Theoretical and Numerical Aspects in the Thermo-Viscoelastic Material Behaviour of Rubber-Like Polymers

Most current models for finite deformation thermo-viscoelasticity are restricted to linear evolution laws for the viscous behaviour and to thermorheologically simple materials. In this paper, we extend a model for finite deformation viscoelasticity that utilizes a nonlinear evolution law to include thermal effects. In particular, we present a thermodynamically consistent framework for the model and give a detailed form for the non-equilibrium Helmholtz free energy of the material in terms of the isothermal free energy function. The use of the model in a computational setting is addressed and it is shown that an efficient predictor-corrector algorithm can be used to integrate the evolution equation of the proposed constitutive model. The integration algorithm makes crucial use of the exponential map as has been done previously in elastoplasticity. Numerical examples are presented to show some interesting features of the new model.