A thermodynamics-based formulation of gradient-dependent plasticity

Abstract

A nonlocal thermodynamic theoretical framework is provided as a basis for a consistent formulation of gradient-dependent plasticity in which a scalar internal variable measuring the material isotropic hardening/softening state is the only nonlocal variable. The main concepts of this formulation are: i) the ‘regularization operator’, of differential nature, which governs the relation between the above nonlocal variable and a related local variable (scalar measure of plastic strain) and confers a unified character to the proposed formulation (this transforms into a formulation for nonlocal plasticity if the regularization operator has an integral nature); ii) the ‘nonlocality residual’, which accounts for energy exchanges between different particles at the microstructural level as a consequence of the hardening/softening diffusion processes within the body; and iii) the (nonambiguous) ‘constitutive’ boundary conditions, which must be satisfied at points of the boundary surface of any (finite) region of the body where an irreversible deformation mechanism takes place (e.g. shear band). The plastic yielding laws for gradient plasticity are established with their domain and boundary equations, and their consistency with the nonlocal Clausius-Duhem inequality is assessed as well. Also, a suitable nonlocal-form maximum intrinsic dissipation theorem is provided, and the response problem of a continuous set of material particles to a given total strain rate field studied. Points of agreement and disagreement between this theory and the related literature are indicated, also via a case-study bar in uniaxial tension for which the analytical solution is worked out.