Effect of surface tension on the adhesion between a rigid flat punch and a semi-infinite neo-Hookean half-space

We study the effect of surface stress on the retraction of a rigid flat circular punch adhering to an incompressible neo-Hookean half space using a large deformation finite element model (FEM). The effect of surface stress is determined by the dimensionless elasto-capillary number, ω=σ/(Ea), where σ is the isotropic solid-air interface surface stress which we shall called surface tension, E is the small strain Young's modulus and a is the radius of punch. Adhesion of the punch to the half space is characterized by work of adhesion Wad. Within the range of retraction displacement of this work (less or equal to the punch radius), the stiffness of the system is insensitive to retraction displacement and depends only on the elasto-capillary number. In general, surface tension increases the slope of load-displacement curve or the stiffness of the system. For a given work of adhesion, the pull-off force (displacement) increases (decreases) with surface tension. Our results show that the apparent contact angle is not 90 degrees, as predicted by linear elastic theory, but varies from 20 to 180 degrees and is very sensitive to ω when it is near zero. This result can be potentially used to measure solid surface tension.