Throughout biology, hierarchy is a recurrent theme in the geometry of structures where strength is achieved with minimal use of material. Acting over vast timescales, evolution has brought about beautiful solutions to problems of optimisation that are only now being understood and incorporated into engineering design. One particular example of this hierarchy is found in the junction between stiff keratinised material and the soft biological matter within the hooves of ungulates. Using this biological interface as a design motif, we investigate the role of hierarchy in the creation of a stiff, robust interface between two materials. We show that through hierarchical design one can manipulate the scaling laws relating constituent material stiffness and overall interface stiffness under both shear and tension loading. Furthermore, we uncover a cascade of scaling laws for the higher order structure and link their origin with competing deformation modes within the structure. We demonstrate that when joining two materials of different stiffness, under shear or tension, hierarchical geometries are linked with beneficial mechanical properties.
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