2606004375
  • Open Access
  • Article

Analysis of Multi-Field Influences on a Fiber-Reinforced Thermoelastic Medium Using the Modified Green–Naghdi Theory

  • Mohamed I.A. Othman *,   
  • Samia M. Said,   
  • Esraa M. Gamal *

Received: 03 Apr 2026 | Revised: 18 May 2026 | Accepted: 23 Jun 2026 | Published: 15 Jul 2026

Abstract

The main interest of the present article is to dealing with wave extension in a fiber-reinforced thermoelastic solid under the influence of magnetic field and initial stress. The immediate problem is represented via different forms of the Green-Naghdi framework. Analytical expressions of the physical variables are acquire by using new analysis of normal mode with eigenvalue approach technique. Numerical outcomes are shown graphically and the results received are analyzed. The most significant points are highlighted. The outcomes are shown the a notable impact of the magnetic field, initial stress, and fiber-reinforcement on the physical fields. The framework is useful in modeling thermoelastic behavior during laser processing, welding, and additive manufacturing, where rapid heating and cooling induce complex stress fields. Fiber-reinforced thermoelastic models are applicable to biological tissues and biomedical devices, particularly in laser-based therapies and thermal diagnostics where finite-speed heat conduction is significant. Applications include reactor components and containment structures where fiber-reinforced materials experience intense thermal gradients and require accurate prediction of thermoelastic stresses under non-Fourier heat transfer.

References 

  • 1.

    Xiong, Q.L.; Tian, X.G. Effect of initial stress on a fiber-reinforced thermoelastic porous media without energy dissipation. Transp. Porous Media 2016, 111, 81–95.

  • 2.

    Abouelregal, A.E. Fibre-reinforced generalized anisotropic thick plate with initial stress under the influence of fractional thermoelasticity theory. Adv. Appl. Math. Mech. 2017, 9, 722–741.

  • 3.

    Othman, M.I.A.; Said, S.M.; Marin, M. A novel model of plane waves of two-temperature fiber-reinforced thermoelastic medium under the effect of gravity with three-phase lag model. Int. J. Numer. Methods Heat Fluid Flow 2019, 29, 4788–4806.

  • 4.

    Zenkour, A.M. Magneto-thermal shock for a fiber-reinforced anisotropic half-space studied with a refined multi-dual-phase-lag model. J. Phys. Chem. Solids 2020, 137, 109213.

  • 5.

    Horrigue, S.; Abbas, I.A. Fractional-order thermoelastic wave assessment in a two-dimensional fiber-reinforced anisotropic material. Mathematics 2020, 8, 1609.

  • 6.

    Fahmy, M.A.; Almehamdi, M.M. Boundary element analysis of rotating functionally graded anisotropic fiber-reinforced magneto-thermoelastic composites. Open Eng. 2022, 12, 313–322.

  • 7.

    Kalkal, K.K.; Deswal, S.; Poonia, R. Reflection of plane waves in a rotating non-local fiber-reinforced transversely isotropic thermoelastic medium. J. Therm. Stress. 2023, 46, 276–292.

  • 8.

    Othman, M.I.A.; Said, S.M.; Gamal, E.M.; et al. Modeling temperature-dependent elasticity and diffusion in fiber-reinforced composites under inclined loading. Iran. J. Sci. Technol. Trans. Mech. Eng. 2025, 49, 2247–2262.

  • 9.

    Othman, M.I.A.; Song, Y.Q. Reflection of plane waves from an elastic solid half-space under hydrostatic initial stress without energy dissipation. Int. J. Solids Struct. 2007, 44, 5651–5664.

  • 10.

    Othman, M.I.A.; Atwa, S.Y. Two-dimensional problems of a fibre-reinforced anisotropic thermoelastic medium comparison with the Green-Naghdi theory. Comput. Math. Model. 2013, 24, 307–325.

  • 11.

    Othman, M.I.A.; Saied, S.M. The effect of rotation on two-dimensional problem of a fibre-reinforced thermoelastic with one relaxation time. Int. J. Thermophys. 2012, 33, 160–171.

  • 12.

    Abo-Dahab, S.M.; Abd-Alla, A.M.; Othman, M.I.A. Reflection of plane waves on generalized thermoelastic medium under effect of temperature dependent properties and initial stress with three-phase-lag model. Mech. Based Des. Struct. Mach. 2020, 50, 1184–1197.

