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Throughout biology, hierarchy is a recurrent theme in the geometry ofstructures where strength is achieved with minimal use of material. Acting overvast timescales, evolution has brought about beautiful solutions to problems ofoptimisation that are only now being understood and incorporated intoengineering design. One particular example of this hierarchy is found in thejunction between stiff keratinised material and the soft biological matterwithin the hooves of ungulates. Using this biological interface as a designmotif, we investigate the role of hierarchy in the creation of a stiff, robustinterface between two materials. We show that through hierarchical design onecan manipulate the scaling laws relating constituent material stiffness andoverall interface stiffness under both shear and tension loading. Furthermore,we uncover a cascade of scaling laws for the higher order structure and linktheir origin with competing deformation modes within the structure. Wedemonstrate that when joining two materials of different stiffness, under shearor tension, hierarchical geometries are linked with beneficial mechanicalproperties.

Hierarchical geometries and adhesion: Bio-inspired designs for stiff interfaces