On the impact deformation of an incompressible half-space under the action of a shear load of variable direction

Abstract

Using the example of a one-dimensional planar problem for a nonlinear elastic incompressible half-space, the loading process is considered in which the shear action on the boundary plane changes with respect to both intensity and direction. It is shown that, in the regions of the space where the nonlinearity of the medium becomes a significant factor, the solution in the nearfront region of the shock wave is determined by a system of nonlinear evolution equations. The general solution of the evolution system is obtained. As an example, a partial solution of the system is considered for one of the simplest boundary conditions. A parametric method is presented for determining the displacements on the basis of solution of the evolution system.