On the Optimal Mechanical Properties of Hierarchical Biomaterials

Nature• favors hierarchical structures; examples include almost all biosystems,such as plant stem [1, 2], antler [3], bone [4, 5], tendon [6], abalone shell [3], andcollagen[7]. Naturalmaterialsaregenerallyhierarchical biosystems(ororganisms)consistingofafewlevelsofhierarchy,withthesmallestbuildingblocksatnanoscale[8–10]. They distinguish themselves from the conventional engineering materialsin many different aspects. First, natural materials grow using the principles ofself-assembly rather than being fabricated [11]. They adapt themselves to externalconditions and allow optimization of the material at each level of hierarchy.Consequently, they are not the exact designs of the species that are stored in thegenes, but rather a recipe to build them. In fact, hierarchical structuring is one ofthe consequences of the growth process of biosystems [11]. Second, biomaterialshave the distinctive capacity of self-repair. This function is realized mainly by twomechanisms: one is structural adaptation to the changing external conditions, andtheotherisremovalandreplacementofthedamagedmaterial.Finally,biosystems,such as plant or animal, are living organisms. They have sensory capacity andfeeling and thus grow and behave better in good environments, such as withlovely music or on sunny days. It is generally believed that natural hierarchicalstructures/biosystems are deliberately evolved and optimized to support differenttypesoffunctions.Itiscertainthatwestillknowverylittleaboutnaturalbiosystems.Fortunately, natural biosystems provide us a constant source of inspiration forsolving a variety of technical challenges in science and technology, such asarchitecture, mechanical engineering, and materials science. We can learn fromNature’sstructuralmaterialsinmanydifferentaspects.Thischapterfocusesonthemechanical properties of hierarchical biomaterials. The presented result is basedon and differs slightly from that of Gao