Nonlinear Finite Element Analysis of a Gecko Spatula Adhesion on a Rigid Substrate

Abstract

Geckos utilize the fibrillar structures on their feet for generating strong adhesive forces as well as for rapid locomotion on a variety of surfaces. Each toe pad of gecko foot contains arrays of fine hair-like structures called setae, which at their tips, further branch into hundreds of nanoscale spatula-shaped structures. These spatulae adhere to substrates through van der Waals interactions. In the present work, numerical simulation of the adhesion mechanism of a gecko spatula on a rigid substrate is carried out using a two-dimensional finite element model. To account for the geometrical and material nonlinearities in the interaction between the spatula and substrate, a nonlinear computational contact formulation is employed. For the material modelling of the spatula, a Neo-Hookean hyperelastic model is used under the plane strain assumption. The van der Waals adhesion between the bodies is described using the Lennard-Jones potential. The spatula is gradually peeled off from the substrate by applying rotation and then a vertical pull. The variation in pull-off forces with the angle from which it is peeled off is studied. It has been observed that the pull-off force decreases with increasing peeling angle and has the lowest value at $\theta = 90^{\text{o}}$ and is equal to $4.82$ nN. It has also been found that the pull-off forces increase with an increase in adhesion strength (or range of adhesion) or decrease in stiffness (or spatula size).