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

Abstract

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.

Keywords::

• gecko adhesion
• van der Waals interaction
• computational contact mechanics
• nonlinear finite element methods
• peeling

Acknowledgements

The authors are grateful to the German Research Foundation (DFG) for supporting this research under project SA1822/5-1 and grant GSC 111. The authors also wish to thank the Institute of Continuum Mechanics for its initial support of this work.

Notes

^1. Graduate student, Email: [email protected]

^2. Further measurements are called for in order to determine the details of the spatula geometry.

^3. Even though the coarse and medium meshes are not suitable to capture adhesion, they can be employed to study the structural properties of the spatula, like its vibration modes (Sauer 2011c).

^4. Strictly, this parameter can only be used to describe surface regions that have fully separated from the substrate. For regions that have only partially separated, the work of adhesion also depends on the inclination of the surface (Sauer 2011d).

^5. In the computations reported here, the contact force is modified in the compression regime, in order to regularise the function for low (Sauer 2011b). Due to this modification, the actual value is .

^6. Here, the terminology ‘pull-off force’ is used to denote the varying, displacement-dependent force during the pull-off process.