Sliding-induced non-uniform pre-tension governs robust and reversible adhesion: a revisit of adhesion mechanisms of geckos

Abstract

Several mechanisms have been proposed in the literature to explain the robust attachment and rapid, controllable detachment of geckos' feet on vertical walls or ceilings, yet, it is still debatable, which one is ultimately responsible for geckos' extraordinary capabilities for robust and reversible adhesion. In this paper, we re-examine some of the key movements of geckos' spatula pads and seta hairs during attachment and detachment, and propose a sequence of simple mechanical steps that would lead to the extraordinary properties of geckos observed in experiments. The central subject under study here is a linear distribution of pre-tension along the spatula pad induced by its sliding motion with respect to a surface. The resulting pre-tension, together with a control of setae's pulling force and angle, not only allows for robust and strong attachment, but also enables rapid and controllable detachment. We perform computational modelling and simulations to validate the following key steps of geckos' adhesion: (i) creation of a linear distribution of pre-tension in spatula through sliding, (ii) operation of an instability envelope controlled by setae's pulling force and angle, (iii) triggering of an adhesion instability leading to partial decohesion along the interface, and (iv) complete detachment of spatula through post-instability peeling. The present work not only reveals novel insights into the adhesion mechanism of geckos, but also develops a powerful numerical simulation approach as well as additional guidelines for bioinspired materials and devices.

Figure 1.

The hierarchical structure of a gecko's toe. A toe consists of hundreds of thousands of seta and each seta contains hundreds of spatula. (a,b) Scanning electron micrograph of setae and (c) spatula. ST, seta; SP, spatula; BR, branch. (Reprinted from Gao et al. [8] with permission from Elsevier.) (Online version in colour.)

Figure 2.

Schematic of a sequence of movements of geckos' setae and spatula pads during attachment and detachment: (a) with a sliding motion on substrate, a seta moves outward and stretches the spatula pad; (b) as a result, the spatula pad, with a linear pre-tension in it, spreads on the substrate, forming van der Waals adhesion along the interface; (c) instability takes place by tuning the pulling force and angle of the setae, breaking portion of the adhesion; (d) finally, when pulled at a larger angle through the hyperextension of the gecko's toe, the spatula pad is peeled off completely from the substrate. (Online version in colour.)

Figure 3.

Traction–separation relations under (a) normal and (b) shear loadings. The shaded areas represent the energies γ_f owing to normal traction and γ_τ owing to shear traction, respectively, at a specific time t. (Online version in colour.)

Figure 4.

Force equilibrium in a spatula pad. (Online version in colour.)

Figure 5.

Calculated distributions of pre-tension in the spatula pad and shear traction along the interface. Squares with solid line, pre-tension L = 100 nm; triangles with dashed line, pre-tension L = 200 nm; dashed-dotted line, shear L = 100 nm; dashed line, shear L = 200 nm. (Online version in colour.)

Figure 6.

Variation of the pulling angle θ during adhesion of the spatula pad on substrate. Solid line, L = 100 nm; dashed line, L = 200 nm. (Online version in colour.)

Figure 7.

Stability envelopes of magnitude and angle of the pulling force under various pre-tensions in the pad, (a) for P₀/EH = 0.1, (b) for P₀/EH = 0.07 and (c) for P₀/EH = 0.04 and P₀/EH = 0, L = 200 nm. (a,b) Squares with dashed line, L = 100 nm; triangles with dashed-dotted line, L = 200 nm; circles with dashed line, L = 300 nm; solid line, Chen et al. [33]. (c) Squares with dashed line, L = 200 nm P₀/EH = 0.04; solid line, Chen et al. [33] P₀/EH = 0.04; triangles with dashed-dotted line, L = 200 nm; P₀/EH = 0; dashed line, Chen et al. [33] P₀/EH = 0. (Online version in colour.)

Figure 8.

Redistributions of pre-tension in the spatula pad and shear traction along the adhesion interface. (a) L = 200 nm at different levels of P₀/EH; and (b) P₀/EH = 0.1 at different values of spatula length L. (a,b) Squares with solid line, pre-tension P₀/EH = 0.1; short dashed line, shear P₀/EH = 0.1; circles with dashed-dotted line, pre-tension P₀/EH = 0.07; long dashed line, shear P₀/EH = 0.07. (Online version in colour.)

Figure 9.

Residual length of adhesion after instability. Squares with solid line, L = 100 nm; triangles with dashed line, L = 200 nm; circles with dashed-dotted line, L = 300 nm; inverted triangles with dashed line, L = 450 nm; diamonds with solid line, L = 600 nm. (Online version in colour.)

Figure 10.

Envelopes of peeling force and angle for spatula detachment from substrate after instability at (a) L = 100 nm, (b) L = 200 nm and (c) L = 300 nm. (Online version in colour.)