The dynamic contact stresses caused by the impact of a nonlinear elastic half-space by an axisymmetrical projectile

A numerical procedure is developed for the treatment of impact-contact problems in which mixed boundary conditions must be satisfied over a time-dependent region which is not known in advance but should be determined from the solution. This procedure involves an iterative process which is continued until the correct solution is obtained. This solution is determined by the equations of motion, the moving boundary conditions, the relation between the mass of the projectile and the reaction of the half-space, and the requirements that the contact normal stress is compressive and that no interpenetration occurs outside the contact region. The reliability of the method is checked in the dynamic indentation problem of a linearly elastic half-space by a conical wedge for which an analytical solution is known, and excellent agreement is obtained. The proposed method is applied to the problem of a rigid axisymmetrical projectile which impacts a nonlinearly elastic compressible half-space, and the problem of an impacted linear half-space is obtained as a special case.