Skip to main content
Top

18-04-2024 | Original Paper

Micropolar viscoelastic nanostructures subjected to laser-induced heat flux using the modified higher-order thermoelasticity model incorporating phase delay effects

Authors: Ahmed E. Abouelregal, Mohamed E. Nasr, Usama Muaz, Mohamed Abouhawwash, Khalil M. Khalil

Published in: Acta Mechanica

Login to get access

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

The gap between classical continuity and nanomechanics can be bridged using the concept of nonlocal elasticity. The Voigt viscoelastic model and the generalized dual-phase thermoelastic micropolar framework (DPL) are considered. Also, higher-order time derivatives with a two-phase delay are included in the heat transfer equation to generalize the proposed model. The mechanical and viscoelastic properties of suspensions, colloidal liquids, concretes, etc., can be described by applying the suggested model. As an example of using the proposed model, the effect of the pulsed heat transfer rate on the thermoelastic micropolar half-space was investigated. The analytical formulas for deformation, nonlocal thermal stress, and temperature change were derived after solving the governing equations using the Laplace transform technique. The graphical representation of numerical simulation results has been utilized to illustrate the effects of micropolarity, higher-order phenomena, phase delay, nonlocal index, and viscosity variables on a given distance. In this specific instance, the conclusions drawn from this analysis also incorporated the results of previously conducted research.
Literature
1.
go back to reference Kar, A., Kanoria, M.: Generalized thermo-visco-elastic problem of a spherical shell with three-phase-lag effect. Appl. Math. Model. 33(8), 3287–3298 (2009)MathSciNetCrossRef Kar, A., Kanoria, M.: Generalized thermo-visco-elastic problem of a spherical shell with three-phase-lag effect. Appl. Math. Model. 33(8), 3287–3298 (2009)MathSciNetCrossRef
2.
go back to reference Kalkal, K.K., Sheokand, S.K., Deswal, S.: Rotation and phase-lag effects in a micropolar thermo-viscoelastic half-space. Iran J. Sci. Technol. Trans. Mech. Eng. 43, 427–441 (2019)CrossRef Kalkal, K.K., Sheokand, S.K., Deswal, S.: Rotation and phase-lag effects in a micropolar thermo-viscoelastic half-space. Iran J. Sci. Technol. Trans. Mech. Eng. 43, 427–441 (2019)CrossRef
3.
go back to reference Ilioushin, A.A., Pobedria, B.E.: Fundamentals of the Mathematical Theories of Thermal Viscoelasticity. Nauka, Moscow (1970) Ilioushin, A.A., Pobedria, B.E.: Fundamentals of the Mathematical Theories of Thermal Viscoelasticity. Nauka, Moscow (1970)
5.
go back to reference Lord, H., Shulman, Y.: A generalized dynamical theory of thermoelasticity. J. Mech. Phys. Solid. 15, 299–309 (1967)CrossRef Lord, H., Shulman, Y.: A generalized dynamical theory of thermoelasticity. J. Mech. Phys. Solid. 15, 299–309 (1967)CrossRef
6.
7.
go back to reference Green, A.E., Naghdi, P.M.: A re-examination of the basic properties of thermomechanics. Proc. R. Soc. Lond. Ser. A 432, 171–194 (1991)CrossRef Green, A.E., Naghdi, P.M.: A re-examination of the basic properties of thermomechanics. Proc. R. Soc. Lond. Ser. A 432, 171–194 (1991)CrossRef
8.
go back to reference Green, A.E., Naghdi, P.M.: On damped heat waves in an elastic solid. J. Therm. Stresses 15, 253–264 (1992)CrossRef Green, A.E., Naghdi, P.M.: On damped heat waves in an elastic solid. J. Therm. Stresses 15, 253–264 (1992)CrossRef
10.
go back to reference Roychoudhuri, S.K.: On a thermoelastic three-phase-lag model. J. Therm. Stresses 30, 231–238 (2007)CrossRef Roychoudhuri, S.K.: On a thermoelastic three-phase-lag model. J. Therm. Stresses 30, 231–238 (2007)CrossRef
11.
