Thermomechanical discussions on constitutive equations for plastic spin and back stress in a theory of dislocation drift rate

A thermomechanical theory of elastoplasticity, including kinematic hardening at finite strain, is developed by introducing the concept of dislocation density tensor. The theory is self-consistent and is based on two fundamental principles, the principle of increase of entropy and the maximal entropy production rate. The thermomechanically consistent constitutive equations for plastic deformation rate, plastic spin and dislocation drift rate are rigorously derived. Constitutive equation of the plastic spin is directly obtained by taking account of a work associating with plastic spin and deriving stress. An expression for the back stress is given as a balance equation expressing equilibrium between internal stress and microstress conjugate to the dislocation density tensor. Moreover, it is shown that the present theory is sufficiently consistent with the theory of non-Riemannian plasticity.