Effect of Sliding Friction on Contact Stresses in a Rectangle Compressed by Rigid Planes

The plane-strain compression of an elastic rectangle by rigid, rough planes with finite coefficient of friction between the surfaces is considered. The contact area is divided into an inner adhesive region in which the surface displacements are known, surrounded by regions in which the friction is limiting and the displacement parallel to the interface is not known. The remaining set of parallel edges of the rectangle is free from tractions. The problem is formulated in terms of Papkovich-Fadle eigenfunctions which lead to the solution of a set of two integral equations of the second kind. Solution of the integral equations which satisfies the finiteness of stresses at the point which separates the adhesive from the slip zone, determines the extent of adhesion. This is found to be independent of the magnitude of load, but depends on the values of frictional coefficients, Poisson’s ratio and the aspect ratio. Numerical results of the quantities of practical interest are reported.