Thermodynamically consistent residual-based gradient plasticity theory and comparison

A gradient plasticity theory for small deformations is presented within the framework of nonlocal continuum thermodynamics. The second principle (Clausius-Duhem inequality), enriched by an additional term named energy residual, is employed in conjunction with the concepts of insulation condition and locality recovery condition, in order to derive all the pertinent restrictions upon the constitutive equations. These include the expressions of the energy residual and of the plastic dissipation density, as well as the PDEs governing the gradient kinematic and isotropic hardening of the material, together with the related higher-order boundary conditions for both the fixed and the moving boundaries. Other formulations, which apparently do not make use of an energy residual, are shown to contain a latent one.