The paper proposes a transparent and compact form of constitutive and equilibrium relations for the plane thermoelasticity of quasicrystal solids. The symmetry and positive definiteness of the obtained extended tensors of material constants are studied. An extension of the Stroh formalism is proposed for solving plane problems of thermoelasticity for quasicrystals. It is proved that the eigenvalues of the Stroh eigenvalue problem in the most general case of 3D quasicrystal materials do are purely complex. The relations between the matrices and vectors of phonon–phason elastic and thermoelastic coefficients of the proposed extended Stroh formalism are obtained. A fundamental solution to the plane problem of thermoelasticity of a quasicrystal medium is derived. The asymptotic behavior of physical and mechanical fields near the vertices of objects whose geometry can be modeled by a discontinuity line (cracks, thin inclusions) is studied, and the concepts of the corresponding generalized field (heat flux and phonon–phason stress) intensity factors are introduced. Examples of the influence of heat sources and sinks on an infinite quasicrystal medium containing a rectilinear heated crack are considered.

中文翻译：

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准晶热弹性平面问题的扩展斯特罗形式主义及其在格林函数和断裂力学中的应用


该论文提出了准晶固体平面热弹性的透明且紧凑的本构关系和平衡关系。研究了所得到的材料常数扩展张量的对称性和正定性。提出了斯特罗形式主义的扩展来解决准晶体热弹性的平面问题。事实证明，在 3D 准晶材料的最一般情况下，Stroh 特征值问题的特征值确实是纯复数。获得了所提出的扩展斯特罗形式主义的声子-相子弹性系数和热弹性系数的矩阵和向量之间的关系。导出了准晶介质热弹性平面问题的基本解。研究了物体顶点附近物理和机械场的渐近行为，其几何形状可以通过不连续线（裂纹、薄夹杂物）进行建模，并研究相应的广义场（热通量和声子相子应力）强度因子的概念被介绍。考虑了热源和热汇对包含直线加热裂纹的无限准晶介质的影响的示例。