Thermomechanical formulation of ductile damage coupled to nonlinear isotropic hardening and multiplicative viscoplasticity

Abstract

In this paper, we present a thermomechanical framework which makes use of the internal variable theory of thermodynamics for damage-coupled finite viscoplasticity with nonlinear isotropic hardening. Damage evolution, being an irreversible process, generates heat. In addition to its direct effect on material's strength and stiffness, it causes deterioration of the heat conduction. The formulation, following the footsteps of [Simo, J.C., Miehe, Ch. [1992]: “Associative coupled thermoplasticity at finite strains: Formulation, numerical analysis and implementation”, Computer Methods in Applied Mechanics and Engineering, Vol. 98, 41–104.], introduces inelastic entropy as an additional state variable. Given a temperature dependent damage dissipation potential, we show that the evolution of inelastic entropy assumes a split form relating to plastic and damage parts, respectively. The solution of the thermomechanical problem is based on the so-called isothermal split. This allows the use of the model in 2D and 3D example problems involving geometrical imperfection triggered necking in an axisymmetric bar and thermally triggered necking of a 3D rectangular bar.