Evolution equations and thermodynamic restrictions for dissipative solids

Heat conduction and viscosity in solids are modelled by means of evolution equations. The appropriate time derivative is determined by requiring that both objectivity and compatibility with thermodynamics be satisfied. This is performed by investigating the balance law and the entropy inequality in the reference configuration. It follows that the evolution for the heat flux and the stress tensor involves the Oldroyd derivative, irrespective of the occurrence of nonlocal terms.