Contact Stresses Between an Elastic Cylinder and a Layered Elastic Solid

The generalized plane strain problem of the contact of layered elastic solids is reduced to an integral equation using Green’s function approach. Approximate numerical solutions are obtained by replacing the integral equation by a matrix inversion when the trapezoidal rule is used to represent the integral. Results for determining the actual contact pressure at the center of the contact zone and size of contact zone for a wide range of layer thicknesses are presented for two most practical cases, (i) when the indenter is rigid, and (ii) when the indenter is elastic having a modulus of elasticity equal to that of the substrate of the indented body. When the layer is softer than the substrate it is found that the actual contact pressure distribution is very closely determined by a weighted sum of elliptic and parabolic functions. For a substrate softer than the layer the pressures substantially deviate from an elliptical or parabolic behavior, for the cases when the layer thickness is finite. The analysis checks with the Hertzian solution in the extreme cases when the layer thickness either tends to zero or approaches infinity.