journal article·2026-09

Nonlocal coupled thermoelasticity and diffusion with multiple relaxation times for hollow solids

Ahmed E. Abouelregal, Mohammed Aldandani, Marin Marin

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OpenAlex topics: Thermoelastic and Magnetoelastic Phenomena · Shape Memory Alloy Transformations · Nonlocal and gradient elasticity in micro/nano structures

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References (68)

Show source-provided references
1. Mehrer, H.: Diffusion in solids: fundamentals, methods, materials, diffusion-controlled processes. Springer Berlin Heidelberg, Berlin, Heidelberg (2007)10.1007/978-3-540-71488-0 ↗
2. Gupta, D. (ed.): Diffusion processes in advanced technological materials. Springer Science & Business Media (2010)
3. Sharma, J.N.: Generalized thermoelastic diffusive waves in heat conducting materials. J. Sound Vib. 301(3–5), 979–993 (2007)10.1016/j.jsv.2006.11.001 ↗
4. Chandrasekharaiah, D.S.: Hyperbolic thermoelasticity: a review of recent literature. Appl. Mech. Rev. 51(12), 705–729 (1998)10.1115/1.3098984 ↗
5. Lord, H.W., Shulman, Y.: A generalized dynamical theory of thermoelasticity. J. Mech. Phys. Solids 15(5), 299–309 (1967)10.1016/0022-5096(67)90024-5 ↗
6. Van der Merwe, A.J., Van Rensburg, N.J., Sieberhagen, R.H.: Comparing the dual phase lag, Cattaneo-Vernotte and Fourier heat conduction models using modal analysis. Appl. Math. Comput. 396, 125934 (2021)
7. Green, A.E., Lindsay, K.: Thermoelasticity. J. Elast. 2(1), 1–7 (1972)10.1007/BF00045689 ↗
8. Wilkinson, D.S.: Mass transport in solids and fluids. Cambridge university press (2000)10.1017/CBO9781139171267 ↗
9. Won, Y.Y., Ramkrishna, D.: Revised formulation of Fick’s, Fourier’s, and Newton’s laws for spatially varying linear transport coefficients. ACS Omega 4(6), 11215–11222 (2019)10.1021/acsomega.9b00736 ↗
10. Nowacki, W.: Dynamic problems of diffusion in solids. Eng. Fract. Mech. 8(1), 261–266 (1976)10.1016/0013-7944(76)90091-6 ↗
11. Nowacki, W.: Dynamic Problems of Thermoelasticity. Springer Science & Business Media (1975a)
12. Nowacki, W.: Thermodiffusion in solids. NASA STI/Recon Techn. Rep. A 13(2), 143–158 (1975b)
13. Sherief, H.H., Hamza, F.A., Saleh, H.A.: The theory of generalized thermoelastic diffusion. Int. J. Eng. Sci. 42(5–6), 591–608 (2004)
14. Knyazeva, A.G.: Thermodynamic generalization of the theory of thermoelastic diffusion for a medium with changing density. PNRPU Mech. Bull. 3, 101–113 (2025)10.15593/perm.mech/2025.3.09 ↗
15. Mallick, A., Biswas, S.: Dynamic analysis of Rayleigh waves in nonlocal porous orthotropic thermoelastic medium with diffusion: Mallick A et al. Appl. Phys. A 131(6), 506 (2025)10.1007/s00339-025-08607-7 ↗
16. Abouelregal, A.E., Marin, M., Alhassan, Y., Atta, D.: A novel space–time nonlocal thermo-viscoelastic model with two-phase lags for analyzing heat diffusion in a half-space subjected to a heat source. Iran. J. Sci. Technol. Trans. Mech. Eng. 49(3), 1315–1332 (2025a)10.1007/s40997-025-00835-9 ↗
17. Othman, M.I., Said, S.M., Gamal, E.M., Gepreel, K.A.: Modeling temperature-dependent elasticity and diffusion in fiber-reinforced composites under inclined loading. Iran. J. Sci. Techn. Trans. Mech. Eng. 49(5), 2247–2262 (2025)10.1007/s40997-025-00884-0 ↗
18. Abbas, M.F., Zaky, M.F., Ahmed, B.A., Mahrous, S.A.: A study of the dynamic response of two concentric spheres in the context of thermoelastic diffusion with internal heat source. Case Stud. Therm. Eng. 73, 106540 (2025)10.1016/j.csite.2025.106540 ↗