  • 13.

    Abd-Alla, A.M.; Salah, D.M. Effect of initial stress and rotation on magneto-thermoelastic half-space with gravity field and without energy dissipation. J. Strain Anal. Eng. Des. 2023, 59, 56–66.

  • 14.

    Abouelregal, A.E.; Rashid, A.F. Deformation in a micropolar material under the influence of Hall current and initial stress fields in the context of a double-temperature thermoelastic theory involving phase lag and higher orders. Acta Mech. 2024, 235, 4311–4337.

  • 15.

    Lianngenga, R.; Laldinmawia, T.B.C.; Lalvohbika, J. Effect of initial stress and micropolar couple modulus on the reflection of wave in thermoelastic materials with voids. J. Vib. Eng. Technol. 2025, 13, 187.

  • 16.

    Paria, G. Magneto-elasticity and magneto-thermoelasticity. Adv. Appl. Mech. 1966, 10, 73–112.

  • 17.

    Sherief, H.H.; Helmy, K.A. A two-dimensional problem for a half-space in magneto-thermoelasticity with thermal relaxation. Int. J. Eng. Sci. 2002, 40, 587–604.

  • 18.

    Othman, M.I.A.; Lotfy, K.H. Two-dimensional problem of generalized magneto-thermoelasticity with temperature dependent elastic moduli for different theories. Multidiscip. Model. Mater. Struct. 2009, 5, 235–242.

  • 19.

    Said, S.M. Influence of gravity on generalized magneto-thermoelastic medium for three-phase-lag model. J. Comput. Appl. Math. 2016, 291, 142–157.

  • 20.

    Sarkar, N.; De, S.; Sarkar, N. Memory response in plane wave reflection in generalized magneto-thermoelasticity. J. Electromagn. Waves Appl. 2019, 33, 1354–1374.

  • 21.

    Purkait, P.; Sur, A.; Kanoria, M. Magneto-thermoelastic interaction in a functionally graded medium under gravitational field. Waves Random Complex Media 2021, 31, 1633–1654.

  • 22.

    Gupta, S.; Dutta, R.; Das, S.; et al. Double poro-magneto-thermoelastic model with microtemperatures and initial stress under memory-dependent heat transfer. J. Therm. Stress. 2023, 46, 743–774.

  • 23.

    Chaudhary, S.; Ahlawat, A.; Panwar, V. Impact of variable thermal conductivity on plane waves between a magneto-thermoelastic medium with Hall current, voids and magneto-thermoelastic medium with Hall current. Phys. Fluids 2025, 37, 077123.

  • 24.

    Abbas, I.A.; Marin, M. Analytical solutions of a two-dimensional generalized thermoelastic diffusions problem due to laser pulse. Iran. J. Sci. Technol. Trans. Mech. Eng. 2018, 42, 57–71.

  • 25.

    Abouelregal, A.E.; Marin, M.; Öchsner, A. The influence of a non-local Moore-Gibson-Thompson heat transfer model on an underlying thermoelastic material under the model of memory-dependent derivatives. Contin. Mech. Thermodyn. 2023, 35, 545–562.

  • 26.

    Belfield, A.J.; Rogers, T.G.; Spencer, A.J.M. Stress in elastic plates reinforced by fiber lying in concentric circles. J. Mech. Phys. Solids 1983, 31, 25–54.

  • 27.

    Zenkour, A.M. Thermoelastic diffusion problem for a half-space due to a refined dual-phase-lag Green-Naghdi model. J. Ocean Eng. Sci. 2020, 5, 214–222.

  • 28.

    Das, N.C.; Bhakata, P.C. Eigenfunction expansion method to the solution of simultaneous equations and its application in mechanics. Mech. Res. Commun. 1985, 12, 19–29.

Share this article:
How to Cite
Othman, M. I. A.; Said, S. M.; Gamal, E. M. Analysis of Multi-Field Influences on a Fiber-Reinforced Thermoelastic Medium Using the Modified Green–Naghdi Theory. Journal of Applied Mathematics, Mechanics and Engineering 2026, 1 (1), 4.
RIS
BibTex
Copyright & License
article copyright Image
Copyright (c) 2026 by the authors.