go back to reference Abouelregal, A.E., Sedighi, H.M., Eremeyev, V.A.: Thermomagnetic behavior of a semiconductor material heated by pulsed excitation based on the fourth-order MGT photothermal model. Continuum Mech. Thermodyn. 35, 81–102 (2023)MathSciNetCrossRef Abouelregal, A.E., Sedighi, H.M., Eremeyev, V.A.: Thermomagnetic behavior of a semiconductor material heated by pulsed excitation based on the fourth-order MGT photothermal model. Continuum Mech. Thermodyn. 35, 81–102 (2023)MathSciNetCrossRef
12.
go back to reference Abouelregal, A.E., Sedighi, H.M.: Elastic thermal deformation of an infinite copper material due to cyclic heat supply using higher-order nonlocal thermal modeling. Metals 12(11), 1927 (2022)CrossRef Abouelregal, A.E., Sedighi, H.M.: Elastic thermal deformation of an infinite copper material due to cyclic heat supply using higher-order nonlocal thermal modeling. Metals 12(11), 1927 (2022)CrossRef
13.
go back to reference Moaaz, O., Abouelregal, A.E., Alesemi, M.: Moore–Gibson–Thompson photothermal model with a proportional caputo fractional derivative for a rotating magneto-thermoelastic semiconducting material. Mathematics 10(17), 3087 (2022)CrossRef Moaaz, O., Abouelregal, A.E., Alesemi, M.: Moore–Gibson–Thompson photothermal model with a proportional caputo fractional derivative for a rotating magneto-thermoelastic semiconducting material. Mathematics 10(17), 3087 (2022)CrossRef
14.
go back to reference Eringen, A.C.: Linear theory of micropolar elasticity. J. Appl. Math. Mech. 15, 909–923 (1966)MathSciNet Eringen, A.C.: Linear theory of micropolar elasticity. J. Appl. Math. Mech. 15, 909–923 (1966)MathSciNet
15.
go back to reference Eringen, A.C.: Foundations of Micropolar Thermoelasticity, Udline Course and Lectures 23, International Centre for Mechanical Science. Springer, Berlin (1970) Eringen, A.C.: Foundations of Micropolar Thermoelasticity, Udline Course and Lectures 23, International Centre for Mechanical Science. Springer, Berlin (1970)
16.
go back to reference Eringen, A.C.: Microcontinuum Field Theories—I, Foundations and Solids. Springer, Berlin (1999)CrossRef Eringen, A.C.: Microcontinuum Field Theories—I, Foundations and Solids. Springer, Berlin (1999)CrossRef
17.
go back to reference Nowacki, W.: Theory of Asymmetric Elasticity. Pergamon, Oxford (1986) Nowacki, W.: Theory of Asymmetric Elasticity. Pergamon, Oxford (1986)
18.
19.
go back to reference Chandrasekharaiah, D.S.: Heat-flux dependent micropolar thermoelasticity. Int. J. Eng. Sci. 24(8), 1389–1395 (1986)CrossRef Chandrasekharaiah, D.S.: Heat-flux dependent micropolar thermoelasticity. Int. J. Eng. Sci. 24(8), 1389–1395 (1986)CrossRef
20.
go back to reference Boschi, E., Ieşan, D.: A generalized theory of linear micropolar thermoelasticity. Meccanica 8(3), 154–157 (1973)CrossRef Boschi, E., Ieşan, D.: A generalized theory of linear micropolar thermoelasticity. Meccanica 8(3), 154–157 (1973)CrossRef
21.
go back to reference Nowacki, W.: Couple stresses in the theory of thermoelasticity I. Bull. Acad. Polon. Sci. Ser. Sci. Tech. 14, 129–138 (1966) Nowacki, W.: Couple stresses in the theory of thermoelasticity I. Bull. Acad. Polon. Sci. Ser. Sci. Tech. 14, 129–138 (1966)
22.
