Mathematical and numerical analysis in thermo-gradient-dependent theory of plasticity

Abstract

In this paper, we develop new governing equations for thermo-gradient-dependent theory of plasticity. They include the coupled effects of thermal elastic-plastic theory, including balance and constitutive equations. To demonstrate the salient feature of the gradient-dependent model of plasticity, particular attention is addressed to isotropic hardening with second sound effects to eliminate the paradox of infinite speed of thermal signals. The resulting system of partial differential equations formally describes the coupled thermomechanical behavior of the gradient-dependent elasto-plastic system. Then, we develop an appropriate state-space form and, by using the semigroup theory, we prove the well-posedness and the exponential stability of the thermo-gradient-dependent elasto-plastic one-dimensional problem. Finally, we perform numerical simulations to validate the proposed model and to show its capability.