JKR solution for an anisotropic half space

In this paper, the classical JKR theory of the adhesive contact of isotropic elastic spheres is extended to consider the effect of anisotropic elasticity. The contact area will then generally be non-circular, but in many cases it can reasonably be approximated by an ellipse whose dimensions are determined by imposing the energy release rate criterion at the ends of the major and minor axes. Analytical expressions are obtained for the relations between the contact force, the normal displacement and the ellipse semi-axes. It is found that the eccentricity of the contact area decreases during tensile loading and for cases when the point load solution can be accurately described by only one Fourier term, it is almost circular at pull-off, permitting an exact closed form solution for this case. As in the isotropic JKR solution, the pull-off force is independent of the mean elastic modulus, but we find that anisotropy increases the pull-off force and this effect can be quite significant.