go back to reference Nowacki, W.: Couple stresses in the theory of thermoelasticity II. Bull Acad. Polon. Sci. Ser. Sci. Tech. 14, 263–272 (1966) Nowacki, W.: Couple stresses in the theory of thermoelasticity II. Bull Acad. Polon. Sci. Ser. Sci. Tech. 14, 263–272 (1966)
23.
go back to reference Nowacki, W.: Couple stresses in the theory of thermoelasticity III. Bull. Acad. Polon. Sci. Ser. Sci. Tech. 14, 801–809 (1966) Nowacki, W.: Couple stresses in the theory of thermoelasticity III. Bull. Acad. Polon. Sci. Ser. Sci. Tech. 14, 801–809 (1966)
24.
go back to reference Tauchert, T.R., Claus, W.D., Jr., Ariman, T.: The linear theory of micropolar thermoelasticity. Int. J. Eng. Sci. 6, 37–47 (1968)CrossRef Tauchert, T.R., Claus, W.D., Jr., Ariman, T.: The linear theory of micropolar thermoelasticity. Int. J. Eng. Sci. 6, 37–47 (1968)CrossRef
25.
go back to reference Dhaliwal, R.S., Singh, A.: Micropolar thermoelasticity. In: Hetnarski, R. (ed.) Thermal Stresses II, Mechanical and Mathematical Methods ser 2. North Holland, Amsterdam (1987) Dhaliwal, R.S., Singh, A.: Micropolar thermoelasticity. In: Hetnarski, R. (ed.) Thermal Stresses II, Mechanical and Mathematical Methods ser 2. North Holland, Amsterdam (1987)
26.
go back to reference Chandrasekharaiah, D.S.: Variational and reciprocal principles in micropolar thermoelasticity. Int. J. Eng. Sci. 25, 55–63 (1987)MathSciNetCrossRef Chandrasekharaiah, D.S.: Variational and reciprocal principles in micropolar thermoelasticity. Int. J. Eng. Sci. 25, 55–63 (1987)MathSciNetCrossRef
27.
go back to reference Ciarletta, M.: A theory of micropolar thermoelasticity without energy dissipation. J. Therm. Stress. 22, 581–594 (1999)MathSciNetCrossRef Ciarletta, M.: A theory of micropolar thermoelasticity without energy dissipation. J. Therm. Stress. 22, 581–594 (1999)MathSciNetCrossRef
28.
go back to reference Eringen, A.C.: Nonlocal Continuum Field Theories. Springer, New York (2002) Eringen, A.C.: Nonlocal Continuum Field Theories. Springer, New York (2002)
29.
go back to reference Fleck, N.A., Muller, G.M., Ashby, M.F., Hutchinson, J.W.: Strain gradient plasticity: theory and experiment. Acta Metall. Mater. 42(2), 475–487 (1994)CrossRef Fleck, N.A., Muller, G.M., Ashby, M.F., Hutchinson, J.W.: Strain gradient plasticity: theory and experiment. Acta Metall. Mater. 42(2), 475–487 (1994)CrossRef
30.
go back to reference Wang, B.L., Li, J.E.: A rigid line inclusion in a nonlocal elastic medium—mode I deformation. Eng. Fract. Mech. 267, 108433 (2022)CrossRef Wang, B.L., Li, J.E.: A rigid line inclusion in a nonlocal elastic medium—mode I deformation. Eng. Fract. Mech. 267, 108433 (2022)CrossRef
32.
go back to reference Eringen, A.C.: Theory of nonlocal thermoelasticity. Int. J. Eng. Sci. 12(12), 1063–1077 (1974)CrossRef Eringen, A.C.: Theory of nonlocal thermoelasticity. Int. J. Eng. Sci. 12(12), 1063–1077 (1974)CrossRef
33.
go back to reference Eringen, A.C.: Memory-dependent nonlocal electromagnetic elastic solids and superconductivity. J. Math. Phys. 32(3), 787–796 (1991)MathSciNetCrossRef Eringen, A.C.: Memory-dependent nonlocal electromagnetic elastic solids and superconductivity. J. Math. Phys. 32(3), 787–796 (1991)MathSciNetCrossRef
34.
