On the Motion of Shock Waves at a Constant Speed in Multimodulus Elastic Media
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For piecewise linear models of multimodulus elastic media, exact analytical solutions of one-dimensional dynamic deformation problemswith plane or sphericalwave surfaces are presented. Compression-extension regimes with the appearance of a centered Riemann wave and extensioncompression with formation of a shock wave are considered. As the main solution method for the compression phase, we use the method of inverse determination of the boundary condition from known information on the nature ofmotion of the shock wave. Essential qualitative differences of the solutions obtained from the corresponding classical results for linearly elastic media are especially important in the study of the dynamics of porous and cohesive granular media.
Keywordselasticity multimodulus property piecewise linear model plane waves spherical waves shock wave simple discontinuity centered Riemann wave
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- 1.I. V. Baklashov and B. A. Kartozia, RockMechanics (Nedra, Moscow, 1975) [in Russian].Google Scholar
- 2.A. V. Berezin, Effect of Damage on Strain and Strength of Solids (Nauka, Moscow, 1990) [in Russian].Google Scholar
- 3.E. V. Lomakin and Yu. N. Rabotnov, “A Theory of Elasticity for an Isotropic Body with Different Moduli in Tension and Compression,” Izv. AN SSSR. MTT, No. 6, 29–34 (1978) [Mech. Solids (Engl. Transl.) 13 (6), 25–30 (1978)].Google Scholar
- 4.V. P. Myasnikov and A. I. Oleinikov, Fundamentals of Mechanics of Heterogeneous-Resisting Media (Dal’nauka, Vladivostok, 2007) [in Russian].Google Scholar
- 5.S. A. Ambartsumyan and A. A. Khachatryan, “The Basic Equations of the Theory of Elasticity for Materials with Different Stiffnesses in Tension and Compression,” Izv. AN SSSR. MTT. No. 2, 44–53 (1966) [Mech. Solids (Engl. Transl.) 1 (2), 29–34 (1966)].Google Scholar
- 6.O. V. Dudko, A. A. Lapteva, and V. E. Ragozina, “About the Occurrence of Plane and SphericalWaves in an Elastic Medium, Different Resistance to Tension and Compression,” Vestnik Chuvash. Gos. Ped. Univ. im I. Ya. Yakovleva. Ser.Mekh. Pred. Sost. No. 4(14), 147–155 (2012).Google Scholar
- 8.O. V. Dudko, A. A. Lapteva, and K. T. Semenov, “About Distribution of Flat One-Dimensional Waves and Their Interaction with Barrier in theMedia DifferentlyReacting to a Stretching and Compression,” Dal’nevost. Mat. Zh. 6 (1–2), 94–105 (2005).Google Scholar