A finite strain thermo-viscoelastic constitutive model to describe the self-heating in elastomeric materials during low-cycle fatigue

A thermo-visco-hyperelastic constitutive model, in accordance with the second thermodynamics principle, is formulated to describe the self-heating evolution in elastomeric materials under cyclic loading. The mechanical part of the model is based upon a Zener rheological representation in which the specific free energy potential is dependent on an added internal variable, allowing the description of the time-dependent mechanical response. The large strain mechanical behavior is described using a Langevin spring, while the continuous stress-softening under cyclic loading is taken into account by means of a network alteration kinetics. The thermo-mechanical coupling is defined by postulating the existence of a dissipation pseudo-potential, function of the viscous dilatation tensor. The proposed model is fully three-dimensional and is implemented into a finite element code. The model parameters are identified using experimental data obtained on a styrene-butadiene rubber under a given strain rate for different strain conditions. Predicted evolutions given by the model for other strain rates are found in good agreement with the experimental data.