The Contact Problem of an Elastic Half Space with an Adhered Rigid Punch

Abstract

A contact problem of an elastic half space with an adhered rigid punch under tension is considered on the basis of the three-dimensional theory of elasticity. The behaviour of the adhesion is approximated by a combination of tension and shear springs. The normal and shearing stresses on the adhesive plane of the half space are expressed by Jacobi polynomials. This mixed boundary value problem is reduced to solving two infinite systems of simultaneous equations. The distributions of stresses and displacements on the surface of the half space are illustrated in various cases of the adhesion. The effect of the adhesion on these results is discussed in detail.