Thermomechanical deformation in a micropolar thermoviscoelastic solid under the Moore-Gibson-Thompson heat equation with non-local and hyperbolic two-temperature effects

Document Type : Research Paper

Authors

1 Cheminde Chandieu 25, 1006 Lausanne, Switzerland

2 Department of Mathematics and Computer Science, Transilyania University of Brasov,500036 Brasov, Romania

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

4 Department of Mathematics, Kurukshetra University, Kurukshetra 136119, Haryana, India

Abstract

This study addresses an axisymmetric problem within the framework of micropolar thermoviscoelasticity, governed by the Moore-Gibson-Thompson (MGT) heat conduction equation. The analysis incorporates non-local elasticity and hyperbolic two-temperature (HTT) effects under applied mechanical loading. By introducing appropriate potential functions, the governing system is reformulated into a dimensionless form and solved using Laplace and Hankel transform techniques. Boundary conditions involving a normally distributed mechanical force and a ramp-type thermal input are considered to examine their impact. Analytical expressions for displacements, stress components, tangential couple stress, conductive temperature, and thermodynamic temperature are derived in the transformed domain and subsequently recovered using a numerical inversion method. Graphical representations illustrate how variations in viscosity, non-locality, and HTT parameters influence thermal and mechanical responses. Special cases are also examined to validate the model's generality. This research holds relevance for industrial applications in steel manufacturing and petroleum engineering, as well as in geomechanical modeling, particularly in understanding stress and temperature behavior during seismic activities.

Keywords

Main Subjects

[1]          P. J. Chen, M. E. Gurtin, On a theory of heat conduction involving two temperatures, 1968.
[2]          P. J. Chen, M. E. Gurtin, W. O. Williams, On the thermodynamics of non-simple elastic materials with two temperatures, Zeitschrift für angewandte Mathematik und Physik ZAMP, Vol. 20, No. 1, pp. 107-112, 1969/01/01, 1969.
[3]          H. M. Youssef, Theory of two-temperature-generalized thermoelasticity, IMA Journal of Applied Mathematics, Vol. 71, No. 3, pp. 383-390, 2006.
[4]          H. M. Youssef, A. A. El-Bary, Theory of hyperbolic two-temperature generalized thermoelasticity, Mater. Phys. Mech, Vol. 40, No. 2, pp. 158-171, 2018.
[5]          A. Hobiny, I. Abbas, M. Marin, The Influences of the Hyperbolic Two-Temperatures Theory on Waves Propagation in a Semiconductor Material Containing Spherical Cavity, Mathematics, Vol. 10, No. 1, pp. 121, 2022.
[6]          A. C. Eringen, D. Edelen, On nonlocal elasticity, International journal of engineering science, Vol. 10, No. 3, pp. 233-248, 1972.
[7]          A. C. Eringen, Linear theory of micropolar elasticity, Journal of Mathematical Mechanics, Vol. 15, No. 6, pp. 909-923, 1966.
[8]          M. Marin, Weak Solutions in Elasticity of Dipolar Porous Materials, Mathematical Problems in Engineering, Vol. 2008, No. 1, pp. 158908, 2008.
[9]          K. Sharma, M. Marin, Reflection and transmission of waves from imperfect boundary between two heat conducting micropolar thermoelastic solids, Analele Stiintifice ale Universitatii Ovidius Constanta, Seria Matematica, Vol. 22, pp. 151-175, 06/01, 2014.
[10]        R. Quintanilla, Moore–Gibson–Thompson thermoelasticity, Mathematics and Mechanics of Solids, Vol. 24, pp. 108128651986200, 07/21, 2019.
[11]        M. Marin, On existence and uniqueness in thermoelasticity of micropolar bodies, Comptes rendus de l'Académie des Sciences Paris, Série II, Vol. 321, No. 12, pp. 375-480, 1995.
[12]        S. Sharma, S. Khator, Power generation planning with reserve dispatch and weather uncertainties including penetration of renewable sources, International Journal of Smart Grid and Clean Energy, pp. 292-303, 01/01, 2021.
[13]        S. Sharma, S. Khator, Micro-Grid Planning with Aggregator’s Role in the Renewable Inclusive Prosumer Market, Journal of Power and Energy Engineering, Vol. 10, No. 4, pp. 47-62, 2022.
[14]        M. Marin, On weak solutions in elasticity of dipolar bodies with voids, Journal of Computational and Applied Mathematics, Vol. 82, No. 1, pp. 291-297, 1997/09/15/, 1997.
[15]        A. Zeeshan, M. I. Khan, R. Ellahi, M. Marin, Computational Intelligence Approach for Optimising MHD Casson Ternary Hybrid Nanofluid over the Shrinking Sheet with the Effects of Radiation, Applied Sciences, Vol. 13, No. 17, pp. 9510, 2023.
[16]        A. E. Abouelregal, S. S. Askar, M. Marin, B. Mohamed, The theory of thermoelasticity with a memory-dependent dynamic response for a thermo-piezoelectric functionally graded rotating rod, Scientific Reports, Vol. 13, No. 1, pp. 9052, 2023/06/03, 2023.
[17]        S. Sharma, M. Marin, H. Altenbach, Elastodynamic interactions in thermoelastic diffusion including non-local and phase lags, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 105, No. 1, pp. e202401059, 2025.
[18]        M. Marin, S. Sharma, R. Kumar, S. Vlase, Fundamental solution and Green's function in orthotropic photothermoelastic media with temperature-dependent properties under the Moore–Gibson–Thompson model, ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Vol. 105, No. 6, pp. e70124, 2025.
[19]        A. C. Eringen, Plane waves in nonlocal micropolar elasticity, International Journal of Engineering Science, Vol. 22, No. 8, pp. 1113-1121, 1984/01/01/, 1984.
[20]        R. S. Dhaliwal, A. Singh, 1980, Dynamic Coupled Thermoelasticity, Hindustan Publishing Corporation,
Volume 56, Issue 4
October 2025
Pages 720-736
  • Receive Date: 27 June 2025
  • Accept Date: 27 June 2025