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

A thermodynamical theory of elastoplasticity 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 principle of increase of entropy and maximal entropy production rate. The thermodynamically consistent governing equations of plastic spin and back stress are rigorously derived. An expression for the plastic spin tensor is obtained from the constitutive equation of dislocation drift rate tensor and an expression for the back stress tensor is given as a balance equation expressing an equilibrium between internal stress and microstress conjugate to the dislocation density tensor. Moreover, it is shown that, in order to obtain a thermodynamically consistent theory for kinematic hardening, the free energy density should have the dislocation density tensor as one of its arguments.