COMPLETE AND INCOMPLETE PLASTICITY STATES FOR INITIALLY ANISOTROPIC MEDIA
A. I. Chanyshev1,2, I. M. Abdulin1, I. V. Gutarova2, L. L. Efimenko2, I. V. Frolova2, O. A. Lukyashko1
1Chinakal Institute of Mining, Siberian Branch, Russian Academy of Sciences, Novosibirsk, Russia
2Novosibirsk State University of Economics and Management, Novosibirsk, Russia
Keywords: Анизотропия, полная пластичность, неполная пластичность, жесткий клин, предельная нагрузка, глубина проникания, Anisotropy, complete plasticity, incomplete plasticity, rigid wedge, limit load, penetration depth
Abstract
For initially anisotropic media, a theory of plasticity based on the multiplicity of eigenvalues is constructed. If the eigenvalues are simple, then the condition of plasticity of such medium is a parallelepiped, and the position on the edge of the parallelepiped is called the state of complete plasticity, the position on the face is called the state of incomplete plasticity. To illustrate these states, the problem of forcing down a rigid wedge into the initial anisotropic medium with the condition of plasticity in the form of a parallelepiped is solved. The limit load and the maximum penetration depth with a given initial speed of the striker are determined.
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