Effect of nonlocality and memory responses in the thermoelastic problem with a Mode I crack

Abstract

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.

Keywords:

• Mode I crack
• dual integral equations
• Fredholm integral equations
• Bellman method
• memory-dependent derivative

Acknowledgements

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

Disclosure statement

No potential conflict of interest was reported by the author(s).