Non-local elasto-viscoplastic models with dislocations in finite elasto-plasticity. Part I: Constitutive framework

Abstract

In the first part of the paper we elaborate on a theoretical framework for elasto-plastic materials, based on the decomposition of the second-order deformation, associated with the motion, into its elastic and plastic second-order components, and applied to solids with lattice defects at the micro-structure level. Only the dislocations have been considered as possible lattice defects, which are modelled through the non-zero torsion of the plastic connection as a tensorial measure of the dislocations and through the scalar dislocation density and its gradient. The non-local evolution equations for the scalar dislocation density as well as for the plastic distortion have been derived to be compatible with the principle of the imbalance of the free energy. A coupling term dependent on the gradient of the scalar dislocation density influences the evolution of the plastic distortion. The internal power included the power dissipated by micro-forces, which consist from micro-stress and micro-momenta satisfying their own balance equations and being related not only with the plastic distortion but also with the scalar dislocation density. The free energy is defined to be dependent on the elastic strain and on the second-order plastic deformation, as well as on the scalar dislocation density and its gradient. Different constitutive non-local dissipative models have been derived and compared with the already existing ones.