A generalized thermoelastic problem due to nonlocal effect in presence of mode I crack

• Published in: Journal of thermal stresses Vol. 43; no. 10; pp. 1277 - 1299
• Main Authors: Sur, Abhik, Mondal, Sudip
• Format: Journal Article
• Language: English
• Published: Philadelphia Taylor & Francis 03.07.2020; Taylor & Francis Ltd
• Subjects: Bellman method; dual integral equations; Fourier transforms; Fredholm integral equations; Integral equations; Laplace transforms; Mathematical models; mode I crack; Phase lag; Stress concentration; Temperature distribution; Thermoelasticity
• ISSN: 0149-5739; 1521-074X
• DOI: 10.1080/01495739.2020.1788475

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.