Abstract
A one-dimensional problem for a viscoelastic half space is considered in the context of the generalized theory of thermoviscoelasticity with one relaxation time. The bounding plane is acted upon by a combination of thermal and mechanical shock acting for short times. The Laplace transform technique is used to solve the problem. The solution in the transformed domain is obtained by a direct approach. The inverse transforms are obtained in an approximate analytical manner using asymptotic expansions valid for small values of time. The temperature, displacement, and stress are computed and represented graphically.
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References
B. Gross, Mathematical Structures of the Theories of Viscoelasticity (Hermann, Paris, 1953)
E.M. Gurtin, E. Sternberg, Arch. Ration. Mech. Anal. 11, 182 (1962)
M.M. Stratonova, Mech. Compos. Mater. 7, 646 (1971)
E.B. Pobedrya, Mech. Compos. Mater. 15, 271 (1979)
A. A. Il’yushin, E. B. Pobedrya (Nauka, Moscow, 1970) [in Russian]
E.B. Pobedrya, Mech. Compos. Mater. 5, 353 (1969)
E.B. Pobedrya, Int. Appl. Mech. 41, 1031 (2005)
G. Medri, Meccanica 23, 226 (1988)
M. Hajar, H.R. Blanc, Acta Mechanica 130, 175 (1998)
M. Hajar, H.R. Blanc, Acta Mechanica 130, 185 (1998)
S.A. Lychev, Mech. Solids 43, 769 (2008)
H. Sherief, M. Allam, M. Elhagary, Int. J. Thermophys 32, 1271 (2011)
H. Lord, Y. Shulman, J. Mech. Phys. Solids 15, 299 (1967)
R. Dhaliwal, H. Sherief, Quart. Appl. Math. 33, 1 (1980)
H. Sherief, J. Therm. Stresses 9, 151 (1986)
H. Sherief, Int. J. Eng. Sci. 32, 313 (1994)
H. Sherief, M. Anwar, J. Therm. Stresses 9, 165 (1986)
H. Sherief, A. Elmisiery, M. Elhagary, J. Therm. Stresses 27, 885–902 (2004)
R. Churchill, Operational Mathematics, 3rd edn. (McGraw-Hill, New York, 1972)
F. Oberhettinger, L. Badii, Tables of Laplace Transforms (Springer, New York, 1973)
N.G. Watson, A Treatise on the Theory of Bessel Functions, 2nd edn. (Cambridge University Press, London, New York, 1996)
H. Sherief, R. Dhaliwal, J. Therm. Stresses 4, 407 (1981)
R. Hetnarski, Arch. Mech. Stosow 13, 295 (1961)
R. Hetnarski, Bull. Acad. Pol. Sci. Ser. Sci. Tech. 12, 49 (1964)
B. Boley, Quart. Appl. Math. 19, 273 (1962)
G. Honig, U. Hirdes, J. Camp, Appl. Math. 10, 113 (1984)
H. Sherief, M. Anwar, J. Therm. Stresses 17, 213 (1994)
M. Anwar, H. Sherief, Appl. Math. Model. 12, 161 (1988)
M. Anwar, H. Sherief, J. Therm. Stresses 17, 257 (1994)
P. Hosseini-Tehrani, M.R. Eslami, Eng. Anal. Bound. Elem. 24, 249 (2000)
S. Bargmann, P. Steinmann, A Continuous Galerkin Finite Element Method for Thermoelasticity Without Energy Dissipation (III European Conference on Computational Mechanics, Lisbon, 2006)
I. Abbas, Forsch Ingenieurwesen 71, 215 (2007)
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Elhagary, M.A. A Thermo-mechanical Shock Problem for Generalized Theory of Thermoviscoelasticity. Int J Thermophys 34, 170–188 (2013). https://doi.org/10.1007/s10765-013-1395-1
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DOI: https://doi.org/10.1007/s10765-013-1395-1