Hierarchical geoemtries and adhesion: Bioinsipired designs for stiff interfaces

Throughout biology hierarchy is a reccurent theme in the geometry of sturctures required to withstand large loads while retaining minimal weight cost. Acting over vast timescales, evolution has bought about beautiful solutions to problems of optimisation that are only now being understood and incorporated into engineering design. One particular example of hierarchy in action is to be found in the adhesive connections between stiff keretinised materials and soft biological matter. This design is of particular interest as many hierarchical orders of the same base motif can be seen in different species, thus giving the possibility of observing dependence of the optimal design on various input parameters. Here we present results of analytic calculations, confirmed through finite element simulation, demonstrating that one driving factor in the utilisation of hierarchy in this biological setting is related to stiffness of the resulting interface. We show that through altering the hierarchy of a structure, the scaling of interface stiffness against adhesive potential can be varied in a systematic, beneficial manner. We present measurements of the geometric parameters that make up the connection between the hoof wall and the biological material within the equine species and discuss the implications for stiffness and robustness of the resulting interface.