Material forces in finite elasto-plasticity with continuously distributed dislocations

In this paper we propose a thermodynamically consistent model for elasto-plastic material with structural inhomogeneities such as dislocations, subjected to large deformations, in isothermal processes. The plastic measure of deformation is represented by a pair of plastic distortion, and plastic connection with non-zero torsion (in order to have the non-zero Burgers vector). The developments are focused on the balance equations (for material forces and for physical force system), derived from an appropriate principle of the virtual power formulated within the constitutive framework of finite elasto-plasticity and on constitutive restrictions imposed by the free energy imbalance. The presence of the material forces (microforce and microstress momentum) is a key point in the exposure, and viscoplastic (generally rate dependent) constitutive representation are derived.