Photothermally Excited Micropolar Thermo-Viscoelastic Half-Spaces: Nonlocal DPL Heat Transfer with Variable Conductivity and Viscous Damping

Abouelregal, Ahmed; Marin, Marin; Alhazmi, Mofareh

doi:10.22059/jcamech.2026.422459.1952

Photothermally Excited Micropolar Thermo-Viscoelastic Half-Spaces: Nonlocal DPL Heat Transfer with Variable Conductivity and Viscous Damping

Document Type : Research Paper

Authors

Ahmed Abouelregal ¹

Marin Marin ² ^{, 3}

Mofareh Alhazmi ¹

¹ Mathematics Department, College of Science, Jouf University, P.O. Box: 2014, Sakaka, Saudi Arabia

² Department of Mathematics and Computer Science, Transilvania University of Brasov, Brasov, Romania

³ Academy of Romanian Scientists, Ilfov Street 3, Bucharest, 050045, Romania

10.22059/jcamech.2026.422459.1952

Abstract

A unified analytical model is developed for a micropolar semiconducting half-space under photothermal loading, incorporating nonlocal DPL heat transport, temperature-dependent conductivity, and Kelvin–Voigt viscoelasticity. Constitutive relations are extended with rate-dependent terms, yielding complex moduli that capture wave attenuation and dispersion. The Kirchhoff transformation linearizes the variable-conductivity equation, and normal-mode analysis provides closed-form solutions. Numerical results show that variable conductivity reduces surface temperature by 45% and halves thermal penetration depth, nonlocality redistributes energy to interior regions with 62% enhancement at depth, and viscosity lowers peak stresses by 19–25%. These benchmark solutions offer quantitative guidance for semiconductor devices, MEMS, thermal barrier coatings, and composites under high-frequency photothermal excitation.

Keywords

Micropolar thermo-viscoelasticity

Photothermal

Nonlocal dual-phase-lag

Variable conductivity

Kelvin–Voigt

Normal mode analysis

Subjects

Experimental fluid mechanics and heat transfer

[1] M. A. Biot, Thermoelasticity and irreversible thermodynamics, Journal of applied physics, Vol. 27, No. 3, pp. 240-253, 1956.

[2] H. W. Lord, Y. Shulman, A generalized dynamical theory of thermoelasticity, Journal of the Mechanics and Physics of Solids, Vol. 15, No. 5, pp. 299-309, 1967.

[3] A. E. Green, K. Lindsay, Thermoelasticity, Journal of elasticity, Vol. 2, No. 1, pp. 1-7, 1972.

[4] A. E. Green, N. Laws, On a global entropy production inequality, The Quarterly Journal of Mechanics and Applied Mathematics, Vol. 25, No. 1, pp. 1-11, 1972.

[5] A. Green, P. Naghdi, Thermoelasticity without energy dissipation, Journal of elasticity, Vol. 31, No. 3, pp. 189-208, 1993.

[6] D. Y. Tzou, A unified field approach for heat conduction from macro-to micro-scales, 1995.

[7] D. S. Chandrasekharaiah, Thermoelasticity with second sound: A review, Applied Mechanics Reviews, Vol. 39, No. 3, pp. 355-376, 1986.

[8] D. Chandrasekharaiah, Hyperbolic thermoelasticity: a review of recent literature, 1998.

[9] A. C. Eringen, On differential equations of nonlocal elasticity and solutions of screw dislocation and surface waves, Journal of applied physics, Vol. 54, No. 9, pp. 4703-4710, 1983.

[10] D. Y. Tzou, Z.-Y. Guo, Nonlocal behavior in thermal lagging, International Journal of Thermal Sciences, Vol. 49, No. 7, pp. 1133-1137, 2010.

[11] H. M. Youssef, I. A. Abbas, Thermal shock problem of generalized thermoelasticity for an infinitely long annular cylinder with variable thermal conductivity, Computational Methods in Science and Technology, Vol. 13, No. 2, pp. 95-100, 2007.

[12] A. C. Eringen, E. S. Suhubi, Nonlinear theory of simple micro-elastic solids—I, International Journal of Engineering Science, Vol. 2, No. 2, pp. 189-203, 1964.

[13] E. S. Suhubi, A. C. Eringen, Nonlinear theory of micro-elastic solids—II, International Journal of Engineering Science, Vol. 2, No. 4, pp. 389-404, 1964.

