Indentation of an Elastic Half-space by a Concave Rigid Punch

Abstract

The present paper is concerned with the indentation of an elastic half-space by an axisymmetric, slightly concave rigid punch. When the indenting load is small, the contact area will be an annulus, the outer circumference of which coincides with the edge of the punch. The inner circumference of which coincides with the edge of the punch. The inner circumference of which coincides with the edge of the punch. The inner circumference will shrink with an increasing force. The stress state of such a problem is analyzed based on the theory of three-dimensional elasticity. For each case of parabolical and conical concaves, we obtain the distributions of surface displacements and contact stresses and their relations to the indenting force, indenting depth and concave's shape.