How to cite this paper
Sur, A & Kanoria, M. (2016). Three dimensional viscoelastic medium under thermal shock.Engineering Solid Mechanics, 4(4), 187-200.
Refrences
Alfery, T., & Gurnee, E. F. (1956). In: Eirich, F.R. (Ed.), In Rheology: Theory and Applications, vol. 1. Academic Press, New York.
Bandyopadhyay, N., & Roychoudhuri, S. K. (2005). Thermoelastic wave propagation without energy dissipation in an elastic half space. Bulletin of Calcutta Mathematical Society, 97(6), 489-502.
Banik, S., Mallik, S. H., & Kanoria, M. (2007). Thermoelastic interaction with energy dissipation in an infinite solid with distributed periodically varying heat sources. International Journal of Pure and Applied Mathematics, 34(2), 231-245.
Banik, S., Mallik, S. H., & Kanoria, M. (2009). A unified generalized thermoelasticity formulation: application to an infinite body with a cylindrical cavity and variable material properties. International Journal of Applied Mechanics and Engineering, 14(1), 113-126.
Bland, D. R. (1960). The Theory of Linear Viscoelasticity. Pergamon Press, Oxford.
Biot, M. A. (1954). Theory of stress-strain relations in an isotropic viscoelasticity and relaxation phenomena. Journal of Applied Physics, 25(11), 1385-1391.
Biot, M. A. (1955). Variational principal in irreversible thermodynamics with application to viscoelasticity. Physics Review, 97(6), 1463-1469.
Biot, M. A. (1956). Thermoelasticity and irreversible thermodynamics. Journal of Applied Physics, 27(3), 240-253.
Chandrasekharaiah, D. S. (1986). Thermoelasticty with second sound; A review. Applied Mechanics Review, 39(3), 355-375.
Chandrasekharaiah, D. S. (1996a). A uniqeness theorem in the theory of thermoelasticity without energy dissipation. Journal of Thermal Stresses, 19(3), 267-272.
Chandrasekharaiah, D. S. (1996b). A note on the uniqueness of solution in the linear theory of thermoelasticity without energy dissipation. Journal of Elasticity, 43(3), 279-283.
Chandrasekharaiah, D. S. (1998). Hyperbolic thermoelasticity: A review of recent literature. Applied Mechanics Review, 51(12), 705-729.
Ferry, J. D. (1970). Viscoelastic Properties of Polymers. J. Wiley and Sons, New York.
Freudenthal, A. M. (1954). Effect of rheological behaviour on thermal stress. Journal of Applied Physics, 25(9), 1-10.
Green, A. E., & Lindsay, K. A. (1972). Thermoelasicity. Journal of Elasticity, 2, 1-7.
Green, A. E., & Laws, N. (1972). On the entropy production inequality. Archive for Rational Mechanics and Analysis, 45(1), 47-53.
Green, A. E., & Naghdi, P. M. (1991). A re-examination of the basic postulates of thermomechanics. Proceedings of Royal Society, Series A 432, 171-194.
Green, A. E., Naghdi, P. M. (1993). Thermoelasticity without energy dissipation. Journal of Elasticity, 31(3), 189-208.
Gross, B. (1953). Mathematical structure of the theories of viscoelasticity. Hermann: Paris.
Gurtin, M. E., & Sternberg, E. (1962). On the linear theory of viscoelasticity. Archive for Rational Mechanics and Analysis, 11(1), 291-356.
Hetnarski, R. B., Ignaczak, J. (1996). Soliton-like waves in a low-temperature nonlinear thermoelastic solid. International Journal of Engineering Science, 34(15), 1767-1787.
Hetnarski, R. B., & Ignaczak, J. (1999). Generalized thermoelasticity. Journal of Thermal Stresses, 22(4-5), 451-476.
Ignaczak, J. (1989). Generalized thermoelasticity and its applications. Thermal Stresses III, chap. 4. In: Hetnarski, R.B. (Ed.), Mechanical and Mathematical Methods. North Holland.
Iiioushin, A. A., & Pobedria, B. E. (1970). Mathematical Theory of Thermal Viscoelasticity. Nauka, Moscow.
Kalkal, K. K., & Deswal, S. (2014). Effects of phase-lags on three-dimensional wave propagation with temperature dependent properties. International Journal of Thermophysics, 35, 952-969.
Kar, A., & Kanoria, M. (2009b). Generalized thermoe-visco-elastic problem of a spherical shell with three-phase-lag effect. Applied Mathematical Modelling, 33, 3287-3298.
