Frame-indifferent discretization in nonlinear thermoviscoelasticity: Analysis and numerical simulations
For researchers in computational mechanics, this work improves the physical consistency of finite-strain thermoviscoelastic simulations by ensuring frame indifference in time-discrete schemes.
The paper refines discretization schemes for nonlinear thermoviscoelasticity to enforce frame indifference at the discrete level, providing analytical justification and numerical validation.
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-Roub\'ıček '20] by imposing frame indifference already at a time-discrete level. This is justified both analytically and numerically.