A general solution to the axisymmetric frictional contact problem of a thin bonded elastic layer

The configuration of a thin elastic layer bonded firmly to a rigid substrate and pressed by a spherical punch has been used as a model to many problems arising in the field of biomechanics. This work presents a rigorous analysis of a thin bonded layer indented by a punch of general profile in the presence of the radial tangential traction. The method is based on perturbation theory. Formulae for stresses, strains and deformations are derived in terms of layer thickness, material properties and surface tractions. The results are illustrated by the evaluation of the expressions for several simple punch shapes. The influence of friction on the results is also examined. Good agreement is found between the present solution and the results reported in the literature.