Karmakar, R., Sur, A., & Kanoria, M. (2016). Thermoelastic interaction in an infinite body under dual phase lags. Journal of Applied Mechanics and Technical Physics, In Press.
Kosinski, W., & Cimmelli, V. A. (1997). Gradient generalization to inertial state variables and a theory of super fluidity. Journal of Theoretical and Applied Mechanics, 35, 763-779.
Kosinski, W. (1989). Elastic Waves in the Presence of a New Temperature Scale, in Elastic Wave Propagation. Elsevier, New York, 629-634.
Lakes, R. S. (1998). Viscoelastic Solids. CRC Press, New York.
Lord, H. W., & Shulman, Y. H. (1967). A generalized dynamical theory of thermoelasticity. Journal of Mechanics and Physics of Solids, 15(5), 299-309.
Mallik, S. H., & Kanoria, M. (2007). Generalized thermoelastic functionally graded solid with a periodically varying heat source. International Journal of Solids and Structures, 44(22-23), 7633-7645.
Mallik, S. H., & Kanoria, M. (2008). A two dimensional Problem for a transversely isotropic generalized thermoelastic thick plate with spatially varying heat source. European Journal of Mechanics A/Solids, 27(4), 607-621.
Mallik, S. H., Kanoria, M. (2009). A unified generalized thermoelasticity formulation: application to penny shaped crack analysis. Journal of Thermal Stresses, 32(9), 1-23.
Muller, I. M. (1971). The Coldness, a universal function in thermoelastic bodies. Archive for Rational Mechanics and Analysis, 41(5), 319-332.
Prasad, R., Kumar, R., & Mukhopadhyay, S. (2010). Propagation of harmonic plane waves under thermoelasticity with dual-phase-lags. International Journal of Engineering Science, 48(12), 2028-2043.
Quintanilla, R., & Horgan, C. O. (2005). Spatial behaviour of solutions of the dual-phase-lag heat equation. Mathematical Methods in Applied Sciences, 28(1), 43-57.
Quintanilla, R, Racke, R. (2006) A note on stability in dual-phase-lag heat conduction. International Journal of Heat and Mass Transfer, 49(7), 1209-1213.
Quintanilla, R. (2009). A well-posed problem for the three-dual-phase-lag heat conduction. Journal of Thermal Stresses, 32(12), 1270-1278.
Quintanilla, R. (2002). Exponential stability in the dual-phase-lag heat conduction theory. Journal of Non-Equilibrium Thermodynamics, 27(3), 217-227.
Quintanilla, R. (2003). A condition on the delay parameters in the one-dimensional dual-phase-lag thermoelastic theory. Journal of Thermal Stresses, 26(7), 713-721.
Roychoudhuri, S. K., & Bandyopadhyay, N. (2005). Thermoelastic wave propagation in rotating elastic medium without energy dissipation. International Journal of Mathematics and Mathematical Sciences, 1, 99-107.
Roychoudhuri, S. K., & Dutta, P. S. (2005). Thermoelastic interaction without energy dissipation in an infinite solid with distributed periodically varying heat sources. International Journal of Solids and Structures, 42(14), 4192-4203.
Roychoudhury, S. K. (2007). One-dimensional thermoelastic waves in elastic half-space with dual-phase-lag effect. Journal of Mechanics of Materials and Structures, 2(3), 489-502.
Suhubi, E. S. (1975). Thermoelastic solids (Chapter 2). In: Eringen, A.C. (Ed.), Continuum Physics, Part 2, vol. 2. Academic Press, New York.
Sur A., & Kanoria, M. (2014a). Thermoelastic interaction in a viscoelastic functionally graded half-space under three-phase-lag model. European Journal of Computational Mechanics, 23(5-6), 179-198.
Sur A., & Kanoria, M. (2014b). Fractional heat conduction with finite wave speed in a thermo-visco-elastic spherical shell. Latin American Journal of Solids and Structures, 11(7), 1132-1162.
Sur, A., & Kanoria, M. (2014). Finite thermal wave propagation in a half-space due to variable thermal loading. Applications and Applied Mathematics, 9(1), 94-120.
Taheri, H., Fariborz, S. J., & Eslami, M. R. (2005). Thermoelastic analysis of an annulus using the Green-Naghdi model. Journal of Thermal Stresses, 28(9), 911-927.
Tanner, R. I. (1988). Engineering Rheology. Oxford University Press.
