Penetration of a Half Space by a Rectangular Cylinder

Abstract

The stress and displacement fields are determined in an elastic half space loaded by a rectangular frictionless, rigid block normally at its surface. The semi-infinite solid is considered to be an elastic solid with nonlocal interatomic interaction. The field equations of the nonlocal elasticity and boundary conditions are employed to treat this contact problem. Interestingly the classical stress singularity at the edges of the block are not present in the nonlocal solutions. Consequently the critical applied load for the initiation of penetration of the rigid cylinder into the semi-infinite solid can be determined without recourse to any criterion foreign to the theory. The stress field obtained is valid even for penetrators of submicroscopic width.