Mode-mixity-dependent adhesive contact of a sphere on a plane surface

Tangential loading in the presence of adhesion is highly relevant to biological locomotion, but mixed-mode contact of biological materials or similar soft elastomers remains to be well understood. To better capture the effects of dissipation in such contact problems owing to viscoelasticity or irreversible interfacial adhesive processes, a model is developed for the combined adhesive and tangential loading of a rigid sphere on a flat half-space which incorporates a phenomenological model of energy dissipation in the form of increased effective work of adhesion with increasing degree of mode mixity. To verify the model, contact experiments are performed on polydimethylsiloxane (PDMS) samples using a custom-built microtribometer. Measurements of contact area during mixed normal/tangential loading indicate that the strong dependence of the effective work of adhesion upon mode mixity can be captured effectively by the phenomenological model in the regime where the contact area stayed circular and the slip was negligible. Rate effects were seen to be described by a power-law dependence upon the crack front velocity, similar to observations of rate-dependent contact seen for pure normal loading.