A numerical study of JKR-type adhesive contact of ellipsoids

The approximate solution by Johnson and Greenwood (2005 J. Phys. D: Appl. Phys. 38 1042–6) for an adhesive contact of an ellipsoid and an elastic half-space is revisited numerically using the fast Fourier transformation-based boundary element method. While for moderate values of the ratio of principal radii of the ellipsoid, R ₁/R ₂, predictions of the Johnson–Greenwood approximate theory are very good, they become increasingly inaccurate for large values of this parameter. On the basis of numerical simulations, we provide analytical expressions for the dependencies between load, approach and contact area and compare the exact shape of the contact area with the elliptical one assumed in the Johnson–Greenwood-theory. (paper)