Effect of Viscosity and Magnetic Field on Thermoelastic Fiber-Reinforced Porous Solid using 3PHL Model

Document Type : Research Paper

Authors
Department of Mathematics, Faculty of Science, Zagazig University, P.O. Box 44519, Zagazig, Egypt
Abstract
This study investigates the effect of magnetic field and viscosity on the behavior of thermoelastic fiber-reinforced porous solid materials using a 3PHL model. The study aims to understand how these factors affect the mechanical properties and thermal response of the material. The results will provide valuable insights into the design and optimization of these materials for various applications, such as in the aerospace and automotive industries. The findings from this study will contribute to ongoing research in the field of advanced materials and help in the development of innovative and efficient materials for practical use. Our study introduces a pioneering application of the 3PHL model to thermoelastic fiber-reinforced porous solids, integrating the effects of viscosity and magnetic fields for the first time. This approach provides a more nuanced understanding of the material behavior under varying operational conditions. Unlike traditional models, our framework accounts for the interactions between magnetic fields and viscosity, revealing new insights into the thermoelastic response of composite materials. This enhancement allows for more precise predictions of material performance in dynamic environments.
Keywords
Subjects

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[1] Nunziato, J.W., Cowin, S.C., A nonlinear theory of elastic materials with voids, Archive for Rational Mechanics and Analysis, 72(2), 1979, 175–201.
[2] Cowin, S.C., Nunziato, J.W., Linear elastic materials with voids, Journal of Elasticity, 13(2), 1983, 125–147.
[3] Puri, P., Cowin, S.C., Plane waves in linear elastic materials with voids, Journal of Elasticity, 15(2), 1985, 167–183.
[4] Dhaliwal, R.S., Wang, J., Domain of influence theorem in the theory of elastic materials with voids, International Journal of Engineering Science, 32(2), 1994, 1823–1828.
[5] Cowin, S.C., The viscoelastic behavior of linear elastic materials with voids, Journal of Elasticity, 15(2), 1985, 185–191.
[6] Ieşan, D., A theory of thermoelastic materials with voids, Acta Mechanica, 60(1–2), 1986, 67–89.
[7] Ieşan, D., On a theory of thermoviscoelastic materials with voids, Journal of Elasticity, 104(1–2) ,2011, 369–384.
[8] Chattopadhyay, A., Choudhury, S., Propagation, reflection and transmission of magnetoelastic shear waves in a self-reinforced medium, International Journal of Engineering Science, 28(6), 1990, 485–495.
[9] Singh, B., Wave propagation in thermally conducting linear fibre-reinforced composite materials, Archive of Applied Mechanics, 75, 2006, 513–520.
[10] Said, S.M., Othman, M.I.A., Wave propagation in a two-temperature fiber-reinforced magneto-thermoelastic medium with three-phase-lag model, Structural Engineering and Mechanics, 57(2), 2016, 201–220.
[11] Abbas, I.A., Generalized magneto–thermoelastic interaction in a fiber-reinforced anisotropic hollow cylinder, International Journal of Thermophysics, 33, 2012, 567–579.
[12] Sarkar, N., Atwa, S.Y., Othman, M.I.A., The effect of hydrostatic initial stress on the plane waves in a fiber-reinforced magneto-thermoelastic medium with fractional derivative heat transfer, International Applied Mechanics, 52, 2016, 203–216.
[13] Alharbi, A.M., Said, S.M., Othman, M.I.A., The effect of multi-phase-lag and Coriolis acceleration on a fiber-reinforced isotropic thermoelastic medium, Steel & Composite Structures, 39(2), 2021, 125–134.
[14] Yu, Y.J., Zhao, L.J., Fractional thermoelasticity revisited with new definitions of    fractional derivative, European Journal of Mechanics A/Solids, 84, 2020, 104043.
[15] Abouelregal, A.E., Alesemi, M., Evaluation of the thermal and mechanical waves in anisotropic fiber-reinforced magnetic viscoelastic solid with temperature-dependent properties using the MGT thermoelastic model, Case Studies in Thermal Engineering, 36, 2022, 102187. 
[16] Othman, M.I.A., Abouelregal, A.E., Said, S.M., The effect of variable thermal conductivity on an infinite fiber-reinforced thick plate under initial stress, Journal of Mechanics of Materials and Structures, 14(2), 2019, 277-293.
[17] Zenlour, A.M., Abouelregal, A.E., On the generalized thermoelasticity problem for an infinite fibre-reinforced thick plate under initial stress, Advances in Applied Mathematics and Mechanics, 6(6), 2014, 783-796.
