Effect of geometry on frictional interaction at a soft interface

Geometry plays an important role in the interfacial behavior of soft materials. In particular, if the two surfaces involved are geometrically incompatible, a rich range of phenomena emerges, for example, the beautiful static wrinkle patterns seen in thin sheets confined to substrates having a mismatch in Gaussian curvature. In this work, we present a simple experimental setup to study the role of geometry in the frictional interaction between a highly bendable thin polymer sheet and a hydrogel substrate. We find that in this regime friction depends strongly on the relative geometry of the two surfaces and is significantly modified if the surfaces have incompatible geometries. We show that the residual stress in the sheet due to its geometrically incompatible confinement makes an important contribution to friction. Our model also successfully explains the observed dependence of friction on sheet size, where we see a transition in the nature of friction. We present a phase diagram showing the strength of frictional interaction as a function of sheet size and thickness.