go back to reference Yang, F., Chong, A., Lam, D.C.C., Tong, P.: Couple stress based strain gradient theory for elasticity. Int. J. Solids Struct. 39(10), 2731–2743 (2002)CrossRef Yang, F., Chong, A., Lam, D.C.C., Tong, P.: Couple stress based strain gradient theory for elasticity. Int. J. Solids Struct. 39(10), 2731–2743 (2002)CrossRef
35.
go back to reference Reddy, J.: Nonlocal theories for bending, buckling and vibration of beam. Int. J. Eng. Sci. 45(2–8), 288–307 (2007)CrossRef Reddy, J.: Nonlocal theories for bending, buckling and vibration of beam. Int. J. Eng. Sci. 45(2–8), 288–307 (2007)CrossRef
36.
go back to reference Li, L., Li, X., Hu, Y.: Free vibration analysis of nonlocal strain gradient beams made of functionally graded material. Int. J. Eng. Sci. 102, 77–92 (2016)CrossRef Li, L., Li, X., Hu, Y.: Free vibration analysis of nonlocal strain gradient beams made of functionally graded material. Int. J. Eng. Sci. 102, 77–92 (2016)CrossRef
37.
go back to reference Eringen, A.C.: Plane waves in nonlocal micropolar elasticity. Int. J. Eng. Sci. 22(8–10), 1113–1121 (1984)CrossRef Eringen, A.C.: Plane waves in nonlocal micropolar elasticity. Int. J. Eng. Sci. 22(8–10), 1113–1121 (1984)CrossRef
39.
go back to reference Eringen, A.C.: Microcontinuum Field Theories: I. Foundations and Solids. Springer, New York (1999)CrossRef Eringen, A.C.: Microcontinuum Field Theories: I. Foundations and Solids. Springer, New York (1999)CrossRef
40.
go back to reference Eringen, A.C.: On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J. Appl. Phys. 54, 4703–4710 (1983)CrossRef Eringen, A.C.: On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves. J. Appl. Phys. 54, 4703–4710 (1983)CrossRef
41.
go back to reference Tzou, D.Y.: Experimental support for the lagging behavior in heat propagation. J. Thermophys. Heat Transf. 9(4), 686–693 (1995)CrossRef Tzou, D.Y.: Experimental support for the lagging behavior in heat propagation. J. Thermophys. Heat Transf. 9(4), 686–693 (1995)CrossRef
42.
go back to reference Tzou, D.Y.: A unified field approach for heat conduction from macro-to micro-scales. J. Heat Transf. 117(1), 8–16 (1995)CrossRef Tzou, D.Y.: A unified field approach for heat conduction from macro-to micro-scales. J. Heat Transf. 117(1), 8–16 (1995)CrossRef
43.
go back to reference Abouelregal, A.E., Zenkour, A.M.: Effect of phase lags on thermoelastic functionally graded microbeams subjected to ramp-type heating. IJST Trans. Mech. Eng. 38(M2), 321–335 (2014) Abouelregal, A.E., Zenkour, A.M.: Effect of phase lags on thermoelastic functionally graded microbeams subjected to ramp-type heating. IJST Trans. Mech. Eng. 38(M2), 321–335 (2014)
44.
go back to reference Abouelregal, A.E., Moustapha, M.V., Nofal, T.A., Rashid, S., Ahmad, H.: Generalized thermoelasticity based on higher-order memory-dependent derivative with time delay. Results Phys. 20, 103705 (2021)CrossRef Abouelregal, A.E., Moustapha, M.V., Nofal, T.A., Rashid, S., Ahmad, H.: Generalized thermoelasticity based on higher-order memory-dependent derivative with time delay. Results Phys. 20, 103705 (2021)CrossRef
45.
go back to reference Mallik, S.H., Kanoria, M.: Generalized thermoviscoelastic interaction due to periodically varying heat source with three–phase–lag effect. Eur. J. Mech. A/Solids 29, 695–703 (2010)CrossRef Mallik, S.H., Kanoria, M.: Generalized thermoviscoelastic interaction due to periodically varying heat source with three–phase–lag effect. Eur. J. Mech. A/Solids 29, 695–703 (2010)CrossRef
46.