[14] T. R. Tauchert, W. D. Claus Jr., T. Ariman, The linear theory of micropolar thermoelasticity, International Journal of Engineering Science, Vol. 6, No. 1, pp. 37-47, 1968.

[15] E. Boschi, D. Ieşan, A generalized theory of linear micropolar thermoelasticity, Meccanica, Vol. 8, No. 3, pp. 154-157, 1973.

[16] M. Ciarletta, A theory of micropolar thermoelasticity without energy dissipation, Journal of Thermal Stresses, Vol. 22, No. 6, pp. 581-594, 1999.

[17] H. H. Sherief, F. A. Hamza, A. M. El-Sayed, Theory of generalized micropolar thermoelasticity and an axisymmetric half-space problem, Journal of Thermal Stresses, Vol. 28, No. 4, pp. 409-437, 2005.

[18] J. Gordon, R. Leite, R. Moore, S. Porto, J. Whinnery, Long‐transient effects in lasers with inserted liquid samples, Journal of Applied Physics, Vol. 36, No. 1, pp. 3-8, 1965.

[19] L. B. Kreuzer, Ultralow Gas Concentration Infrared Absorption Spectroscopy, Journal of Applied Physics, Vol. 42, No. 7, pp. 2934-2943, 1971.

[20] D. M. Todorović, P. M. Nikolić, A. I. Bojičić, Photoacoustic frequency transmission technique: Electronic deformation mechanism in semiconductors, Journal of Applied Physics, Vol. 85, No. 11, pp. 7716-7726, 1999.

[21] Y. Song, D. Todorovic, B. Cretin, P. Vairac, Study on the generalized thermoelastic vibration of the optically excited semiconducting microcantilevers, International Journal of Solids and Structures, Vol. 47, pp. 1871-1875, 07/01, 2010.

[22] A. M. Freudenthal, Effect of rheological behavior on thermal stresses, Journal of Applied Physics, Vol. 25, No. 9, pp. 1110-1117, 1954.

[23] M. A. Biot, Variational principles in irreversible thermodynamics with application to viscoelasticity, Physical Review, Vol. 97, No. 6, pp. 1463-1469, 1955.

[24] M. A. Biot, Theory of stress-strain relations in anisotropic viscoelasticity and relaxation phenomena, Journal of Applied Physics, Vol. 25, No. 11, pp. 1385-1391, 1954.

[25] D. R. Bland, 1960, The Theory of Linear Viscoelasticity, Pergamon Press, Oxford

[26] A. A. Ilyushin, B. E. Pobedria, 1970, Fundamentals of the Mathematical Theory of Thermal Viscoelasticity, Nauka, Moscow

[27] R. I. Tanner, 1988, Engineering Rheology, Clarendon Press, Oxford

[28] R. R. Huilgol, N. Phan-Thien, 1997, Fluid Mechanics of Viscoelasticity: General Principles, Constitutive Modelling, Analytical and Numerical Techniques, Elsevier Science, Amsterdam, 1sted.

[29] A. E. Abouelregal, M. Marin, A. Foul, S. S. Askar, Coupled responses of thermomechanical waves in functionally graded viscoelastic nanobeams via thermoelastic heat conduction model including Atangana–Baleanu fractional derivative, Scientific Reports, Vol. 14, No. 1, pp. 9122, 2024.

[30] J. Zhang, Y. Ma, Investigation of the thermoelastic behaviour of magneto-thermo-viscoelastic rods based on the Kelvin-Voigt viscoelastic model, Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, Vol. 48, No. 6, pp. 1533-1549, 2024.

[31] R. Tiwari, A. E. Abouelregal, Thermo-viscoelastic transversely isotropic rotating hollow cylinder based on three-phase lag thermoelastic model and fractional Kelvin–Voigt type, Acta Mechanica, Vol. 233, No. 6, pp. 2453-2470, 2022.

[32] W. Peng, Z. Qi, T. He, Nonlocal dual-phase-lag thermoviscoelastic response of a polymer microbeam incorporating modified couple stress and fractional viscoelastic theories, The Journal of Strain Analysis for Engineering Design, Vol. 58, No. 5, pp. 376-388, 2023.

[33] C. Dascalu, G. A. Maugin, The thermoelastic material-momentum equation, Journal of Elasticity, Vol. 39, No. 3, pp. 201-212, 1995.

[34] Y. Chahlaoui, S. Widatalla, A. K. Kareem, M. Soliyeva, S. Sujai, S. Singh, V. S. Mann, A. Kedia, A. R. Al-Tameemi, M. Alhedrawe, Analysis of thermoelastic dissipation in couple stress-based beams with two-dimensional Moore–Gibson–Thompson heat conduction, Archive of Applied Mechanics, Vol. 95, No. 2, pp. 63, 2025.

