×

zbMATH — the first resource for mathematics

The effect of slight anisotropy on the properties of shock waves in a compressible elastic medium. (English. Russian original) Zbl 0891.73015
J. Appl. Math. Mech. 59, No. 5, 763-767 (1995); translation from Prikl. Mat. Mekh. 59, No. 5, 793-798 (1995).
Summary: The effect of slight anisotropy on the behaviour of shock waves in a compressible elastic medium is investigated. Particular attention is paid to the properties of shock waves which are not close to plane-polarized waves (the properties of plane-polarized shock waves only change slightly). Some results are obtained for an arbitrary form of anisotropy when the behaviour of shock waves is known in media which differ from those without anisotropy.
MSC:
74M20 Impact in solid mechanics
74E10 Anisotropy in solid mechanics
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Sveshnikova, Ye.I., Shock waves in a weakly anisotropic elastic incompressible material, Prikl mat. mekh., 58, 3, 144-153, (1994)
[2] Kulikovskii, A.Cr.; Sveshnikova, Ye.I., Riemann waves in an elastic medium with slight anisotropy, Prikl. mat. mekh., 57, 3, 90-101, (1993)
[3] Bland, D.R., Non-linear dynamic theory of elasticity, (1972), Mir Moscow · Zbl 0242.73002
[4] Kulikovskii, A.G.; Lyubimov, G.A., Magnetohydnxlynamics, (1962), Fizmatgiz Moscow
[5] Hanyga, A., Shear waves 1-III, Publs. inst. geophys. Pol. acad sci., 87, 1-61, (1975)
[6] Hanyga, A., On the solution to the Riemann problem for arbitrary hyperbolic system of conservation laws, Publs. inst. geophys. Pol. acad. sci., 1, 98, 123, (1976)
[7] Lenskii, E.V., On the shock adiabatic curve of a plane longitudinal shear discontinuity, Vesm. mosk GoS. univ. ser. mat., mekh., 1, 94-96, (1981)
[8] Lenskii, E.V., Plane compression-shear waves in a non-linearly elastic incompressible medium, Izv akad nauk SSSR, MTT, 6, 90-98, (1983)
[9] Lax, P., Hyperbolic system of conservation laws II, Comm. pure and appl. math., 10, 4, 537-566, (1957) · Zbl 0081.08803
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.