A thermodynamical theory of gradient elastoplasticity with dislocation density tensor. I: Fundamentals

A thermodynamical theory of gradient elastoplasticity, including kinematic hardening, is developed by introducing the concept of dislocation density t ensor. The theory is self-consistent and is based on two fundamental princi ples, the principle of increase of entropy and the maximal entropy producti on rate. Thermodynamically consistent constitutive equations for plastic st retching, plastic spin and back stress are rigorously derived. Also. an exp ression for the plastic spin is obtained from the constitutive equation of dislocation drift rate and an expression for the back stress is given as a balance equation expressing equilibrium between internal stress and microst ress conjugate to the dislocation density tensor. Moreover, it is shown tha t the present gradient theory yields a symmetric stress tensor. Some genera lities and utility of this theory are discussed and comparisons with other gradient theories are given. (C) 1999 Elsevier Science Ltd. All rights rese rved.