Impact of a Rigid Sphere on an Elastic Homogeneous Half-Space

The impact of a rigid sphere moving at constant velocity on elastic homogeneous half-space was analyzed by the finite element method. Frictionless dynamic contact was modeled with special contact elements at the half-space surface. A dimensionless parameter, β, was introduced to study the effect of wave propagation on the deformation behavior. For small surface interference (β⩽1), the front of the faster propagating dilatational waves extends up to the contact edge, the real contact area is equal to the truncated area, and the contact pressure distribution is uniform. However, for large surface interference (β>1), the dilatation wave front extends beyond the contact edge, the real contact area is less than the truncated area, and the contact pressure exhibits a Hertzian-like distribution. The mean contact pressure increases abruptly at the instant of initial contact, remains constant for β⩽1, and increases gradually for β>1. Based on finite element results for the subsurface stress, strain, and velocity fields, a simple theoretical model that yields approximate closed-form relationships for the mean contact pressure and kinetic and strain energies of the half-space was derived for small surface interference (β⩽1), and its validity was confirmed by favorable comparisons with finite element results.