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IssuesArchive of Issues2004-6pp.78-86

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A. D. Avdeeva and E. I. Sveshnikova, "Quasi-transverse shock waves in an elastic medium with a complex form of the elastic potential energy," Mech. Solids. 39 (6), 78-86 (2004)
Year 2004 Volume 39 Number 6 Pages 78-86
Title Quasi-transverse shock waves in an elastic medium with a complex form of the elastic potential energy
Author(s) A. D. Avdeeva (Moscow)
E. I. Sveshnikova (Moscow)
Abstract Weak shock waves in slightly anisotropic elastic media are considered. In the previous studies of this problem, the elastic potential (internal) energy of the medium was represented as a series in small strains and small entropy variation, in which only the leading terms responsible for the nonlinearity and anisotropy were retained. In the present study, subsequent terms of this series are taken into account. This makes it possible to extend the range of applicability of the results to larger shock wave amplitudes and to examine the accuracy of the previous model. The complex problem formulation is linearized with respect to the previous solution regarded as zero approximation. For quasi-transverse shock waves, the shock velocities and the corrected shape of the shock adiabat are found. The states behind the shock, which satisfy the evolution and entropy no-decrease conditions, are obtained.
References
1.  D. R. Bland, Nonlinear Dynamic Elasticity, Toronto, London, Waltham, 1969.
2.  A. G. Kulikovskii and E. I. Sveshnikova, Nonlinear Waves in Elastic Media [in Russian], Moskovskii Litsei, Moscow, 1998.
3.  A. G. Kulikovskii and E. I. Sveshnikova, "Influence of the entropy change on the shock adiabat form for quasi-transverse elastic waves," PMM [Applied Mathematics and Mechanics], Vol. 67, No. 1, pp. 88-98, 2003.
4.  A. G. Kulikovskii and E. I. Sveshnikova, "Investigation of the shock adiabat for quasi-transverse shock waves in the prestressed elastic medium," PMM [Applied Mathematics and Mechanics], Vol. 46, No. 5, pp. 831-841, 1982.
5.  L. I. Sedov, Continuum Mechanics.Volume 2 [in Russian], Nauka, Moscow, 1984.
Received 31 July 2003
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