Abstract This article constructs a new model of nonlocal thermoelasticity which resolves a dynamical problem of a homogeneous, isotropic infinite space weakened by a finite linear mode I crack. The boundary of the crack is being subjected to a prescribed temperature distribution and stress. In the context of three-phase lag model of generalized thermoelasticity, the governing equations have been solved employing the Laplace and the Fourier transforms, which reduces to four dual integral equations, the solution of which is equivalent to solving the Fredholm’s integral equation of the first kind. These integral equations have been solved employing the Maple software package, while the numerical inversion of the Laplace transform is carried out with the help of Bellman method. Numerical computations for a copper material are performed and demonstrated graphically. The results provide a motivation to further investigate the problem and draw concluding remarks due to the influence of nonlocality also.

中文翻译：

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存在 I 型裂纹时由非局部效应引起的广义热弹性问题

摘要 本文构建了一个新的非局域热弹性模型，该模型解决了由有限线性模 I 裂纹削弱的均匀、各向同性无限空间的动力学问题。裂纹的边界受到规定的温度分布和应力。在广义热弹性三相滞后模型的背景下，利用拉普拉斯和傅立叶变换求解了控制方程，简化为四个对偶积分方程，其解等效于求解第一个的 Fredholm 积分方程。种类。这些积分方程已使用 Maple 软件包求解，而拉普拉斯变换的数值反演则借助 Bellman 方法进行。以图形方式执行和演示铜材料的数值计算。由于非定域性的影响，结果提供了进一步调查问题和得出结论的动机。