Variational models of coupled gradient thermoelasticity and thermal conductivity


We consider generalized variational non-local models of media with fields of defects and show that the methods of continuum mechanics are very effective in modeling connected reversible and irreversible thermomechanical processes. It is postulated that the tensor of free distortions is determined only by the spherical tensor, which is interpreted as a dilatation associated with a change in temperature. A variational model of coupled thermoelasticity and hyperbolic thermal conductivity is under construction. It describes the general case of non-locality, when gradient properties are determined by scale parameters that are responsible for both mechanical and temperature effects. The analysis of boundary value problems is given, the physical interpretation of all model parameters is given through known thermomechanical parameters. We also offer a variation model of irreversible thermodynamic processes, which is based on the principle of L.I. Sedov. In this case, the variation form for the dissipative part of the change in energy is based on the non-integrability condition proposed by the authors.