Mind the Gap: The Shape of the Free Surface of a Rubber-Like Material in Proximity to a Rigid Contactor

Extending Andreussi and Gurtin's [1] pioneering work on the wrinkling of a free surface, we investigate the wrinkling stability of an incompressible elastic-like half-space whose surface is proximate to a contactor. Assuming a plane-strain deformation and accounting for both surface prestress and curvature dependence of the surface free-energy density, we impose balances of forces and torques both in the bulk and on the surface. From the resulting linearized bulk and superficial equations, we derive a quintic dimensionless dispersion relation and perform a parametric study to see when stable or unstable behavior of the free surface is manifested. When compared with the quadratic dispersion relation of Andreussi and Gurtin [1], we see here that the combined effects associated with surface prestress, curvature-dependence of the surface free-energy density, and the interactions between the surface and the proximate contactor always lead to an increased number of linearly stable wrinkled configurations.