The impact of a rigid sphere with an elastic layer of finite thickness

Summary

The problem of the impact of a rigid sphere with an elastic isotropic layer is considered in the initial stage of dynamic interaction. The initial stage is characterized by the fact that the velocity of the displacement of the intersection points of the sphere with the upper boundary of the layer is larger than the velocity of longitudinal waves, hence the free surface normal to the contact domain with the body is undisturbed. The method of successive approximations as well as the ray method, according to which the solution behind the fronts of incident and reflected waves is constructed in terms of power series (ray expansions), are used as methods of solution. In the problem under consideration, we used one-term ray expansions whereby the main characteristics of the shock interaction have been obtained, and the possibility of localized damage of the material of the layer at the points lying along the central ray has been examined.