Frame-indifferent discretization in nonlinear thermoviscoelasticity: Analysis and numerical simulations

We consider a quasi-static nonlinear model in thermoviscoelasticity at a finite-strain setting in the Kelvin-Voigt rheology where both the elastic and viscous stress tensors comply with the principle of frame indifference under rotations. We refine the discretization schemes in [Badal-Friedrich-Kružík '23, Mielke-Roubíček '20] by imposing frame indifference already at a time-discrete level. This is justified both analytically and numerically.