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.

此贡献的目的是利用具体的物理参数，将热弹性的概念扩展到可追溯到 Green 和 Naghdi 的无能量耗散的阻尼解决方案。具体而言，假设外部供热率$r$，这是在原始模型中正式考虑的，以便在其中包括热能对外部环境的辐射效应。考虑了可变形热导体的情况，特别是细长杆，并调用奇异表面理论来更详细地分析所提出的线性模型的行为。期望这项工作实际上可以确定一个新的视角，从中可以观察到一个很好的热弹性理论。