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

References

• F. Delale and F. Erdogan, “On the mechanical modeling of the interfacial region in bonded half-planes,” ASME J. Appl. Mech., vol. 55, no. 2, pp. 317–324, 1988. DOI: 10.1115/1.3173677.
   Web of Science ®Google Scholar
• Y. F. Chen, “Interface crack in nonhomogeneous bonded materials of finite thickness,” 1990. Ph.D. dissertation,” Lehigh University.
   Google Scholar
• M. Ozturk and F. Erdogan, “Axisymmetric crack problem in bonded materials with a graded interfacial region,” Int. J. Solids Struct., vol. 33, no. 2, pp. 193–219, 1996. DOI: 10.1016/0020-7683(95)00034-8.
   Web of Science ®Google Scholar
• A. C. Eringen, “Linear crack subject to shear,” Int. J. Fract., vol. 14, no. 4, pp. 367–379, 1978. DOI: 10.1007/BF00015990.
   Web of Science ®Google Scholar
• A. C. Eringen, “Linear crack subject to anti-plane shear,” Engng. Frac. Mech., vol. 12, pp. 211–219, 1979. DOI: 10.1016/0013-7944(79)90114-0.
   Google Scholar
• A. C. Eringen, C. G. Speziale and B. S. Kim, “Crack tip problem in non-local elasticity,” J. Mech. Phys. Solids, vol. 25, no. 5, pp. 339–346, 1977. DOI: 10.1016/0022-5096(77)90002-3.
   Web of Science ®Google Scholar
• D. G. B. Edelen, “Non-local field theory,” in Continuum Physics,” vol. 4, A. C. Eringen, Ed. Academic Press, New York, 1976, pp. 75–204.
   Google Scholar
• A. E. Green and R. S. Rivilin, “Multipolar continuum mechanics: Functional theory I,” Proc. Roy. Soc. Lond. A, vol. 284, pp. 303–315, 1965.
   Web of Science ®Google Scholar
• A. C. Eringen, “Non-local polar field theory,” in Continuum Physics,” vol. 4, A. C. Eringen, Ed. Academic Press, New York, pp. 205–267, 1976.
   Google Scholar
• K. L. Pan, “The image force on a dislocation near an elliptic hole in non-local elasticity,” Arch. Appl. Mech, vol. 62, pp. 557–564, 1992.
   Web of Science ®Google Scholar
• K. L. Pan, “The image force theorem for a screw dislocation near a crack in non-local elasticity,” J. Phys. D: Appl. Phys., vol. 27, no. 2, pp. 344–346, 1994. DOI: 10.1088/0022-3727/27/2/024.
   Web of Science ®Google Scholar
• K. L. Pan and J. Fang, “Non-local interaction of dislocation with a crack,” Arch. Appl. Mech., vol. 64, no. 1, pp. 44–51, 1993. DOI: 10.1007/BF00792343.
   Web of Science ®Google Scholar
• K. L. Pan, “Interaction of a dislocation with a surface crack in non-local elasticity,” Int. J. Fract., vol. 69, no. 4, pp. 307–318, 1995. DOI: 10.1007/BF00037381.
   Web of Science ®Google Scholar
• A. Sur and M. Kanoria, “Thermoelastic interaction in a functionally graded half-space subjected to a Mode-I crack,” Int. J. Adv. Appl. Math. Mech., vol. 3, no. 2, pp. 33–44, 2015.
   Google Scholar
• R. Prasad, S. Das and S. Mukhopadhyay, “A two-dimensional problem of a mode I crack in a type III thermoelastic medium,” Math. Mech. Solids, vol. 18, no. 5, pp. 506–523, 2013. DOI: 10.1177/1081286512443237.
   Web of Science ®Google Scholar
• A. Sur, S. Mondal and M. Kanoria, “Influence of moving heat source on skin tissue in the context of two-temperature Caputo-Fabrizio heat transport law,” J. Multiscale Model, 2019. DOI: 10.1142/S175697372050002X.
