Peeling off an adhesive layer with spatially varying topography and shear modulus

Inspired by recent experiments on hierarchically structured adhesives, we analyze here the effect of spatial variation in surface topography and shear modulus of an elastomeric adhesive on its ability to adhere strongly to a flexible contactor. The undulation of surface and modulus both were assumed to be periodic with periodicity, which is either identical or different for the two parameters; for identical periodicity, the phase lag between the respective undulations is also systematically varied. Calculations show that during continuous lifting of the flexible contactor from complete initial contact, the interfacial crack between the two adherents does not propagate continuously but intermittently, with crack arrest and initiation at the vicinity of minimum thickness and modulus of the layer; the torque required to initiate an arrested crack increases significantly over that required to propagate it on a smooth adhesive surface. The adhesion strength estimated from the corresponding force vs displacement plot is calculated to be higher than that achieved on a smooth and featureless adhesive surface. For in-phase variation in topography and shear modulus of the layer, the adhesive strength is found to be higher than for nonzero phase lag between the two parameters. The adhesion strength is found to diminish also for nonidentical periodicity between modulus and surface undulation. We have derived a scaling law for relating adhesion strength to several of these parameters.