An Axisymmetric Contact Problem with Given Region of Adhesion

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Abstract
The indentation of an elastic half-space by an axisymmetric rigid punch under normal load is considered. The contact area is divided into an inner region with adhesion, the dimension of which is known beforehand, surrounded by an annular slip zone. Two different cases of the problem, given by the assumptions of friction-free slip or Coulomb friction, are treated. In the friction-free case the problem is formulated in terms of a coupled pair of Cauchy type integrals for Abel transforms of the normal and shear stresses at the surface of the half-space. These are combined to an inhomogeneous Fredholm equation which is solved by a method of successive approximations, and the stresses are obtained as Abel transform inversions of its solution. In the case with Coulomb friction the problem is solved by a numerical method based on piecewise constant approximations to the surface stresses.

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