A detailed 3D finite element analysis of the peeling behaviour of a gecko spatula

This paper presents a detailed finite element analysis of the adhesion of a gecko spatula. The gecko spatulae form the tips of the gecko foot hairs that transfer the adhesional and frictional forces between substrate and foot. The analysis is based on a parameterised description of the 3D geometry of the spatula that only requires 12 parameters. The adhesion is described by a nonlinear computational contact formulation that accounts for the van der Waals interaction between spatula and substrate. The spatula adhesion model is implemented using an enriched contact finite element formulation recently developed by the first author. The finite element model is then used to simulate the peeling behaviour of the gecko spatula under applied vertical and rotational loading for various model parameters. Variations of the material stiffness, adhesional strength and range, stiction, spatula size and spatula inclination are considered to account for the natural variation of spatula properties. The study demonstrates that the spatula can function over a wide range of conditions. The computed pull-off forces are in agreement with experimental results reported in the literature. The study also examines the energy required for the spatula pull-off. The proposed model is ideal to study the influence of substrate roughness on the spatula adhesion, as is finally demonstrated.