the free energy density should have the dislocation density tensor as one of its arg uments.