Thermal stresses that depend on temperature gradients.

This paper deals with a linear theory of thermoviscoelasticity within the framework of Green–Naghdi thermomechanics. We use some notation and terminology introduced by Green and Naghdi, but instead of using the entropy balance law we employ an entropy production inequality. We introduce the entropy flux tensor and present a theory of materials of Kelvin–Voigt type in which the stress tensor depends on the temperature gradients. The theory leads to a fourth-order equation for temperature. The boundary conditions for thermal displacement are presented. In the dynamical theory of anisotropic solids, we formulate boundary-initial value problems and present a uniqueness theorem. We derive the continuous dependence of solutions upon initial data and supply terms. In the case of homogeneous and isotropic bodies, we establish a representation of the solution that is expressed in terms of two potentials and present an application of this result. [ABSTRACT FROM AUTHOR]