ABSTRACT
The shapes of the deformed surfaces given above were obtained by solving the equations of continuum elasticity theory in the semi-infinite half-space approximation [38, 42]
Here the elasticity parameter E is given in terms of Young's moduli and Poisson's ratios of the two bodies, 2/E = (1 - v\)/Ei + (1 - v\)/E2\ r = |r| and s = |s| are the lateral distances from the central axis connecting the centres of the bodies (the integration is over the two-dimensional plane bisecting the two bodies); and p(h) is the pressure between two infinite planar walls at a separation of h. The total deformation normal to the surfaces at each position is u(r) and hence the local separation between the two bodies is h(r) = ho(r) — u(r). Here the local separation of the undeformed surfaces is ho(r) = ho + r2/2R, where ho is the separation on the axis, and where R~l = i?^1 + R^1 is the effective radius of the interacting bodies; in general, the Ri is related to the principal radius of curvature of each body [43].
