Adhesion analysis of multi-level hierarchical attachment system contacting with a rough surface

Several creatures, including insects, spiders and lizards, have a unique ability to cling to ceilings and walls utilizing dry adhesion. Geckos in particular have developed the most complex adhesion structures capable of smart adhesion, i.e., the ability to cling to and detach from different smooth and rough surfaces and detach at will. Their foot pads are covered by a large number of small hairs (setae) that contain many branches per seta with a lower level of spatulae. This hierarchical structure gives the gecko the adaptability to create a large real area of contact with rough surfaces. van der Waals attraction between the large numbers of spatulae in contact with the rough surface is responsible for high adhesion. In order to investigate the effect of the gecko's hierarchical structure, a three-level hierarchical model for a gecko lamella consisting of setae, branches and spatulae has been developed. We consider one-, two-and three-level hierarchically structured spring models for simulation of a seta contacting with random rough surfaces and demonstrate the effect of the multi-level hierarchical structure on the efficiency of seta attachment. Rough surfaces with various roughness parameters which cover a common range of most natural and artificial rough surfaces at the scale of a gecko's pad were generated. It is shown that a multi-level hierarchical structure produces adhesion enhancement, and this enhancement increases with an increase in the applied load and a decrease in the stiffness of springs. A significant adhesion enhancement occurs when the maximum spring deformation is greater than 2-3-times the root mean square amplitude of surface roughness.