Directional adhesion of gecko-inspired two-level fibrillar structures

• An adhesion model is proposed to predict the directional adhesion behavior of a two-level fibrillar adhesive structure.
• The effects of structural parameters and the applied shear force on the normal pull-off force are studied.
• An approximately optimal structure behaving consistently with geckos' hierarchical setal arrays is obtained.

Recently gecko's feet and gecko-inspired two-level fibrillar adhesives have been found to show directional adhesion property. In this paper, a theoretical model is proposed to predict the directional adhesion law of a two-level seta. The model predicts that for a typical two-level seta, there exists a structural parameters-dependent critical shear force, below and above which the bending deformation dominates or the axial deformation dominates. In the bending deformation dominated region, the adhesion force increases almost linearly with the applied shear force and the adhesion law can be tuned effectively by varying the structural parameters; while in the axial deformation dominated region, the adhesion force is no longer limited by the bending deformation and the adhesion law is almost the same with that predicted by the classical Kendall model. Additionally, an approximately optimum structure behaving consistently with geckos' hierarchical setal arrays is obtained by designing the structural parameters properly, especially the slanted angles. Thus this model can aid in interpreting the experimental test outcomes and designing optimal biomimetic two-level adhesives.