准晶体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

IF 5.7 1区 工程技术 Q1 ENGINEERING, MULTIDISCIPLINARY International Journal of Engineering Science Pub Date : 2024-08-02 DOI:10.1016/j.ijengsci.2024.104124
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引用次数: 0

摘要

本文提出了一种透明、紧凑的准晶体固体平面热弹性的构成和平衡关系形式。对所获得的材料常数扩展张量的对称性和正定性进行了研究。为解决准晶体的平面热弹性问题,提出了斯特罗形式主义的扩展。研究证明,在三维准晶体材料的最一般情况下,斯特罗特征值问题的特征值是纯复数。获得了所提出的扩展斯特罗形式的声波弹性和热弹性系数矩阵和向量之间的关系。推导出了准晶体介质热弹性平面问题的基本解。研究了几何形状可由不连续线(裂缝、薄夹杂物)建模的物体顶点附近的物理和机械场的渐近行为,并引入了相应的广义场(热通量和声波应力)强度因子的概念。研究还考虑了热源和热汇对含有直线受热裂缝的无限准晶体介质的影响实例。
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Extended Stroh formalism for plane problems of thermoelasticity of quasicrystals with applications to Green’s functions and fracture mechanics

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.

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来源期刊
International Journal of Engineering Science
International Journal of Engineering Science 工程技术-工程:综合
CiteScore
11.80
自引率
16.70%
发文量
86
审稿时长
45 days
期刊介绍: The International Journal of Engineering Science is not limited to a specific aspect of science and engineering but is instead devoted to a wide range of subfields in the engineering sciences. While it encourages a broad spectrum of contribution in the engineering sciences, its core interest lies in issues concerning material modeling and response. Articles of interdisciplinary nature are particularly welcome. The primary goal of the new editors is to maintain high quality of publications. There will be a commitment to expediting the time taken for the publication of the papers. The articles that are sent for reviews will have names of the authors deleted with a view towards enhancing the objectivity and fairness of the review process. Articles that are devoted to the purely mathematical aspects without a discussion of the physical implications of the results or the consideration of specific examples are discouraged. Articles concerning material science should not be limited merely to a description and recording of observations but should contain theoretical or quantitative discussion of the results.
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