Axisymmetric Contact Problem of an Elastic Half-Space with a Spherical Inclusion.

Abstract

A solution is presented to an axisymmetric contact problem of a circular rigid punch penetrating an elastic half-space in which a spherical inclusion coaxial with the punch is embedded. By expressing the contact stress under the punch and the interface displacements and stresses between the half-space and the inclusion as appropriate series, the doubly mixed boundary-value problem is reduced to the solution of an infinite system of simultaneous equations. Numerical results are obtained for stress distributions under the punch and around the inclusion as well as for the force transmission underneath the punch due to the presence of the inclusion. Comparisons with the results in the absence of the inclusion are made in order to illustrate the effect of the presence of the inclusion on the stress field.