19. Goel, S., Gupta, V., Kumar, M.: Effect of three-phase-lag thermal and three-phase-lag diffusion models on waves at the boundary of elastic and thermoelastic diffusion medium. Int. J. Mod. Phys. B 39(03), 2550025 (2025)10.1142/S0217979225500250 ↗
20. Abouelregal, A.E., Marin, M., Alhassan, Y., Elzayady, M.: Thermoelastic microbeams subjected to axial force and laser pulse energy absorption embedded in a viscoelastic foundation with fractional Kelvin-Voigt model. J. Therm. Stress. 48(7), 753–782 (2025b)10.1080/01495739.2025.2486769 ↗
21. Li, Y., Zhao, L., He, T., Tian, X., Liao, K.: The ultrashort pulse laser ablation model of silicon based on the generalized thermoelastic theory with spatio-temporal nonlocal effect. J. Therm. Stress. 46(12), 1329–1358 (2023)10.1080/01495739.2023.2268141 ↗
22. Lazopoulos, K.: Non-local continuum mechanics and fractional calculus. Mech. Res. Commun. 33(6), 753–757 (2006)10.1016/j.mechrescom.2006.05.001 ↗
23. Guyer, R.A., Krumhansl, J.A.: Solution of the linearized phonon Boltzmann equation. Phys. Rev. 148(2), 766 (1966)10.1103/PhysRev.148.766 ↗
24. Li, X., Li, Y., Luo, P., Tian, X.: Relationship between the nonlocal effect and lagging behavior in bioheat transfer. J. Heat Transf. 143(5), 051201 (2021a)10.1115/1.4049997 ↗
25. Tzou, D.Y., Guo, Z.Y.: Nonlocal behavior in thermal lagging. Int. J. Therm. Sci. 49(7), 1133–1137 (2010)10.1016/j.ijthermalsci.2010.01.022 ↗
26. Tzou, D.Y.: The generalized lagging response in small-scale and high-rate heating. Int. J. Heat Mass Transf. 38(17), 3231–3240 (1995)10.1016/0017-9310(95)00052-B ↗
27. Tzou, D.Y., Chen, J.K.: Thermal lagging in random media. J. Thermophys. Heat Transf. 12(4), 567–574 (1998)10.2514/2.6377 ↗
28. Kumar, R., Vashishth, A.K., Ghangas, S.: Nonlocal heat conduction approach in a bi-layer tissue during magnetic fluid hyperthermia with dual phase lag model. Bio-Med. Mater. Eng. 30(4), 387–402 (2019)10.3233/BME-191061 ↗
29. Sherief, H.H., El-Sayed, A.M.A., Abd El-Latief, A.: Fractional order theory of thermoelasticity. Int. J. Solids Struct. 47(2), 269–275 (2010)10.1016/j.ijsolstr.2009.09.034 ↗
30. Yu, Y.J., Tian, X.G., Lu, T.J.: On fractional order generalized thermoelasticity with micromodeling. Acta Mech. 224(12), 2911–2927 (2013)10.1007/s00707-013-0913-3 ↗
31. Ahmadi, H.R., Rahimi, Z., Sumelka, W.: Thermoelastic damping in orthotropic and isotropic NEMS resonators accounting for double nonlocal thermoelastic effects. J. Therm. Stresses 44(3), 342–358 (2020)10.1080/01495739.2020.1853639 ↗
32. Aydinlik, S., Kiris, A., Sumelka, W.: Three-dimensional plate dynamics in the framework of space-fractional generalized thermoelasticity: theory and validation. AIAA J. 62(3), 1076–1093 (2024)10.2514/1.J063310 ↗
33. Hobiny, A., Abbas, I.A.: A study on the thermoelastic interaction in two-dimension orthotropic materials under the fractional derivative model. Alex. Eng. J. 64, 615–625 (2023)10.1016/j.aej.2022.08.047 ↗
34. Nika, G.: A gradient system for a higher-gradient generalization of Fourier’s law of heat conduction. Mod. Phys. Lett. B 37(11), 2350011 (2023)10.1142/S0217984923500112 ↗
35. Webb, S.W., Pruess, K.: The use of Fick’s law for modeling trace gas diffusion in porous media. Transp. Porous Media 51(3), 327–341 (2003)10.1023/A:1022379016613 ↗
36. Cervera, M., Lafontaine, N., Rossi, R., Chiumenti, M.: Explicit mixed strain–displacement finite elements for compressible and quasi-incompressible elasticity and plasticity. Comput. Mech. 58(3), 511–532 (2016)10.1007/s00466-016-1305-z ↗
