Singular surfaces in long, thin radiating rods under Green and Naghdi's type II theory of thermoelasticity

The purpose of this contribution is to extend the concept of thermoelasticity without energy dissipation traceable back to Green and Naghdi to damped solutions, making use of concrete physical arguments. Specifically, it is assumed that the external rate of supply of heat r, which is formally taken into account in the original model, is such as to include in it an effect of radiation of thermal energy towards the external environment. The case of a deformable thermal conductor is considered, specifically, a long, thin rod, and singular surface theory is invoked to analyze the behavior of the proposed linear model in more detail. The expectation is that this work can actually identify a new perspective from which to observe a well-settled thermoelastic theory.