An internal state variable model of micropolarelasto-viscoplasticity

An internal state variable theory of micorpolar elasto-viscoplasticity is developed based upon the physics associated with dislocations and disclinations. Elastic-plastic kinematics are modified to include an additional rotational degree of freedom from which non-symmetric elastic and plastic strains and curvatures are defined. Dislocations and disclinations can then be easily identified in terms of the incompatibilities associated with the elastic deformation and elastic curvature. The state variables introduced are the nonsymmetric internal elastic strain and elastic curvature resulting from the presence of the dislocations and disclinations, as well as scalar measure of the elastic strain field associated with the statistically stored dislocations. The conjugate thermodynamic internal micro-stress and micro-moment are required to satisfy micro linear and angular momentum balances, while the macro stress (the derivative of the free energy with the respect to the macro elastic strain) satisfies standard linear and angular (symmetry of stress tensor) momentum balance laws. Expressions for the plastic velocity gradient and plastic curvature are proposed as well as an equation describing the evolution of the statistically stored dislocation density. The resulting expression describing the dissipation associated with the micro and macro stress fields follows naturally as a result of the second law, and the ramifications these restrictions on localized deformation is discussed.