Response of an Elastic Body whose Heat Conduction Is Pressure Dependent

he properties of many real materials such as the viscosity, thermal and electrical conductivity, specific heat, relaxation time, as well as optical properties, depend upon the pressure to which the body is subject. For instance, the viscosity of fluids can vary by several orders of magnitude due to the variation in the pressure. In this paper we investigate the change in the response of an elastic solid due to the thermal conductivity being pressure dependent. It is well known that higher pressure leads to reduced molecular mobility, in rubber-like materials, leading in turn to higher cross-linking reaction rates. We find that the response of the solid is quite different from the classical response that is obtained by using Fourier's law of heat conduction. The theoretical predictions according to the assumption that the thermal conductivity is pressure dependent, are in keeping with experimental results concerning the vulcanization of rubbers wherein one observes the conduction to be dependent on the pressure. To our knowledge, this is the first theoretical study that evaluates the response of non-linear elastic solids due the thermal conductivity depending on the pressure.