Spherically Symmetric Shock Waves in Materials with a Nonlinear Stress-Strain Dependence

Abstract:

Article Preview

The paper considers the dynamic deformation features of constructional materials with nonlinear stress-strain dependence. For the one-dimensional shock waves with nonzero curvature arising in constructions under dynamic loading the propagation regularities are studied on the basis of the matched asymptotic expansions method. In the nonstationary problem with the longitudinal spherical shock wave the relations for simultaneous consideration of dynamic properties in the outer and inner problem of the perturbation method are obtained. The solution in the front-line area is constructed on the basis of the evolution equation different from ones for a plane longitudinal wave. The need for a solving of an additional ODE system for matching outer and inner expansions is shown. It is obtained that the outer solution asymptotics in the spherically symmetric problem contains waves reflected from the leading front in contrast to the solution behavior behind the front of the plane shock wave.

Info:

Periodical:

Edited by:

Dr. Denis Solovev

Pages:

807-812

Citation:

V. E. Ragozina and Y. E. Ivanova, "Spherically Symmetric Shock Waves in Materials with a Nonlinear Stress-Strain Dependence", Materials Science Forum, Vol. 945, pp. 807-812, 2019

Online since:

February 2019

Export:

Price:

$41.00

* - Corresponding Author

[1] D.R. Bland, Nonlinear Dynamic Elasticity, Blaisdell, London, (1969).

[2] I.I. Goldenblat, Nonlinear Problems of the Elasticity, Nauka, Moscow, 1969. (in Russian).

[3] A.I. Lurie, Nonlinear Theory of Elasticity, North-Holland, Amsterdam, (1990).

[4] A.G. Kulikovskii, E.I. Sveshnikova, Nonlinear Waves in Elastic Media, CRC Press, Boca Raton, (1995).

[5] A.G. Kulikovskii, A.P. Chugainova, Classical and nonclassical discontinuities and their structures in nonlinear elastic media with dispersion and dissipation, Proc. Steklov Inst. Math. 276 (2012) 1-68.

DOI: https://doi.org/10.1134/s0081543812030017

[6] A.A. Burenin, A.D. Chernyshov, Shock waves in an isotropic elastic space, J. Appl. Math. Mech. 42 (1978) 758-765.

[7] A.V. Porubov, Localization of Nonlinear Deformation Waves, Fizmatlit, Moscow, 2009. (in Russian).

[8] M.D. Van Dyke, Perturbation Methods in Fluid Mechanics, Academic Press, New York, (1964).

[9] J.D. Cole, Perturbation Methods in Applied Mathematics, Blaisdell Pub. Co., Waltham, (1968).

[10] A.H. Nayfeh, Introduction to Perturbation Techniques, Wiley-VCH, New York, (1993).

[11] G.I. Bykovtsev, D.D. Ivlev, Theory of Plasticity, Dalnauka, Vladivostok, 1998. (in Russian).

[12] L.I. Sedov, Mechanics of continuous media (IN 2 VOLS), World Scientific, New Jersey, (1997).

[13] T.Y. Thomas, Plastic Flow and Fracture in Solids, Academic Press, New York, (1961).

[14] V.E. Ragozina, Yu.E. Ivanova, About the evolutionary equations of problems of a shock straining with plane discontinuity surfaces, Computational Continuum Mechanics. (2) 2009 82-95. (in Russian).

DOI: https://doi.org/10.7242/1999-6691/2009.2.3.25

[15] V.E. Ragozina, Yu.E. Ivanova, Mathematical model of movement of shear shock waves of nonzero curvature on the basis of their evolution equation, Siberian Journal of Industrial Mathematics. 15 (2012) 77-85. (in Russian).

[16] V.E. Ragozina, Yu.E. Ivanova, On the impact deformation of an incompressible half-space under the action of a shear load of variable direction, J. Appl. Ind. Math. 8(2014) 366-374.

DOI: https://doi.org/10.1134/s1990478914030090

[17] V.E. Ragozina, Yu.E. Ivanova, Effect of the Medium Inhomogeneity on the Evolution Equation of Plane Shock Waves, J. Appl. Mech. Tech. Ph. 5 (2013) 809-818.

DOI: https://doi.org/10.1134/s0021894413050143

[18] J.K. Engelbrecht, V.E. Fridman, E.N. Pelinovsky, Nonlinear Evolution Equations (Pitman Research Notes in Mathematics Series, No. 180), Longman, London, (1988).

[19] G.B. Whitham, Linear and Nonlinear Waves, John Wiley & Sons, New York, (1974).