Thermoviscoplasticity at Finite Strains: A Thermoelastic Predictor-Viscoplastic Corrector Algorithm

This contribution aims at describing the numerical background associated to an efficient time integration procedure for thermomechanical elastic-viscoplastic constitutive model in a large deformation context.

First, from the continuum mechanics point of view, the constitutive model is established. Within the framework of viscoplasticity, we have tried to remain as general as possible and the presented model encompasses under the same unified format, both {\it Perzyna-Chaboche} model of viscoplasticity which is well suited for moderate strain rates, as well as {\it Johnson-Cook} model which is a reference for metals submitted to high strain rates. Both incorporate nonlinear isotropic and kinematic hardening models. The classical rate-independent elastic-plastic model can then be easily recovered by setting the viscous terms to zero.

Second, as the resulting continuum model is a stiff first order ordinary differential system in time, an integration algorithm is presented. This algorithm generalizes the classical "radial return algorithm", well established for elasto-plasticity, to thermo-elastic-viscoplastic models. The differential equations are numerically integrated using a thermoelastic predictor-viscoplastic corrector algorithm. The resulting algorithm is once again quite general and contains as special cases isothermal viscoplastic cases as well as classical rate-independent plasticity. Thanks to that generality, only one unified algorithm can be used both for plastic (rate-independent) as well as viscoplastic (rate-dependent) material models. Besides, in the formulation, a special care has also been taken so that all material parameters, including thermal dilatation, can be temperature dependent. As a consequence, it is also possible to model a continuous transition from elevated temperatures (that require the use of a viscoplastic model) to room temperature where rate-independent models are sometimes better suited by using a temperature-dependent viscosity that goes to zero as the room temperature is approached.