Tzou, D. Y. (1995). A unified field approach for heat conduction from macro to micro scales. ASME Journal of Heat Transfer, 117(1), 8-16.
Bandyopadhyay, N., & Roychoudhuri, S. K. (2005). Thermoelastic wave propagation without energy dissipation in an elastic half space. Bulletin of Calcutta Mathematical Society, 97(6), 489-502.
Banik, S., Mallik, S. H., & Kanoria, M. (2007). Thermoelastic interaction with energy dissipation in an infinite solid with distributed periodically varying heat sources. International Journal of Pure and Applied Mathematics, 34(2), 231-245.
Banik, S., Mallik, S. H., & Kanoria, M. (2009). A unified generalized thermoelasticity formulation: application to an infinite body with a cylindrical cavity and variable material properties. International Journal of Applied Mechanics and Engineering, 14(1), 113-126.
Bland, D. R. (1960). The Theory of Linear Viscoelasticity. Pergamon Press, Oxford.
Biot, M. A. (1954). Theory of stress-strain relations in an isotropic viscoelasticity and relaxation phenomena. Journal of Applied Physics, 25(11), 1385-1391.
Biot, M. A. (1955). Variational principal in irreversible thermodynamics with application to viscoelasticity. Physics Review, 97(6), 1463-1469.
Biot, M. A. (1956). Thermoelasticity and irreversible thermodynamics. Journal of Applied Physics, 27(3), 240-253.
Chandrasekharaiah, D. S. (1986). Thermoelasticty with second sound; A review. Applied Mechanics Review, 39(3), 355-375.
Chandrasekharaiah, D. S. (1996a). A uniqeness theorem in the theory of thermoelasticity without energy dissipation. Journal of Thermal Stresses, 19(3), 267-272.
Chandrasekharaiah, D. S. (1996b). A note on the uniqueness of solution in the linear theory of thermoelasticity without energy dissipation. Journal of Elasticity, 43(3), 279-283.
Chandrasekharaiah, D. S. (1998). Hyperbolic thermoelasticity: A review of recent literature. Applied Mechanics Review, 51(12), 705-729.
Ferry, J. D. (1970). Viscoelastic Properties of Polymers. J. Wiley and Sons, New York.
Freudenthal, A. M. (1954). Effect of rheological behaviour on thermal stress. Journal of Applied Physics, 25(9), 1-10.
Green, A. E., & Lindsay, K. A. (1972). Thermoelasicity. Journal of Elasticity, 2, 1-7.
Green, A. E., & Laws, N. (1972). On the entropy production inequality. Archive for Rational Mechanics and Analysis, 45(1), 47-53.
Green, A. E., & Naghdi, P. M. (1991). A re-examination of the basic postulates of thermomechanics. Proceedings of Royal Society, Series A 432, 171-194.
Green, A. E., Naghdi, P. M. (1993). Thermoelasticity without energy dissipation. Journal of Elasticity, 31(3), 189-208.
Gross, B. (1953). Mathematical structure of the theories of viscoelasticity. Hermann: Paris.
Gurtin, M. E., & Sternberg, E. (1962). On the linear theory of viscoelasticity. Archive for Rational Mechanics and Analysis, 11(1), 291-356.
Hetnarski, R. B., Ignaczak, J. (1996). Soliton-like waves in a low-temperature nonlinear thermoelastic solid. International Journal of Engineering Science, 34(15), 1767-1787.
Hetnarski, R. B., & Ignaczak, J. (1999). Generalized thermoelasticity. Journal of Thermal Stresses, 22(4-5), 451-476.
Ignaczak, J. (1989). Generalized thermoelasticity and its applications. Thermal Stresses III, chap. 4. In: Hetnarski, R.B. (Ed.), Mechanical and Mathematical Methods. North Holland.
Iiioushin, A. A., & Pobedria, B. E. (1970). Mathematical Theory of Thermal Viscoelasticity. Nauka, Moscow.
Kalkal, K. K., & Deswal, S. (2014). Effects of phase-lags on three-dimensional wave propagation with temperature dependent properties. International Journal of Thermophysics, 35, 952-969.
Kar, A., & Kanoria, M. (2009b). Generalized thermoe-visco-elastic problem of a spherical shell with three-phase-lag effect. Applied Mathematical Modelling, 33, 3287-3298.
Karmakar, R., Sur, A., & Kanoria, M. (2016). Thermoelastic interaction in an infinite body under dual phase lags. Journal of Applied Mechanics and Technical Physics, In Press.
