Theoretical limits in detachment strength for axisymmetric bi-material adhesives

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 ideal adhesive is then soft but rigid. The solution to this controversial requirement is a bi-material adhesive having a soft tip, for surface conformation, and a rigid backing, for reduced strain energy release, hence, better adhesive strength. This design strategy is widely observed in nature across multiple species. However, the detachment mechanisms of these adhesives are poorly 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 estimates for the detachment stress independent of the crack size, rendering the interface flaw tolerant.