go back to reference Sharma, S.R., Sharma, M.K., Sharma, D.K.: Vibrations of inhomogeneous visco thermoelastic nonlocal hollow sphere under the effect of three-phase-lag model. J. Solid Mech. 13(1), 95–113 (2021)MathSciNet Sharma, S.R., Sharma, M.K., Sharma, D.K.: Vibrations of inhomogeneous visco thermoelastic nonlocal hollow sphere under the effect of three-phase-lag model. J. Solid Mech. 13(1), 95–113 (2021)MathSciNet
47.
go back to reference Jha, B.K., Danjuma, Y.J.: Transient Dean flow in a channel with suction/injection: A semi-analytical approach. Proc. Inst. Mech. Eng. Part E J. Proc. Mech. Eng. 233(5), 1036–1044 (2019)CrossRef Jha, B.K., Danjuma, Y.J.: Transient Dean flow in a channel with suction/injection: A semi-analytical approach. Proc. Inst. Mech. Eng. Part E J. Proc. Mech. Eng. 233(5), 1036–1044 (2019)CrossRef
48.
go back to reference Honig, G., Hirdes, U.: A method for the numerical inversion of Laplace transforms. Comput. Appl. Math. 10(1), 113–132 (1984)MathSciNetCrossRef Honig, G., Hirdes, U.: A method for the numerical inversion of Laplace transforms. Comput. Appl. Math. 10(1), 113–132 (1984)MathSciNetCrossRef
49.
go back to reference Tzou, D.Y.: Macro to Microscale Heat Transfer: The Lagging Behavior. Taylor and Francis, Washington, D.C. (1997) Tzou, D.Y.: Macro to Microscale Heat Transfer: The Lagging Behavior. Taylor and Francis, Washington, D.C. (1997)
50.
go back to reference Kumar, S., Kadian, A., Kalkal, K.K.: Dual-phase-lag model for a nonlocal micropolar thermoelastic half-space subjected to gravitational field and inclined load. Int. J. Numer. Methods Heat Fluid Flow 32(6), 1999–2026 (2022)CrossRef Kumar, S., Kadian, A., Kalkal, K.K.: Dual-phase-lag model for a nonlocal micropolar thermoelastic half-space subjected to gravitational field and inclined load. Int. J. Numer. Methods Heat Fluid Flow 32(6), 1999–2026 (2022)CrossRef
51.
go back to reference Yang, W., Chen, Z.: Nonlocal dual-phase-lag heat conduction and the associated nonlocal thermal-viscoelastic analysis. Int. J. Heat Mass Transf. 156, 119752 (2020)CrossRef Yang, W., Chen, Z.: Nonlocal dual-phase-lag heat conduction and the associated nonlocal thermal-viscoelastic analysis. Int. J. Heat Mass Transf. 156, 119752 (2020)CrossRef
52.
go back to reference Othman, M.I.A., Abd-Elaziz, E.M.: Dual-phase-lag model on micropolar thermoelastic rotating medium under the effect of thermal load due to laser pulse. Indian J. Phys. 94, 999–1008 (2020)CrossRef Othman, M.I.A., Abd-Elaziz, E.M.: Dual-phase-lag model on micropolar thermoelastic rotating medium under the effect of thermal load due to laser pulse. Indian J. Phys. 94, 999–1008 (2020)CrossRef
53.
go back to reference Othman, M.I.A., Hasona, W.M., Abd-Elaziz, E.M.: Effect of rotation on micropolar generalized thermoelasticity with two temperatures using a dual-phase lag model. Can. J. Phys. 92(2), 149–158 (2014)CrossRef Othman, M.I.A., Hasona, W.M., Abd-Elaziz, E.M.: Effect of rotation on micropolar generalized thermoelasticity with two temperatures using a dual-phase lag model. Can. J. Phys. 92(2), 149–158 (2014)CrossRef
54.
