Design of biomimetic fibrillar interfaces: 2. Mechanics of enhanced adhesion

This study addresses the strength and toughness of generic fibrillar structures. We show that the stress sigma(c) required to pull a fibril out of adhesive contact with a substrate has the form sigma(c) = sigma(0)Phi(chi). In this equation, sigma(0) is the interfacial strength, Phi(chi) is a dimensionless function satisfying 0 <= Phi(chi) <= 1 and chi is a dimensionless parameter that depends on the interfacial properties, as well as the fibril stiffness and radius. Pull-off is flaw sensitive for chi >> 1, but is flaw insensitive for chi < 1. The important parameter X also controls the stability of a homogeneously deformed non-fibrillar (flat) interface. Using these results, we show that the work to fail a unit area of fibrillar surface can be much higher than the intrinsic work of adhesion for a flat interface of the same material. In addition, we show that cross-sectional fibril dimensions control the pull-off force, which increases with decreasing fibril radius. Finally, an increase in fibril length is shown to increase the work necessary to separate a fibrillar interface. Besides our calculations involving a single fibril, we study the concept of equal load sharing (ELS) for a perfect interface containing many fibrils. We obtain the practical work of adhesion for an idealized fibrillated interface under equal load sharing. We then analyse the peeling of a fibrillar surface from a rigid substrate and establish a criterion for ELS.