Abstract

We consider generalized variational models of media with fields of defects and assume that the tensor of free distortions is interpreted as a dilatation associated with changing of temperature. A variational model of coupled thermoelasticity and stationary thermal conductivity is considered. The model is consistent with the thermodynamics and based parameters of the model are identified from the famous thermomechanical parameters. We assume, that gradient properties are determined by scale parameters which are defined by both mechanical and temperature multiscale effects. The analysis of the boundary value problems is given, and the structure of the fundamental solutions are studied. The fundamental solutions are constructed on the based of generalized Papkovich–Neuber representation using the radial multiplies and are written explicitly in analytical form. It is shown that characteristic roots for the coupled model are satisfied to the algebraic equation of the third order and strong depend on the additional parameters of the model, which describe the coupled effects. As a particular, it is shown that pure oscillation modes can be appear for the temperature, that show the possibility of the thermal waveguide and dynamic instability effects due to coupled effects.

中文翻译：

---

关于耦合热弹性和热传导率问题的基本解的结构

摘要

我们考虑具有缺陷场的介质的广义变分模型，并假设自由变形的张量被解释为与温度变化相关的膨胀。考虑了耦合热弹性和固定热导率的变分模型。该模型与热力学一致，并且该模型的基础参数是从著名的热机械参数中识别出来的。我们假设梯度特性由机械和温度多尺度效应定义的尺度参数决定。分析了边值问题，研究了基本解的结构。基本解基于使用径向乘法的广义 Papkovich-Neuber 表示构建，并以解析形式明确写出。结果表明，耦合模型的特征根满足三阶代数方程，并且强烈依赖于描述耦合效应的模型附加参数。特别是，它表明温度可以出现纯振荡模式，这表明热波导和动态不稳定效应的可能性是由于耦合效应。