nonlinear elastic incompressible inhomogeneous medium, transverse shock waves, shear load with variable directivity, the evolution equations system, the evolution equation for the change of shear intensity, the evolution equation for the change of shear direction.

The paper presents a generalization of the asymptotic analysis method of frontline areas for problems of impact deformation of nonlinear elastic medium, based on the derivation of the evolution equation. This method can be extended from one-dimensional boundary value problems on multi-dimensional ones due to the transition to the linear approximation of the ray coordinate. It is shown that the evolution equation contains a eikonal coordinate only as a parameter, ie, the ray coordinate of frontal area has a dominant significance in the assessment of the rate of deformation change. The solution of two-dimensional problem of antiplane deformation of an incompressible nonlinear elastic medium is constructed as a model example. 

1. Ragozina Victoria Evgenevna Candidate of Phys.&Math., Senior Researcher, Institution of Russian Academy of Sciences Institute of Automation and Control Processes of Far Eastern Branch of Russian Academy of Sciences, Vladivostok

2. Ivanova Yulia Evgenevna Candidate of Phys.&Math., Researcher, Institution of Russian Academy of Sciences Institute of Automation and Control Processes of Far Eastern Branch of Russian Academy of Sciences, Vladivostok