Bioinspired hierarchical designs for stiff, strong interfaces between materials of differing stiffness

Throughout biology, geometric hierarchy is a recurrent theme in structures where strength is achieved with efficient material usage. Acting over vast timescales, evolution has brought about beautiful solutions to problems of mechanics that are only now being understood and incorporated into engineering designs. One particular example of structural 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, we can manipulate the scaling laws relating constituent material stiffness and overall interface stiffness under loading. Furthermore, we demonstrate that through use of a hierarchical geometry, we can reduce the maximum stress the materials experience for a given loading, and tailor the ratio of maximum stresses in the constituent materials. We demonstrate that when joining two materials of different stiffness hierarchical geometries are linked with beneficial mechanical properties and enhanced tailorability of mechanical response.