The analysis of fracture is very important along with the miniaturization of the device and wide application of ultra-fast lasers, where size effect on heat conduction and elastic deformation increase and classical theory of thermoelastic coupling does not hold any more. Due to these, size-dependent thermoelastic model have been introduced for higher order simple material to adopt both the size effect of heat conduction and elasticity with the aids of extended irreversible thermodynamics and generalized free energy. With this motivation, the present study is now formulated to provide the nonlocal phenomena of a homogeneous, isotropic infinite space weakened by a finite linear mode I crack. The boundary of the crack is subjected to prescribed temperature and stress. The governing equations have been solved on 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. The Bellman method has been used to compute numerical inversion of the Laplace transform. The result provides the direction how the nonlocality and size-dependence can control the fracture and what is the significant effect of various kernel functions and the effect of memory is also reported.

随着器件的小型化和超快激光的广泛应用，对热传导和弹性变形的尺寸效应增加，热弹性耦合的经典理论不再成立，断裂分析变得非常重要。因此，借助扩展的不可逆热力学和广义自由能，为高阶简单材料引入了尺寸相关的热弹性模型，以同时采用热传导和弹性的尺寸效应。有了这个动机，现在制定本研究以提供由有限线性模式 I 裂纹削弱的均匀、各向同性无限空间的非局部现象。裂纹的边界受到规定的温度和应力。利用拉普拉斯变换和傅里叶变换求解了控制方程，将其简化为四个对偶积分方程，其解等效于求解第一类Fredholm积分方程。贝尔曼方法已被用于计算拉普拉斯变换的数值反演。该结果为非定域性和尺寸依赖性如何控制断裂提供了方向，并报告了各种核函数的显着影响以及记忆的影响。