A Computational Model for Nanoscale Adhesion between Deformable Solids and Its Application to Gecko Adhesion

A computational contact formulation is presented that is suitable for simulating contact interaction problems at very small length scales. The contact model is based on the coarse-graining of the intermolecular forces between neighboring bodies, like van der Waals attraction, into an effective continuum contact description. The model is cast into a nonlinear 3D finite element implementation that is capable of integrating the challenges encountered in the modeling of adhesive systems. The contact model is then applied to the dynamic modeling and simulation of the adhesion and deformation of a gecko seta based on a 3D multiscale approach. The approach spans six orders of magnitude and combines three distinct modeling levels, that describe the effective adhesion behavior at the seta scale, the spatula scale and the molecular scale. The rate-dependent pull-off behavior of adhering setae and spatulae is computed and it is shown that the model is successful in capturing pull-off forces that have been observed experimentally.