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2017 year, number 5

Dynamics of Deformation of an Elastic Medium with Initial Stresses

E. I. Romenskii1,2, E. B. Lys3, V. A. Cheverda3, M. I. Epov3
1Sobolev Institute of Mathematics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
2Novosibirsk State University, Novosibirsk, 630090 Russia
3Trofimuk Institute of Oil and Gas Geology and Geophysics, Siberian Branch, Russian Academy of Sciences, Novosibirsk, 630090 Russia
Keywords: движение упругой среды, начальные напряжения, упругие волны, motion of an elastic medium, initial stresses, elastic waves

Abstract

The constitutive equations of motion of an elastic medium with given initial stresses are formulated in the form of a hyperbolic system of differential equations of the first order. Equations describing the propagation of small perturbations in a prestressed isotropic medium with an arbitrary energy dependence of the elastic deformation in the strain tensor are derived, and equations for the quadratic dependence of elastic strain energy on the strain tensor are given.