[18] El-Bary, A.A., Numerical solution of electro-magneto-thermo-mechanical shock problem, Computational Methods in Science & Technology, 12(2), 2006, 101-108.         
[19] Nayfeh, A.H., Nemat-Nasser, S., Electromagneto-thermoelastic plane waves in solids with thermal relaxation, Journal of Applied Mechanics, 39(1), 1972, 108–113
[20] Othman, M.I.A., Song, Y.Q., Effect of rotation on plane waves of generalized electro-magneto-thermo-viscoelasticity with two relaxation times, Applied Mathematical Modelling, 32(5), 2008, 811–825.
[21] Othman, M.I.A., Atwa, S.Y., Farouk, R., Generalized magneto-thermovisco-elastic plane waves under the effect of rotation without energy dissipation, International Journal of Engineering Science, 46(7), 2008, 639–653.
[22] Othman, M.I.A., Generalized electromagneto-thermoviscoelastic in case of 2-D thermal shock problem in a finite conducting medium with one relaxation time, Acta Mechanica, 169(1–4), 2004, 37–51.
[23] Othman, M.I.A., Fekry, M., Moving loads on thermo-viscoelastic micropolar solid medium with voids and two-temperature, Journal of Applied and Computational Mechanics, 2024, doi: 10.22055/jacm.2024.46821.4600.
[24] Ferry, J.D., Viscoelastic Properties of Polymers, John Wiley & Sons, New York, 1980.
[25] Gross, B., Mathematical Structure of the Theories of Viscoelasticity, Hermann, Paris, 1953.
[26] Biot, M., Theory of stress-strain relations in anisotropic viscoelasticity and relaxation phenomena, Journal of Applied Physics, 25(11), 1954, 1385–1391.
[27] Biot, M., Variational principles in irreversible thermodynamics with application to viscoelasticity, Physical Review, 97(6), 1955, 1463.
[28] Bland, D.R., The Theory of Linear Viscoelasticity, Pergamon Press, New York, 1960.
[29] Gurtin, M.E., Sternberg, E., On the linear theory of viscoelasticity, Archive for Rational Mechanics and Analysis, 11(1), 1962, 291–356.
[30] Pobedria, B., Coupled problems in continuum mechanics, Journal of Durability Plasticity, Moscow State University, Moscow, 1 ,1984.
[31] Ilioushin, A., Pobedria, B., Mathematical Theory of Thermal Viscoelasticity, Nauka, Moscow, 1970.
[32] Othman, M.I.A., The uniqueness and reciprocity theorems for generalized thermo-viscoelasticity with thermal relaxation times, Mechanics and Mechanical Engineering, 7(2), 2004, 77–87.
[33] Sharma, J., Othman, M.I.A., Effect of rotation on generalized thermo-viscoelastic Rayleigh–Lamb waves, International Journal of Solids and Structures, 44(13), 2007, 4243–4255.
[34] Hetnarski, R.B., Ignaczak, J., Generalized thermoelasticity, Journal of Thermal Stresses, 22, 1999, 451-476.
[35] Green, A.E., Naghdi, P.M., A re-examination of the basic postulates of thermo-mechanics, Proceedings of the Royal Society of London A, 432, 1991, 171-194.
[36] Tzou, D.Y., A unified field approach for heat conduction from macro-to micro scales, Journal of Heat Transfer, 117, 1995, 8-16.
[37] Choudhuri, S.K.R., On thermoelastic three phase lag model, Journal of Thermal Stresses, 30, 2007, 231-238.
[38] Quintanilla, R., Racke, R., A note on stability in three-phase-lag heat conduction, International Journal of Heat and Mass Transfer, 51, 2008, 24-29.
[39] Mukhopadhyay, S., Kumar, R., Analysis of phase-lag effects on wave propagation in a thick plate under axisymmetric temperature distribution, Acta Mechanica, 210, 2010, 331-341.
[40] Othman, M.I.A., Eraki, E.E.M., Generalized magneto-thermoelastic half-space with diffusion under initial stress using three-phase-lag model, Mechanics Based Design of Structures and Machines, 45(2), 2017, 145-159.
[41] Youssef, H.M., El-Bary, A.A., Thermal shock problem for one dimensional generalized thermoelastic layered composite material, Mathematical and Computational Applications, 11(2), 2006, 91-94.
[42] Youssef, H.M., El-Bary, A.A., Two-temperature thermoelastic damping of a gold    nano-beam resonator with variable Young's modulus, International Journal of Acoustics & Vibration, 24(3), 2019, 540-545.
[43] Youssef, H.M., El-Bary, A.A., The reference temperature dependence of Young’s modulus of two-temperature thermoelastic damping of gold nano-beam, Mechanics of Time-Dependent Materials, 22(4), 2018, 435-445.
[44] Youssef, H.M., El-Bary, A.A., Characterization of the photothermal interaction of a semiconducting solid sphere due to the mechanical damage and rotation under Green-Naghdi theories, Mechanics of Advanced Materials and Structures, 29(6), 2020, 889-904.