References
- Lord H, Shulman Y. A generalized dynamic theory of thermoelasticity. J Mech Phys Solids. 1967;15:299–309.
- Roy Choudhuri SK. On a thermoelastic three-phase-lag model. J Therm Stress. 2007;30:231–238.
- Sur A, Mondal S. A generalized thermoelastic problem due to nonlocal effect in presence of mode I crack. J Therm Stress. 2020. doi:https://doi.org/10.1080/01495739.2020.1788475.
- Sur A, Mondal S, Kanoria M. Memory response on wave propagation in a thermoelastic plate due to moving band-type thermal loads and magnetic field. Mech Based Des Struct Mach. 2019. doi:https://doi.org/10.1080/15397734.2019.1672558.
- Mondal S, Sur A, Kanoria M. A graded spherical tissue under thermal therapy: the treatment of cancer cells. Waves Random Complex Media. 2020. doi:https://doi.org/10.1080/17455030.2020.1779388.
- Mondal S. Interactions of a heat source moving over a visco-Thermoelastic rod kept in a magnetic field in the lord–Shulman model under a memory dependent derivative. Comput Math Model. 2020;31(2):256–276. doi:https://doi.org/10.1007/s10598-020-09490-y.
- Othman MIA, Mondal S. Memory-dependent derivative effect on 2D problem of generalized thermoelastic rotating medium with Lord–Shulman model. Indian J Phys. 2020;94(8):1169–1181. doi:https://doi.org/10.1007/s12648-019-01548-x.
- Othman MIA, Mondal S. Memory-dependent derivative effect on wave propagation of micropolar thermoelastic medium under pulsed laser heating with three theories. Int J Numer Methods Heat Fluid Flow. 2019;30(3):1025–1046. doi:https://doi.org/10.1108/HFF-05-2019-0402.
- Wang JL, Li HF. Surpassing the fractional derivative: concept of the memory-dependent derivative. Comput Math Appl. 2011;62(3):1562–1567.
- Mainardi F. Fractional calculus and waves in linear viscoelasticity. London: Imperial College Press; 2011.
- Sur A, Kanoria M. Fractional order two-temperature thermoelasticity with finite wave speed. Acta Mech. 2012;223:2685–2701.
- Shaw S. Theory of generalized thermoelasticity with memory-Dependent derivatives. J Eng Mech. 2019;145(3):04019003.
- El-Karamany AS, Ezzat MA. Thermoelastic diffusion with memory-dependent derivative. J Therm Stress. 2016;39(9):1035–1050.
- Sur A. A memory response on the elasto-thermodiffusive interaction subjected to rectangular thermal pulse and chemical shock. Mech Based Des Struct Mach. 2020. doi:https://doi.org/10.1080/15397734.2020.1772086.
- Sur A. Non-local memory dependent heat conduction in a magneto-thermoelastic problem. Waves Random Complex Media. 2020. doi:https://doi.org/10.1080/17455030.2020.1770369.
- Mondal S, Sur A, Kanoria M. Transient response in a piezoelastic medium due to the influence of magnetic field with memory-dependent derivative. Acta Mech. 2019;230(7):2325–2338.
- Sur A. Memory responses in a three-dimensional thermo-viscoelastic medium. Waves Random Complex Media. 2020. doi:https://doi.org/10.1080/17455030.2020.1766726.
- Ezzat MA, El-Bary AA. Memory-dependent derivatives theory of thermo-viscoelasticity involving two-temperature. J Mech Sci Tech. 2015;29(10):4273–4279.
- Purkait P, Sur A, Kanoria M. Elasto-thermodiffusive response in a spherical shell subjected to memory-dependent heat transfer. Waves Random Complex Media. 2019. doi:https://doi.org/10.1080/17455030.2019.1599464.
- Purkait P, Sur A, Kanoria M. Magneto-thermoelastic interaction in a functionally graded medium under gravitational field. Waves Random Complex Media. 2019. doi:https://doi.org/10.1080/17455030.2019.1688891.
- Xue ZN, Tian X, Jianlin L. Thermal shock fracture of a crack in a functionally gradient half-space based on the memory-dependent heat conduction model. Appl Math Model. 2020;80:840–858.
- Xue ZN, Chen ZT, Tian XG, et al. Thermoelastic analysis of a cracked strip under thermal impact based on memory-dependent heat conduction model. Eng Fract Mech. 2018;200:479–498.
- Xue ZN, Chen ZT, Tian XG. Transient thermal stress analysis for a circumferentially cracked hollow cylinder based on memory-dependent heat conduction model. Theor Appl Fract Mech. 2018;96:123–133.
- Sur A, Mondal S, Kanoria M. Influence of moving heat source on skin tissue in the context of two-temperature memory-dependent heat transport law. J Therm Stress. 2019;43(1):55–71. doi:https://doi.org/10.1080/01495739.2019.1660288.
- Sur A, Mondal S, Kanoria M. Memory response in the vibration of a micro-scale beam due to time-dependent thermal loading. Mech Based Des of Struct Mach. 2020. doi:https://doi.org/10.1080/15397734.2020.1745078.
