Far Eastern Mathematical Journal

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On the analisis of velocities and stress disconuities in ideal granular elastic-plastic medium

O. V. Sadovskaya

2003, issue 2, P. 242–251

Abstract

With the object of dynamic deformation of granular material description the mathematical model baseol on the hyptesis about additive decomposition of small strain tensor info elastic-granular and plastic parts is used. Elastic properties are desined by the equations of linear theory of elasticity combining with the perception about the Mises-Schleykher limit surface. The plastic constitutive equations are formylated in the frame of the flow theory with the von Mises yield surface. The shock adiabatic curres of longitudinal elastic waves and plastic waves of compression are constructed on the base of such model at different combinations of mechanical parameters. The various admissible plane shock wave configurations arising in insinite solid mass are investigated.

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References

[1] L. I. Sedov, Mexanika sploshnoj sredy, t. II, Nauka, M., 1976, 576 s. [2] V. M. Sadovskij, “Reologicheskie modeli raznomodul'nyx i sypuchix sred”, Dal'nevostochnyj matematicheskij zhurnal, 4:2 (2003), 252–263. [3] G. I. Bykovcev, D. D. Ivlev, Teoriya plastichnosti, Dal'nauka, Vladivostok, 1998, 528 s. [4] V. M. Sadovskij, Razryvnye resheniya v zadachax dinamiki uprugo-plasticheskix sred, Nauka, M., 1997, 208 s.

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