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

Abstract

This study addresses the strength and toughness of generic fibrillar structures. We show that the stress σ _c required to pull a fibril out of adhesive contact with a substrate has the form σ _c = σ ₀ Φ( χ ). In this equation, σ ₀ is the interfacial strength, Φ( χ ) is a dimensionless function satisfying 0=Φ( χ )=1 and χ is a dimensionless parameter that depends on the interfacial properties, as well as the fibril stiffness and radius. Pull-off is flaw sensitive for χ ≫1, but is flaw insensitive for χ χ 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.