nonlinear elastic medium, incompressibility, shock wave, plane strain, characteristics of hyperbolic systems, perturbation method, ray series.

The problem of one-dimensional plane deformation of a nonlinear elastic incompressible half-space under the impact load action on its boundary is solved. The half-space is in a free state until the moment of impact action. This condition leads to the discontinuity in the boundary conditions at the half-space boundary moves as the only plane-polarized shock wave, on which the direction of the preliminary shear remains unchanged. The pointed out properties of the leading edge of the shock action follow from the joint analysis of the characteristic directions of the problem and the shock waves types for a one-dimensional plane problem in an incompressible medium with arbitrary preliminary deformations. Two versions of the problem approximate solution based on the method of matched asymptotic expansions and on the basis of the ray series method are presented.

Ragozina Victoria Evgenievna,

Cand. Sci. Phys. & Math., Senior Researcher, Institute of Automation and Control Processes FEB RAS, Vladivostok, Russia.

Ivanova Yulia Evgenievna, Cand. Sci. Phys. & Math., Researcher, Institute of Automation and Control Processes FEB RAS, Vladivostok, Russia.