Abstract:
The aim of the present contribution is the determination of the thermoelastic temperatures, stress, displacement, and strain in an infinite isotropic elastic body with a spherical cavity in the context of the mechanism of the two-temperature generalized thermoelasticity theory (2TT). The two-temperature Lord–Shulman (2TLS) model and two-temperature dual-phase-lag (2TDP) model of thermoelasticity are combined into a unified formulation with unified parameters. The medium is assumed to be initially quiescent. The basic equations are written in the form of a vector matrix differential equation in the Laplace transform domain, which is then solved by the state-space approach. The expressions for the conductive temperature and elongation are obtained for at small times. The numerical inversion of the transformed solutions is carried out by using the Fourier-series expansion technique. A comparative study is performed for the thermoelastic stresses, conductive temperature, thermodynamic temperature, displacement, and elongation computed by using the Lord–Shulman and dual-phase-lag models.
Citation:
R. Karmakar, A. Sur, M. Kanoria, “Generalized thermoelastic problem of an infinite body with a spherical cavity under dual-phase-lags”, Prikl. Mekh. Tekh. Fiz., 57:4 (2016), 91–106; J. Appl. Mech. Tech. Phys., 57:4 (2016), 652–665
\Bibitem{KarSurKan16}
\by R.~Karmakar, A.~Sur, M.~Kanoria
\paper Generalized thermoelastic problem of an infinite body with a spherical cavity under dual-phase-lags
\jour Prikl. Mekh. Tekh. Fiz.
\yr 2016
\vol 57
\issue 4
\pages 91--106
\mathnet{http://mi.mathnet.ru/pmtf817}
\crossref{https://doi.org/10.15372/PMTF20160409}
\elib{https://elibrary.ru/item.asp?id=26493343}
\transl
\jour J. Appl. Mech. Tech. Phys.
\yr 2016
\vol 57
\issue 4
\pages 652--665
\crossref{https://doi.org/10.1134/S002189441604009X}
Linking options:
https://www.mathnet.ru/eng/pmtf817
https://www.mathnet.ru/eng/pmtf/v57/i4/p91
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Ashraf M. Zenkour, Daoud S. Mashat, Ashraf M. Allehaibi, “Magneto-Thermoelastic Response in an Unbounded Medium Containing a Spherical Hole via Multi-Time-Derivative Thermoelasticity Theories”, Materials, 15:7 (2022), 2432
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Abhik Sur, Mridula Kanoria, “Field equations and corresponding memory responses for a fiber-reinforced functionally graded medium due to heat source”, Mechanics Based Design of Structures and Machines, 49:4 (2021), 511
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Pallabi Purkait, Abhik Sur, M. Kanoria, “Magneto-thermoelastic interaction in a functionally graded medium under gravitational field”, Waves in Random and Complex Media, 31:6 (2021), 1633
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Pallabi Purkait, Abhik Sur, M. Kanoria, “Elasto-thermodiffusive response in a spherical shell subjected to memory-dependent heat transfer”, Waves in Random and Complex Media, 31:3 (2021), 515
Abhik Sur, Sutapa Santra, M. Kanoria, “Memory response on thermal wave propagation in an elastic solid with voids due to influence of magnetic field”, Waves in Random and Complex Media, 31:6 (2021), 1187
Abhik Sur, Sudip Mondal, M. Kanoria, “Memory response on wave propagation in a thermoelastic plate due to moving band-type thermal loads and magnetic field”, Mechanics Based Design of Structures and Machines, 49:2 (2021), 172
Sudip Mondal, Abhik Sur, M. Kanoria, “Thermoelastic response of fiber-reinforced epoxy composite under continuous line heat source”, Waves in Random and Complex Media, 31:6 (2021), 1749
Abhik Sur, M. Kanoria, “Memory response on thermal wave propagation in an elastic solid with voids”, Mechanics Based Design of Structures and Machines, 48:3 (2020), 326
A. Sur, P. Pal, S. Mondal, M. Kanoria, “Finite element analysis in a fiber-reinforced cylinder due to memory-dependent heat transfer”, Acta Mech, 230:5 (2019), 1607
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