Subsonic Frictional Cavitating Penetration of a Thin Rigid Body Into an Elastic Medium

Abstract

Two model problems of plane elasticity on subsonic steady-state motion of a thin rigid body in an elastic medium are analyzed. Both models concern a finite body symmetric with respect to the plane of motion and assume that the body contacts with the surrounding medium according to the Coulomb friction law. The body, while moves, leaves a trailing semi-infinite cracklike cavity moving at the body speed. The first model also assumes that ahead of the body a finite crack-like cavity is formed, and it is moving at the same speed. The second model does not admit the existence of this finite cavity. Both problems reduce to two sequently solved Riemann–Hilbert problems with piece-wise constant coefficients. Analysis of the solution to these problems obtained by quadratures reveals that the normal and tangential traction components and the normal velocity are continuous for any point of separation of the medium from the body. A criterion for the separation point based on the analysis of the sign of the normal traction component is proposed. Numerical results for the length of the fore crack (the first model), the normal traction and the resistance force for some ogive-nose penetrators are reported.