[35] R. Kumar, S. Kaushal, V. Vikram, Vibration Behavior of Nanobeams under Hyperbolic Two-Temperature Thermoelasticity Using Modified Couple Stress Theory, Mechanics of Solids, Vol. 60, No. 6, pp. 4602-4615, 2025.

[36] Y. Q. Song, B. Cretin, D. M. Todorović, P. Vairac, Study of photothermal vibrations of semiconductor cantilevers near the resonant frequency, Journal of Physics D: Applied Physics, Vol. 41, No. 15, pp. 155106, 2008.

[37] J. Zakrzewski, M. Pawlak, O. Matsuda, D. M. Todorović, J. Liu, Semiconductor physics: Plasma, thermal, elastic, and acoustic phenomena, Journal of Applied Physics, Vol. 136, No. 12, pp. 120401, 2024.

[38] D. Y. Tzou, 2014, Macro-to microscale heat transfer: the lagging behavior, John Wiley & Sons,

[39] K. Cao, J. Zong, Z. Liu, Z. Chen, W. Yang, Transient Non-Fourier Fracture Analysis of a Central Crack in Aluminium Foams by Guyer–Krumhansl Theory, Materials, Vol. 19, No. 14, pp. 2933, 2026.

[40] W. Yang, R. Gao, Z. Liu, Y. Cui, A. Pourasghar, Z. Chen, Transient heat conduction in the cracked medium by Guyer–Krumhansl model, International Journal of Fracture, Vol. 246, No. 2-3, pp. 145-160, 2024.

[41] T. He, S. Shi, Effect of temperature-dependent properties on thermoelastic problems with thermal relaxations, Acta Mechanica Solida Sinica, Vol. 27, No. 4, pp. 412-419, 2014.

[42] Y. Z. Wang, D. Liu, Q. Wang, J. Z. Zhou, Thermoelastic behavior of elastic media with temperature-dependent properties under transient thermal shock, Journal of Thermal Stresses, Vol. 39, No. 4, pp. 460-473, 2016.

[43] P. Luo, X. Li, X. Tian, Nonlocal thermoelasticity and its application in thermoelastic problem with temperature-dependent thermal conductivity, European Journal of Mechanics - A/Solids, Vol. 87, pp. 104204, 2021.

[44] S. Kumar, G. Partap, R. Kumar, Impact of temperature-dependent parameters on wave motion in a micropolar thermoelastic plate involving memory-dependent derivatives, Acta Mechanica, Vol. 235, No. 1, pp. 429-439, 2024.

[45] M. Marin, A temporally evolutionary equation in elasticity of micropolar bodies with voids, Bull. Ser. Appl. Math. Phys, Vol. 60, No. 3, 1998.

[46] A. Shahid, H. L. Huang, M. M. Bhatti, M. Marin, Numerical computation of magnetized bioconvection nanofluid flow with temperature-dependent viscosity and Arrhenius kinetic, Mathematics and Computers in Simulation, Vol. 200, pp. 377-392, 2022.

[47] S. Askar, A. E. Abouelregal, M. Marin, A. Foul, Photo-Thermoelasticity Heat Transfer Modeling with Fractional Differential Actuators for Stimulated Nano-Semiconductor Media, Symmetry, Vol. 15, No. 3, pp. 656, 2023.

[48] P. Kadian, S. Kumar, M. Sangwan, Influence of initial stress and gravity on fiber-reinforced thermoelastic solid using Moore–Gibson–Thompson generalized theory of thermoelasticity, Multidiscipline Modeling in Materials and Structures, Vol. 21, No. 1, pp. 217-238, 2025.

[49] A. A. M. Abd-Alla, F. S. Bayones, H. S. Gafel, Effect of Magnetic Field on Photothermal Waves with Diffusive Thermoelastic Semiconductor Media, Mechanics of Solids, Vol. 61, No. 2, pp. 71, 2026.

[50] A. Soleiman, A. E. Abouelregal, M. E.-S. Nasr, Laser-Driven Spatiotemporal Nonlocal Magneto-Thermoelasticity in Micropolar Half-Spaces with Dual-Phase-Lag Thermal Effects, Iranian Journal of Science and Technology, Transactions of Mechanical Engineering, Vol. 50, No. 3, 2026.