   Google Scholar
• A. C. Eringen, Nonlocal Continum Field Theories. Springer Verlag, New York, 2002.
   Google Scholar
• D. G. B. Edelen, A. E. Green and N. Lows, “Nonlocal continuum mechanics,” Arch. Rational Mech. Anal., vol. 43, no. 1, pp. 36–44, 1971. DOI: 10.1007/BF00251544.
   Web of Science ®Google Scholar
• A. C. Eringen and D. G. B. Edelen, “On nonlocal elasticity,” Int. J. Eng. Sci., vol. 10, no. 3, pp. 233–248, 1972. DOI: 10.1016/0020-7225(72)90039-0.
   Web of Science ®Google Scholar
• B. S. Altan, “Uniqueness in the linear theory of nonlocal elasticity,” Bull. Tech. Univ. Istanb., vol. 37, pp. 373–385, 1984.
   Google Scholar
• A. C. Eringen, “On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves,” J. Appl. Phys., vol. 54, no. 9, pp. 4703–4710, 1983. DOI: 10.1063/1.332803.
   Web of Science ®Google Scholar
• P. Zhang and T. He, “A generalized thermoelastic problem with nonlocal effect and memory-dependent derivative when subjected to a moving heat source,” Waves Random Complex Media, vol. 30, no. 1, pp. 142–156, 2020. DOI: 10.1080/17455030.2018.1490043.
   Web of Science ®Google Scholar
• S. Mondal, “Memory response in a magneto-thermoelastic rod with moving heat source based on Eringen’s nonlocal theory under dual-phase lag heat conduction,” Int. J. Comput. Methods, 2019. DOI: 10.1142/S0219876219500762.
   Web of Science ®Google Scholar
• S. Mondal, N. Sarkar and N. Sarkar, “Waves in dual-phase-lag thermoelastic materials with voids based on Eringen’s nonlocal elasticity,” J. Therm. Stress, vol. 42, no. 8, pp. 1035–1050, 2019. vol DOI: 10.1080/01495739.2019.1591249.
   Web of Science ®Google Scholar
• M. Bachher and N. Sarkar, “Nonlocal theory of thermoelastic materials with voids and fractional derivative heat transfer,” Waves Random Complex Media, vol. 29, no. 4, pp. 595–613, 2019. DOI: 10.1080/17455030.2018.1457230.
   Web of Science ®Google Scholar
• A. Sur, “Non-local memory dependent heat conduction in a magneto-thermoelastic problem,” Waves Random Complex Media, 2020. DOI: 10.1080/17455030.2020.1770369.
   Web of Science ®Google Scholar
• H. Lord and Y. Shulman, “A generalized dynamic theory of Thermoelasticity,” J. Mech. Phys. Solids, vol. 15, no. 5, pp. 299–309, 1967. DOI: 10.1016/0022-5096(67)90024-5.
   Web of Science ®Google Scholar
• S. K. Roy Choudhuri, “On a thermoelastic three-phase-lag model,” J. Therm. Stress, vol. 30, no. 3, pp. 231–238, 2007. DOI: 10.1080/01495730601130919.
   Web of Science ®Google Scholar
• A. Sur and M. Kanoria, “Field equations and corresponding memory responses for a fiber-reinforced functionally graded due to heat source,” Mech. Based Design Struct. Mach., 2019. DOI: 10.1080/15397734.2019.1693897.
   Web of Science ®Google Scholar
• A. Sur, S. Mondal and M. Kanoria, “Memory response on wave propagation in a thermoelastic plate due to moving band-type thermal loads and magnetic field,” Mech. Based Design Struct. Mach., pp. 1–22, 2019. DOI: 10.1080/15397734.2019.1672558.
   Google Scholar
• S. Mondal, A. Sur and M. Kanoria, “Photo-thermo-elastic wave propagation in a reinforced semiconductor due to memory responses in presence of magnetic field,” Acta Mech., 2019. DOI: 10.1007/s00707-019-02600-x.