- Mondal S, Sur A, Kanoria M. Transient heating within skin tissue due to time-dependent thermal therapy in the context of memory dependent heat transport law. Mech Based Des of Struct Mach. 2019. doi:https://doi.org/10.1080/15397734.2019.1686992.
- Mondal S, Sur A, Bhattacharya D, et al. Thermoelastic interaction in a magneto-thermoelastic rod with memory-dependent derivative due to the presence of moving heat source. Ind J Phys. 2019. doi:https://doi.org/10.1007/s12648-019-01593-6.
- Truesdell C, Toupin R. The classical field theories. In: Flugge S, editor. Handbuch der Physik. Berlin: Springer-Verlag; 1960.
- Dunkin JW, Eringen AC. On the propagation of waves in an electromagnetic elastic solid. Int J Eng Sci. 1963;1:461–495.
- Ericksen JL. Electromagnetic effects in thermoelastic materials. Math Mech Solids. 2002;7(2):165–189.
- Abbas IA. Generalized magneto-thermoelasticity in a fiber-reinforced anisotropic half-space. Int J Thermophys. 2011;32(5):1071–1085.
- Abbas IA. Eigenvalue approach in a three-dimensional generalized thermoelastic interactions with temperature-dependent material properties. Comput Math Appl. 2014;68(12):2036–2056.
- Abbas IA. Nonlinear transient thermal stress analysis of thick-walled FGM cylinder with temperature-dependent material properties. Meccanica. 2014;49(7):1697–1708.
- Abbas IA. A dual phase lag model on thermoelastic interaction in an infinite fiber-reinforced anisotropic medium with a circular hole. Mech Based Des of Struct Mach. 2015;43(4):501–513.
- Abbas IA, Youssef HM. Finite element analysis of two-temperature generalized magneto-thermoelasticity. Arch Appl Mech. 2009;79(10):917–925.
- Abbas IA, Youssef HM. Two-temperature generalized thermoelasticity under ramp-type heating by finite element method. Meccanica. 2013;48(2):331–339.
- Othman MIA, Abbas IA. Generalized thermoelasticity of thermal-shock problem in a non-homogeneous isotropic hollow cylinder with energy dissipation. Int J Thermophys. 2012;33(5):913–923.
- Othman MIA, Sur A. Transient response in an elasto-thermo-diffusive medium in the context of memory dependent heat transfer. Waves Random Complex Media. 2020. doi:https://doi.org/10.1080/17455030.2020.1737758.
- Sur A, Kanoria M. Modeling of memory-dependent derivative in a fibre-reinforced plate. Thin-Walled Struct. 2018;126:85–93.
- Chen PJ, Gurtin ME. On a theory of heat conduction involving two temperatures. ZAMP. 1968;19:614–627.
- Chen PJ, Gurtin ME, Williams WO. A note on non-simple heat conduction. ZAMP. 1968;19:969–970.
- Chen PJ, Gurtin ME, Williams WO. On the thermodynamics of non-simple elastic materials with two temperatures. ZAMP. 1969;20:107–112.
- Youssef HM. Theory of two-temperature-generalized thermoelasticity. IMA J Appl Math. 2006;71(3):383–390.
- Youssef HM. Two-temperature generalized thermoelastic infinite medium with cylindrical cavity subjected to moving heat source. Arch Appl Mech. 2010;80(11):1213–1224.
- Youssef HM. State-space approach to fractional order two-temperature generalized thermoelastic medium subjected to moving heat source. Mech Adv Mater Struct. 2013;20(1):47–60.
- Tzou DY. Macro to micro-scale heat transfer: the lagging behavior. Washington (DC): Taylor & Francis; 1996.
- Sur A. Wave propagation analysis of porous asphalts on account of memory responses. Mech Based Des of Struct Mach. 2020. doi:https://doi.org/10.1080/15397734.2020.1712553.
- Sur A, Mondal S, Kanoria M. Effect of nonlocality and memory responses in the thermoelatsic problem with a mode I crack. Waves Random Complex Media. 2020. doi:https://doi.org/10.1080/17455030.2020.1800860.
- Mondal S. Interactions due to a moving heat source in a thin slim rod under memory-dependent dual-phase lag magneto-thermo-visco-elasticity. Mech Time Dep Mater. 2019. doi:https://doi.org/10.1007/s11043-019-09418-z.
- Mondal S, Sur A. Photo-thermo-elastic wave propagation in an orthotropic semiconductor with a spherical cavity and memory responses. Waves in Random and Complex Media. 2020. doi:https://doi.org/10.1080/17455030.2019.1705426.
- Mondal S, Sur A, Kanoria M. Thermoelastic response of fiber-reinforced epoxy composite under continuous line heat source. Waves Random Complex Media. 2019. doi:https://doi.org/10.1080/17455030.2019.1699675.
- Deswal S, Kallkal KK. Two temperature magneto-thermoelasticity with initial stress state space formulation. J Thermodyn. 2013;2013:1–12.
- Quintanilla R, Racke R. A note on stability in three-phase-lag heat conduction. J Heat Mass Transf. 2008;51:24–29.
- Weiskopf WH. Stresses in soils under a foundation. J Franklin Inst. 1945;239(6):445–465.