Transient dynamic contact problems of the theory of elasticity with varying width of the contact zone

Abstract

Two transient dynamic contact problems involving the penetration of a rigid punch into an elastic half-space are considered. In the first problem the punch is wedge-shaped, in the second, a paraboloid. The problems are solved by a method developed in previous publications [1, 2]. The requirements imposed on the smoothness of the solutions of the problems lead to additional conditions, due to which the width of the contact area between the punch and the elastic half-space, which varies with time, is determined as a function of time and of the law governing the penetration of punch into the elastic half-space, which is determined from the differential equation of motion of a massive punch on the elastic half-space.