   Google Scholar
• S. Mondal, A. Sur and M. Kanoria, “Photo-thermo-elastic wave propagation under the influence of magnetic field in presence of memory responses,” Mech. Based Design Struct. Mach., 2019. DOI: 10.1080/15397734.2019.1701493.
   Web of Science ®Google Scholar
• A. Sur, “Wave propagation analysis of porous asphalts on account of memory responses,” Mech. Based Design Struct. Mach., DOI: 10.1080/15397734.2020.1712553,.2020.
   Web of Science ®Google Scholar
• S. Mondal and A. Sur, “Photo-thermo-elastic wave propagation in an orthotropic semiconductor with a spherical cavity and memory responses,” Waves Random Complex Media, 2020. DOI: 10.1080/17455030.2019.1705426.
   Web of Science ®Google Scholar
• A. Sur, S. Santra and M. Kanoria, “Memory response on thermal wave propagation in an elastic solid with voids due to influence of magnetic field,” Waves Random Complex Media, pp. 1–24, 2019. DOI: 10.1080/17455030.2019.1654147.
   Web of Science ®Google Scholar
• S. Mondal, A. Sur and M. Kanoria, “Thermoelastic response of fiber-reinforced epoxy composite under continuous line heat source,” Waves Random Complex Media, 2019. DOI: 10.1080/17455030.2019.1699675.
   Web of Science ®Google Scholar
• P. Purkait, A. Sur and M. Kanoria, “Magneto-thermoelastic interaction in a functionally graded medium under gravitational field,” Waves Random Complex Media, 2019. DOI: 10.1080/17455030.2019.1688891.
   Web of Science ®Google Scholar
• A. Sur, “A memory response on the elasto-thermodiffusive interaction subjected to rectangular thermal pulse and chemical shock,” Mech. Based Design Struct. Mach., DOI: 10.1080/15397734.2020.1772086,.2020.
   Web of Science ®Google Scholar
• R. Bellman, R. E. Kolaba, and and J. A. Lockett, Numerical Inversion of Laplace Transform,” New York, Elsevier, 1966,
   Google Scholar
• A. E. Green and P. M. Naghdi, “A re-examination of the basic results of thermomechanics,” Proc. Roy. Soc. London Ser. A, vol. 432, pp. 171–194, 1992.
   Web of Science ®Google Scholar
• A. E. Green and P. M. Naghdi, “On undamped heat waves in an elastic solid,” J Thermal Stresses, vol. 15, pp. 252–264, 1992.
   Web of Science ®Google Scholar
• A. E. Green and P. M. Naghdi, “Thermoelasticity without energy dissipation,” J Elasticity, vol. 31, no. 3, pp. 189–208, 1993. DOI: 10.1007/BF00044969.
   Web of Science ®Google Scholar
• X. C. Zhong and K. Y. Lee, “A thermal-medium crack model,” Mech. Mater., vol. 51, pp. 110–117, 2012. DOI: 10.1016/j.mechmat.2012.04.013.
   Web of Science ®Google Scholar
• H. H. Sherief and N. M. El-Maghraby, “A mode-I crack problemfor an infinite space in generalized thermoelasticity,” J. Therm. Stress, vol. 28, no. 5, pp. 465–484, 2005. DOI: 10.1080/01495730590925001.
   Web of Science ®Google Scholar
• S. H. Mallik and M. Kanoria, “A Unified Generalized Thermoelasticity Formulation: Application to Penny-Shaped Crack Analysis,” J. Therm. Stress, vol. 32, no. 9, pp. 943–965, 2009. DOI: 10.1080/01495730903032284.
   Web of Science ®Google Scholar
• R. Quintanilla and R. Racke, “A note on stability in three-phase-lag heat conduction,” J. Heat. Mass. Transf., vol. 51, no. 1-2, pp. 24–29, 2008. DOI: 10.1016/j.ijheatmasstransfer.2007.04.045.
   Web of Science ®Google Scholar
• L. Delves and J. Mohammed, Computational Methods for Integral Equations. Cambridge: Cambridge University Press, 1985.
   Google Scholar