Large deformation theory of coupled thermoplasticity including kinematic hardening

Abstract

Thermoplasticity is a topic central to important applications such as metalforming, ballistics and welding. The current investigation introduces a thermoplastic constitutive model accommodating the difficult issues of finite strain and kinematic hardening. Two potential functions are used. One is interpreted as the Helmholtz free energy. Its reversible portion describes elastic behavior, while its irreversible portion describes kinematic hardening. The second potential function describes dissipative effects and arises directly from the entropy production inequality. It is shown that the dissipation potential can be interpreted as a yield function. With two simplifying assumptions, the formulation leads to a simple energy equation, which is used to derive a rate variational principle. Together with the Principle of Virtual Work in rate form, finite element equations governing coupled thermal and mechanical effects are presented. Using a uniqueness argument, an inequality is derived which is interpreted as a finite strain thermoplastic counterpart to the classical inequality for “stability in the small”. A simple example is introduced using a von Mises yield function with linear kinematic hardening, linear isotropic hardening and linear thermal softening.