Strain Gradient Effect in Finite Elasto-plastic Damaged Materials

Abstract

In this article we propose a strain gradient model for elasto-plastic materials in which there exist zones with structural inhomogeneities, characterized by nonlocal deformations. We assume the existence of an anholonomic configuration, called damaged configuration, which is associated with the second-order plastic deformation. We proved how the damage may be coupled to the second-order plasticity introducing a tensorial damage variable, Q^d, as a measure of the nonmetricity of the plastic Bilby-type part of the connection, which characterizes peculiar structural defects. The constitutive and evolution equations are subjected to be compatible with the principle of the imbalanced free energy, which is applied for isothermal processes. The free energy density function Ψ, is represented as a function of second-order elastic deformation and it depends on the damaged configuration, K, through the second-order plastic deformation. At the level of plastically deformed configuration, the effects of macro- and microforces are cumulated into the internal power. Two possible nonlocal evolution equations to describe plastic behavior are derived as a consequence of balance equation for microforces. Finally, we look at the influence of the strain gradient in a simple model.