go back to reference Lata, P., Himanshi, H.: Orthotropic magneto-thermoelastic solid with higher order dual-phase-lag model in frequency domain. Struct. Eng. Mech. 77(3), 315–327 (2021) Lata, P., Himanshi, H.: Orthotropic magneto-thermoelastic solid with higher order dual-phase-lag model in frequency domain. Struct. Eng. Mech. 77(3), 315–327 (2021)
55.
go back to reference Abouelregal, A.E.: A novel model of nonlocal thermoelasticity with time derivatives of higher order. Math. Methods Appl. Sci. 43(11), 6746–6760 (2020)MathSciNetCrossRef Abouelregal, A.E.: A novel model of nonlocal thermoelasticity with time derivatives of higher order. Math. Methods Appl. Sci. 43(11), 6746–6760 (2020)MathSciNetCrossRef
56.
go back to reference Li, X.F., Zhang, H., Lee, K.Y.: Dependence of Young’s modulus of nanowires on surface effect. Int. J. Mech. Sci. 81, 120–125 (2014)CrossRef Li, X.F., Zhang, H., Lee, K.Y.: Dependence of Young’s modulus of nanowires on surface effect. Int. J. Mech. Sci. 81, 120–125 (2014)CrossRef
57.
go back to reference Kambali, P. N., V.S., N., Pandey, A.K.: Surface and nonlocal effects on response of linear and nonlinear NEMS devices. Appl. Math. Model. 43, 252–267 Kambali, P. N., V.S., N., Pandey, A.K.: Surface and nonlocal effects on response of linear and nonlinear NEMS devices. Appl. Math. Model. 43, 252–267
58.
go back to reference Yu, Y.J., Xue, Z.N., Li, C.L., Tian, X.G.: Buckling of nanobeams under nonuniform temperature based on nonlocal thermoelasticity. Compos. Struct. 146, 108–113 (2016)CrossRef Yu, Y.J., Xue, Z.N., Li, C.L., Tian, X.G.: Buckling of nanobeams under nonuniform temperature based on nonlocal thermoelasticity. Compos. Struct. 146, 108–113 (2016)CrossRef
59.
go back to reference Strikwerda, J.C., Scott, A.M.: Thermoelastic response to a short laser pulse. J. Therm. Stress. 7(1), 1–17 (1984)CrossRef Strikwerda, J.C., Scott, A.M.: Thermoelastic response to a short laser pulse. J. Therm. Stress. 7(1), 1–17 (1984)CrossRef
60.
go back to reference Abouelregal, A.E., Dassios, I., Moaaz, O.: Moore–Gibson–Thompson thermoelastic model effect of laser-induced microstructures of a microbeam sitting on visco-Pasternak foundations. Appl. Sci. 12, 9206 (2022)CrossRef Abouelregal, A.E., Dassios, I., Moaaz, O.: Moore–Gibson–Thompson thermoelastic model effect of laser-induced microstructures of a microbeam sitting on visco-Pasternak foundations. Appl. Sci. 12, 9206 (2022)CrossRef
61.
go back to reference Tang, D.W., Araki, N.: The wave characteristics of thermal conduction in metallic films irradiated by ultra-short laser pulses. J. Phys. D Appl. Phys. 29, 2527–2533 (1996)CrossRef Tang, D.W., Araki, N.: The wave characteristics of thermal conduction in metallic films irradiated by ultra-short laser pulses. J. Phys. D Appl. Phys. 29, 2527–2533 (1996)CrossRef
Metadata
Title
Micropolar viscoelastic nanostructures subjected to laser-induced heat flux using the modified higher-order thermoelasticity model incorporating phase delay effects
Authors
Ahmed E. Abouelregal
Mohamed E. Nasr
Usama Muaz
Mohamed Abouhawwash
Khalil M. Khalil
Publication date
18-04-2024
Publisher
Springer Vienna
Published in
Acta Mechanica
Print ISSN: 0001-5970
Electronic ISSN: 1619-6937
DOI
https://doi.org/10.1007/s00707-024-03910-5

Premium Partners