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 < 1. The important parameter 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.

Mechanics of adhesive contact on a power-law graded elastic half-space

“…In recent years, it is also becoming a valuable platform to study biological adhesion systems such as cell-cell contact (Chu et al, 2005;Chen and Gao, 2006b), cells on stretched substrates (Chen and Gao, 2006a), as well as adhesion systems of gecko and insects (Autumn and Peattie, 2002;Artz et al, 2003;Glassmaker et al, 2004;Hui et al, 2004;Gao et al, 2005;Spolenak et al, 2005;Yao, 2006;Yao andGao, 2006, 2007;Chen and Gao, 2007a;Chen and Soh, 2008). Among these studies, Yao (2006) and considered an interfacial crack model and showed that graded elastic materials can promote robust adhesion.…”

Compliance of a microfibril subjected to shear and normal loads

“…Recent interest in bio-inspired adhesives has motivated many researchers to fabricate microfibril arrays (Liu & Bhushan 2003;Peressadko & Gorb 2004;Chung & Chaudhury 2005;Crosby et al 2005;Glassmaker et al 2005Glassmaker et al , 2007Huber et al 2005;Northen & Turner 2005;Yurdumakan et al 2005;Kim & Sitti 2006;Majidi et al 2006;Aksak et al 2007;Gorb et al 2007;Greiner et al 2007; and to study their contact mechanics and adhesion (Jagota & Bennison 2002;Gao et al 2003Gao et al , 2005Persson & Gorb 2003;Hui et al 2004;Persson et al 2005;Spolenak et al 2005a,b;Tang et al 2005;Bhushan et al 2006;Tian et al 2006;Yao & Gao 2006;Chen & Gao 2007). Most of these studies focus on how the interface between the microfibrils and a smooth, hard substrate separates under a normal load.…”

Tuning the geometrical parameters of biomimetic fibrillar structures to enhance adhesion

“…Are there any restrictions on the geometrical parameters to attain flaw insensitivity and satisfy ELS in fibrillar structures? The concept of flaw insensitivity has been adopted to understand the mechanics of biological systems (Gao et al 2003;Persson 2003;Gao & Yao 2004;Glassmaker et al 2004;Hui et al 2004;Gao & Chen 2005;Gao 2006). In the state of flaw insensitivity, pre-existing crack-like flaw does not propagate or participate in the failure process so that the biological material failure occurs by uniform rupture at the limiting strength of the material.…”

“…Various mechanical models have been developed to model specific hairy attachment systems (e.g. Hui et al 2002;Persson 2003;Glassmaker et al 2004;Hui et al 2004) within the framework of adhesive contact mechanics (e.g. Johnson et al 1971;Derjaguin et al 1975;Roberts & Thomas 1975;Muller et al 1980;Greenwood & Johnson 1981;Barquins 1988;Maugis 1992;Carpick et al 1996;Chaudhury et al 1996;Baney & Hui 1997;Johnson & Greenwood 1997;Barthel 1998;Greenwood & Johnson 1998;Kim et al 1998;Robbe-Valloire & Barquins 1998;Morrow et al 2003;Schwarz 2003;Chen & Wang 2006).…”

“…The smaller the size, the less important the shape. In order to simulate the fibrillar structure, Glassmaker et al (2004) and Hui et al (2004) studied the concept of equal load sharing (ELS) for a perfect interface containing many fibrils and presented results on how a fibrillar structure enhances adhesion.…”