Theoretical limits in detachment strength for axisymmetric bi-material adhesives

Reversible dry adhesives rely on short-ranged intermolecular bonds, hence requiring a low elastic modulus to conform to the surface roughness of the adhered material. Under external loads, however, soft adhesives accumulate strain energy, which release drives the propagation of interfacial flaws prompting detachment. The tradeoff between the required compliance, for surface conformity, and the desire for a reduced energy release rate, for better strength, can be achieved with a bi-material adhesive having a soft tip and a rigid backing. This design strategy is widely observed in nature across multiple species. However, the detachment mechanisms of these adhesives are not completely understood and quantitative analysis of their adhesive strength is still missing. Based on linear elastic fracture mechanics, we analyze the strength of axisymmetric bi-material adhesives. We observed two main detachment mechanisms, namely (i) center crack propagation and (ii) edge crack propagation. If the soft tip is sufficiently thin, mechanism (i) dominates and provides stable crack propagation, thereby toughening the interface. We ultimately provide the maximum theoretical strength of these adhesives obtaining closed form estimation for an incompressible tip. In some cases, the maximum adhesive strength is independent of the crack size, rendering the interface flaw tolerant. We finally compare our prediction with experiments in the literature and observe good agreement.