37. Nandagopal, P.E., N.S.: Conservation of energy and first law of thermodynamics. In: Fluid and thermal sciences: a practical approach for students and professionals, pp. 341–369. Springer International Publishing, Cham (2022)10.1007/978-3-030-93940-3_14 ↗
38. Vrentas, J.S., Vrentas, C.M.: Diffusion and Mass Transfer. CRC Press (2016)10.1201/b12923 ↗
39. Sherief, H.H., Saleh, H.A.: A half-space problem in the theory of generalized thermoelastic diffusion. Int. J. Solids Struct. 42(15), 4484–4493 (2005)10.1016/j.ijsolstr.2005.01.001 ↗
40. Sherief, H.H., El-Maghraby, N.M.: A thick plate problem in the theory of generalized thermoelastic diffusion. Int. J. Thermophys. 30(6), 2044–2057 (2009)10.1007/s10765-009-0689-9 ↗
41. Jahanian, S., Sabbaghian, M.: Thermoelastoplastic and residual stresses in a hollow cylinder with temperature-dependent properties. J. Press. Vessel. Technol. 112(1), 85–91 (1990)10.1115/1.2928592 ↗
42. Lorge, O., Briscoe, B.J., Dang, P.: Gas induced damage in poly (vinylidene fluoride) exposed to decompression. Polymer 40(11), 2981–2991 (1999)10.1016/S0032-3861(98)00527-8 ↗
43. Rambert, G., Jugla, G., Grandidier, J.C., Cangemi, L.: A modelling of the direct couplings between heat transfer, mass transport, chemical reactions and mechanical behaviour. Numerical implementation to explosive decompression. Compos. Part A Appl. Sci. Manuf. 37(4), 571–584 (2006)10.1016/j.compositesa.2005.05.021 ↗
44. Zverev, N.A., Zemskov, A.V.: Modeling unsteady elastic diffusion processes in a hollow cylinder taking into account the relaxation of diffusion fluxes. Math. Models Comput. Simul. 15(4), 686–697 (2023)10.1134/S2070048223040208 ↗
45. Tzou, D.Y.: Macro-to microscale heat transfer: the lagging behavior. Wiley (2014)10.1002/9781118818275 ↗
46. Abouelregal, A.E., Alesemi, M.: Fractional Moore-Gibson-Thompson heat transfer model with nonlocal and nonsingular kernels of a rotating viscoelastic annular cylinder with changeable thermal properties. PLoS ONE 17(6), e0269862 (2022)10.1371/journal.pone.0269862 ↗
47. Dubner, H., Abate, J.: Numerical inversion of Laplace transforms by relating them to the finite Fourier cosine transform. J. ACM 15(1), 115–123 (1968)10.1145/321439.321446 ↗
48. Crump, K.S.: Numerical inversion of Laplace transforms using a Fourier series approximation. J. ACM 23(1), 89–96 (1976)10.1145/321921.321931 ↗
49. Honig, G., Hirdes, U.: A method for the numerical inversion of Laplace transforms. J. Comput. Appl. Math. 10(1), 113–132 (1984)10.1016/0377-0427(84)90075-X ↗
50. Durbin, F.: Numerical inversion of Laplace transforms: an efficient improvement to Dubner and Abate’s method. Comput. J. 17(4), 371–376 (1974)10.1093/comjnl/17.4.371 ↗
51. Davies, B., Martin, B.: Numerical inversion of the Laplace transform: a survey and comparison of methods. J. Comput. Phys. 33(1), 1–32 (1979)10.1016/0021-9991(79)90025-1 ↗
52. Wang, Q., Zhan, H.: On different numerical inverse Laplace methods for solute transport problems. Adv. Water Resour. 75, 80–92 (2015)10.1016/j.advwatres.2014.11.001 ↗
53. Adel, M., Sharma, R., Kumar, R., Sharma, P.K., Mahdy, A.M., Lotfy, K.: Thermoelastic-diffusive response of a half-space under moving loads via Moore-Gibson-Thompson model. Int. Commun. Heat Mass Transf. 166, 109226 (2025)10.1016/j.icheatmasstransfer.2025.109226 ↗
54. Sharma, S., Marin, M., Altenbach, H.: Elastodynamic interactions in thermoelastic diffusion including non-local and phase lags. ZAMM-J. Appl. Math. Mech. Zeitschrift Für Angewandte Mathematik und Mechanik 105(1), e202401059 (2025a)10.1002/zamm.202401059 ↗
