Nonlinear and Linearized Models in Thermoviscoelasticity

We consider a quasistatic nonlinear model in thermoviscoelasticity at finite-strain setting the Kelvin–Voigt rheology, where both elastic and viscous stress tensors comply with principle of frame indifference under rotations. The force balance is formulated reference configuration by resorting to concept nonsimple materials, whereas heat transfer equation governed Fourier law deformed configurations. Weak solutions are obtained means staggered in-time discretization deformation temperature updated alternatingly. Our result refines recent work Mielke Roubíček (Arch Ration Mech Anal 238:1–45, 2020) since our approximation does not require any regularization viscosity term. Afterwards, we focus on case deformations near identity small temperatures, show rigorous linearization procedure that weak system converge suitable sense linearized thermoviscoelasticity. same property holds for time-discrete approximations provide corresponding commutativity result.