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

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...

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Published inWaves in random and complex media Vol. 32; no. 2; pp. 771 - 796
Main Authors Sur, Abhik, Mondal, Sudip, Kanoria, M.
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 04.03.2022
Taylor & Francis Ltd
Subjects
Bellman method
Conduction heating
Conductive heat transfer
Deformation effects
dual integral equations
Elastic deformation
Fourier transforms
Fredholm integral equations
Free energy
Integral equations
Kernel functions
Laplace transforms
memory-dependent derivative
Miniaturization
Mode I crack
Size effects
Ultrafast lasers
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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.
AbstractList 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.
Author Mondal, Sudip
Kanoria, M.
Sur, Abhik
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  surname: Kanoria
  fullname: Kanoria, M.
  organization: Department of Applied Mathematics, University of Calcutta
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Snippet 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...
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SubjectTerms Bellman method
Conduction heating
Conductive heat transfer
Deformation effects
dual integral equations
Elastic deformation
Fourier transforms
Fredholm integral equations
Free energy
Integral equations
Kernel functions
Laplace transforms
memory-dependent derivative
Miniaturization
Mode I crack
Size effects
Ultrafast lasers
Title Effect of nonlocality and memory responses in the thermoelastic problem with a Mode I crack
URI https://www.tandfonline.com/doi/abs/10.1080/17455030.2020.1800860
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