55. Li, C., Guo, H., Tian, X.: A size-dependent generalized thermoelastic diffusion theory and its application. J. Therm. Stresses 40(5), 603–626 (2017)10.1080/01495739.2017.1300786 ↗
56. Li, Y., He, T., Luo, P., Tian, X.: A generalized thermoelastic diffusion problem of thin plate heated by the ultrashort laser pulses with memory-dependent and spatial nonlocal effect. J. Therm. Stresses 44(3), 261–280 (2021b)10.1080/01495739.2020.1870905 ↗
57. Li, C., He, T., Tian, X.: Nonlocal theory of thermoelastic diffusive materials and its application in structural dynamic thermo-elasto-diffusive responses analysis. Waves Random Complex Media 32(1), 174–203 (2022)10.1080/17455030.2020.1767828 ↗
58. Alshehri, H.M., Lotfy, K.: A photo-thermoacoustic-diffusion model for hydro-poroelastic nano-composite semiconductor medium with chemical potential. Phys. Fluids 37(1), 017121 (2025)10.1063/5.0252033 ↗
59. Sharma, S., Devi, S., Kumar, R., Marin, M.: Examining basic theorems and plane waves in the context of thermoelastic diffusion using a multi-phase-lag model with temperature dependence. Mech. Adv. Mater. Struct. 32(8), 1810–1827 (2025b)10.1080/15376494.2024.2370523 ↗
60. Mahrous, S.A., Zaky, M.F., Abbas, M.F., Sherief, H.H.: Two-dimensional problem for an infinite body of two coaxial cylinders under the action of a solenoidal body force in the theory of thermoelastic diffusion. J. Therm. Stresses 47(10), 1371–1385 (2024)10.1080/01495739.2024.2395575 ↗
61. Sharma, D.K., Thakur, D., Walia, V., Sarkar, N.: Free vibration analysis of a nonlocal thermoelastic hollow cylinder with diffusion. J. Therm. Stress. 43(8), 981–997 (2020)10.1080/01495739.2020.1764425 ↗
62. Eringen, A.C.: Vistas of nonlocal continuum physics. Int. J. Eng. Sci. 30(10), 1551–1565 (1992)
63. Geetanjali, G., Sharma, P.K.: Vibrational analysis of transversely isotropic hollow cylinder based on fractional generalized thermoelastic diffusion models with nonlocal effects. Acta Mech. 235(1), 147–166 (2024)10.1007/s00707-023-03738-5 ↗
64. Guo, Y., Bai, Y., Sun, L., Shi, P., Xiong, C., Yu, K.: Dynamic response of an infinite body with a cylindrical tunnel cavity under fractional-order thermoviscoelastic diffusion theory with various shock loads. Continuum Mech. Thermodyn. 37(1), 1–20 (2025)10.1007/s00161-024-01354-9 ↗
65. Abouelregal, A.E., Elhagary, M.A., Soleiman, A., Khalil, K.M.: Generalized thermoelastic-diffusion model with higher-order fractional time-derivatives and four-phase-lags. Mech. Based des. Struct. Mach. 50(3), 897–914 (2022)10.1080/15397734.2020.1730189 ↗
66. Abouelregal, A.E., Elzayady, M.E., Marin, M., Foul, A., Askar, S.S.: Thermoelastic modeling of functionally graded materials with cylindrical cavities utilizing higher-order fractional heat transfer models incorporating time delays. Continuum Mech. Thermodyn. 37(2), 31 (2025c)10.1007/s00161-025-01360-5 ↗
67. Atta, D., Abouelregal, A.E., Sedighi, H.M., Alharb, R.A.: Thermodiffusion interactions in a homogeneous spherical shell based on the modified Moore–Gibson–Thompson theory with two time delays. Mech. Time-Depend. Mater. 28(2), 617–638 (2024)10.1007/s11043-023-09598-9 ↗
68. Zverev, N.A., Zemskov, A.V., Yaganov, V.M.: Modeling of elastic diffusion processes in a hollow cylinder under the action of unsteady volume perturbations. Chebyshevskii Sb. (2024). https://doi.org/10.22405/2226-8383-2024-25-2-296-31710.22405/2226-8383-2024-25-2-296-317 ↗