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The effect of initial stress on generalized thermoviscoelastic medium with voids and temperature-dependent properties under Green-Neghdi theory

Identyfikatory
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The present paper aims to study the effect of initial stress on the 2-D problem of a homogeneous, isotropic, generalized thermo-viscoelastic material with voids in the context of Green-Naghdi theory. The modulus of elasticity is taken as a linear function of reference temperature. The analytical expressions for the physical quantities are obtained in the physical domain by using the normal mode analysis. These expressions are calculated numerically for a specific material and explained graphically. Comparisons are made with the results predicted by (G-N II) and (G-N III) theory in the presence and absence of the initial stress and temperature-dependent properties.
Rocznik
Strony
291--308
Opis fizyczny
Bibliogr. 33 poz., wykr.
Twórcy
  • Faculty of Science, Department of Mathematics, Zagazig University, P.O. Box 44519, Zagazig, Egypt
autor
  • Faculty of Science, Department of Mathematics, South Valley University, P.O. Box 83523, Qena, Egypt
Bibliografia
  • [1] Gross, B.: Mathematical structure of the theories of viscoelasticity, Hermann, Paris, 1953.
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  • [4] Ferry, J. D.: Viscoelastic properties of polymers, John Wiley & Sons, 1980.
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  • [6] Biot, M.: Theory of stress-strain relations in anisotropic viscoelsticity and relaxation phynomenoa, J. Appl. Phys., 25, 11, 1385-1391, 1954.
  • [7] Huilgol, R. R. and Phan-Thien, N.: Fluid Mechanics of Viscoelasticity: General Principles, Constitutive Modelling, Analytical and Numerical Techniques, 6, Elsevier, 1997.
  • [8] Bland, D. R.: The Theory of Linear Viscoelasticity, 10, Pergamon Press, New York, 1960.
  • [9] Gurtin, M. E. and Sternberg, E.: On the linear theory of viscoelasticity, Archive for Rational Mechanics and Analysis, 11, 1, 291-356, 1962.
  • [10] Ilioushin, A.: The approximation method of calculating the constructures by linear thermal viscoelastic theory, Mekhanika Polimerov, 2, 168178, 1968.
  • [11] Ilioushin, A. and Pobedria, B.: Mathematical Theory of Thermal Viscoelasticity, Nauka, Moscow, 1970.
  • [12] Pobedria, B.: Coupled Problems in Continuum Mechanics, J. Durability and Plasticity, 1, 1984.
  • [13] Koltunov, M.: Creeping and Relaxation, Vysshaya Shkola, Moscow, 1976.
  • [14] Othman, M. I. A.: The uniqueness and reciprocity theorems for generalized thermoviscoelasticity with thermal relaxation times. Mech. and Mech. Eng., 7, 2, 77-87, 2004.
  • [15] Lord, H. W. and Shulman, Y.: A generalized dynamical theory of thermoelasticity, J. the Mech. and Phys. of Solids, 15, 5, 299-309, 1967.
  • [16] Green, A. and Lindsay, K.: Thermoelasticity, J. Elast., 2, 1, 1-7, 1972.
  • [17] Green, A. and Naghdi, P.: A re-examination of the basic postulates of thermomechanics, Proceedings of the Royal Society of London. Series A: Math. and Phys. Sci., 432, 171-194, 1991.
  • [18] Green, A. and Naghdi, P.: On undamped heat waves in an elastic solid, J. Thermal Stresses, 15, 2, 253-264, 1992.
  • [19] Green, A. and Naghdi, P.: Thermoelasticity without energy dissipation, J. Elast., 31, 3, 189-208, 1993.
  • [20] Nunziato, J. W. and Cowin S. C.: A nonlinear theory of elastic materials with voids, Arch. for Rational Mech. and Anal., 72, 2, 175-201, 1979.
  • [21] Nunziato, J. W. and Cowin S. C.: Linear elastic materials with voids, J. Elast., 13, 3, 125-147, 1983.
  • [22] Puri, P. S. and Cowin, C.: Plane waves in linear elastic materials with voids, J. Elast., 15, 2, 167-183, 1985.
  • [23] Dhaliwal, R. S. and Wang, J.: Domain of influence theorem in the theory of elastic materials with voids, Int. J. Eng. Sci., 32, 11, 1823-1828, 1994.
  • [24] Dhaliwal, R. S. and Wang, J.: A heat-flux dependent theory of thermoelasticity with voids, Acta Mechanica, 110, 1-4, 33-39, 1995.
  • [25] Cowin, S. C.: The viscoelastic behavior of linear elastic materials with voids, J. Elast., 15, 2, 185191, 1985.
  • [26] Othman, M. I. A.: Generalized thermoviscoelasticity under three theories, Mech. and Mechanical Engineering, 13, 1, 25-44, 2009.
  • [27] Ie san, D.: On a theory of thermoviscoelastic materials with voids, J. Elast., 104, 1-2, 369-384, 2011.
  • [28] Othman, M. I. A.: The uniqueness and reciprocity theorem for generalized thermoviscoelasticity with thermal relaxation times, Mech. and Mechanical Engineering, 7, 2, 77-87, 2004.
  • [29] Othman, M. I. A. and Abd-Elaziz, E. M.: The effect of thermal loading due to laser pulse in generalized thermoelastic medium with voids in dual phase lag model, J. Thermal Stresses, 38, 9, 1068-1082, 2015.
  • [30] Othman, M. I. A., Zidan, M. E. and Hilal, M. I.: The effect of initial stress on thermoelastic rotating medium with voids due to laser pulse heating with energy dissipation, J. Thermal Stresses, 38, 8, 835-853, 2015.
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  • [33] Othman, M. I. A., Hasona, W. and Eraki, E.: The effect of initial stress on generalized thermoelastic medium with three-phase-lag model under temperature dependent properties, Can. J. Phys., 92, 448-457, 2014.
Uwagi
Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-b1769520-e08b-4f86-af61-420877ec4c0b
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