Kosinski, W., & Cimmelli, V. A. (1997). Gradient generalization to inertial state variables and a theory of super fluidity. Journal of Theoretical and Applied Mechanics, 35, 763-779.
Kosinski, W. (1989). Elastic Waves in the Presence of a New Temperature Scale, in Elastic Wave Propagation. Elsevier, New York, 629-634.
Lakes, R. S. (1998). Viscoelastic Solids. CRC Press, New York.
Lord, H. W., & Shulman, Y. H. (1967). A generalized dynamical theory of thermoelasticity. Journal of Mechanics and Physics of Solids, 15(5), 299-309.
Mallik, S. H., & Kanoria, M. (2007). Generalized thermoelastic functionally graded solid with a periodically varying heat source. International Journal of Solids and Structures, 44(22-23), 7633-7645.
Mallik, S. H., & Kanoria, M. (2008). A two dimensional Problem for a transversely isotropic generalized thermoelastic thick plate with spatially varying heat source. European Journal of Mechanics A/Solids, 27(4), 607-621.
Mallik, S. H., Kanoria, M. (2009). A unified generalized thermoelasticity formulation: application to penny shaped crack analysis. Journal of Thermal Stresses, 32(9), 1-23.
Muller, I. M. (1971). The Coldness, a universal function in thermoelastic bodies. Archive for Rational Mechanics and Analysis, 41(5), 319-332.
Prasad, R., Kumar, R., & Mukhopadhyay, S. (2010). Propagation of harmonic plane waves under thermoelasticity with dual-phase-lags. International Journal of Engineering Science, 48(12), 2028-2043.
Quintanilla, R., & Horgan, C. O. (2005). Spatial behaviour of solutions of the dual-phase-lag heat equation. Mathematical Methods in Applied Sciences, 28(1), 43-57.
Quintanilla, R, Racke, R. (2006) A note on stability in dual-phase-lag heat conduction. International Journal of Heat and Mass Transfer, 49(7), 1209-1213.
Quintanilla, R. (2009). A well-posed problem for the three-dual-phase-lag heat conduction. Journal of Thermal Stresses, 32(12), 1270-1278.
Quintanilla, R. (2002). Exponential stability in the dual-phase-lag heat conduction theory. Journal of Non-Equilibrium Thermodynamics, 27(3), 217-227.
Quintanilla, R. (2003). A condition on the delay parameters in the one-dimensional dual-phase-lag thermoelastic theory. Journal of Thermal Stresses, 26(7), 713-721.
Roychoudhuri, S. K., & Bandyopadhyay, N. (2005). Thermoelastic wave propagation in rotating elastic medium without energy dissipation. International Journal of Mathematics and Mathematical Sciences, 1, 99-107.
Roychoudhuri, S. K., & Dutta, P. S. (2005). Thermoelastic interaction without energy dissipation in an infinite solid with distributed periodically varying heat sources. International Journal of Solids and Structures, 42(14), 4192-4203.
Roychoudhury, S. K. (2007). One-dimensional thermoelastic waves in elastic half-space with dual-phase-lag effect. Journal of Mechanics of Materials and Structures, 2(3), 489-502.
Suhubi, E. S. (1975). Thermoelastic solids (Chapter 2). In: Eringen, A.C. (Ed.), Continuum Physics, Part 2, vol. 2. Academic Press, New York.
Sur A., & Kanoria, M. (2014a). Thermoelastic interaction in a viscoelastic functionally graded half-space under three-phase-lag model. European Journal of Computational Mechanics, 23(5-6), 179-198.
Sur A., & Kanoria, M. (2014b). Fractional heat conduction with finite wave speed in a thermo-visco-elastic spherical shell. Latin American Journal of Solids and Structures, 11(7), 1132-1162.
Sur, A., & Kanoria, M. (2014). Finite thermal wave propagation in a half-space due to variable thermal loading. Applications and Applied Mathematics, 9(1), 94-120.
Taheri, H., Fariborz, S. J., & Eslami, M. R. (2005). Thermoelastic analysis of an annulus using the Green-Naghdi model. Journal of Thermal Stresses, 28(9), 911-927.
Tanner, R. I. (1988). Engineering Rheology. Oxford University Press.
Tzou, D. Y. (1995). A unified field approach for heat conduction from macro to micro scales. ASME Journal of Heat Transfer, 117(1), 8-16.