Stress relaxation and viscous energy in nonlinear viscoelasticity: A rational extended thermodynamics framework

We investigate uniaxial stress relaxation under constant strain using a recent hyperbolic model of nonlinear viscoelasticity based on the principles of Rational Extended Thermodynamics, as proposed in Ruggeri (2024). We determine the viscous dissipated energy such that the stress decays over time as a combination of exponential functions (Prony Series) with different relaxation times. We show that the obtained viscous energy satisfies all the requirements of the model such that the original system is symmetric hyperbolic and in particular satisfy the dissipation principle. According to the model, which requires that the viscous energy depends solely on the viscous stress, we are able to determine the analytical form of the coefficients in terms of the initial step deformation. This approach allows us to predict the decay of the viscous stress for any deformation jump, relying only on the fitting coefficients obtained from an experiment. This fully nonlinear viscoelastic model can be applied in conjunction with any hyperelastic law for the quasi-static stress component. We successfully applied our results to reproduce experimental data from uniaxial relaxation tests of a woven Dacron fabric currently used in aortic grafts.