Effect of large deformation and material nonlinearity on the JKR (Johnson-Kendall-Roberts) test of soft elastic materials

We study in detail the effect of large deformation and material nonlinearity on the JKR (Johnson-Kendall-Roberts) theory of adhesive contact for two systems. The first is a Neo-Hookean hemisphere in adhesive contact with a smooth rigid substrate. The second is a smooth rigid spherical indenter in adhesive contact with a Neo-Hookean half space. We show that our results are special cases of a general theory that models large deformation adhesive contact of spherical lenses. This theory shows that the solution of any large deformation JKR (LDJKR) problem can be obtained from the solution of a corresponding large deformation Hertz (LDH) problem. Using this theory, we extend the small strain JKR theory to the large deformation regime, the only restriction being that the materials are nonlinear elastic or hyperelastic. The adhesive contact problem for the two systems is solved using two methods. In method one, the LDJKR theory is obtained using finite element simulation results for a corresponding LDH problem; in method two, we solve the adhesive contact problems directly using a cohesive zone model to quantify adhesive interaction.