Modeling contact between rigid sphere and elastic layer bonded to rigid substrate

An approximate mechanical model is developed for predicting the radius of contact between a sphere and a layered substrate. The complex solution of Chen and Engel is reduced to the simple root finding procedure for the unknown contact radius. Numerical data from the model of Chen and Engel are obtained for several combinations of layer material. It is shown that with the proper selection of dimensionless parameters the numerical results fall on a single curve that is easily correlated. Radius predictions show good agreement with experimental measurements.