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

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.

Keywords:

• Bellman method
• dual integral equations
• Fredholm integral equations
• mode I crack

Acknowledgements

The authors would like to thank the Editor and the anonymous referees for their comments and suggestions on this article.

Disclosure statement

The author declares that there is no conflict of interest.