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Journal Club Theme of July 2012: Mechanics of Biological and Biomimetic Cellular Structures
Cellular structures in nature: There are two structural features which can be found in many biological systems: Cellular organization with heterogeneity including functional gradient; and hierarchical organization. These features are believed to be largely responsible for the superior energy absorption of biological systems. As an example, elk antler is a tough structure capable of absorbing high energy impact, whose functionality is crucial to the animal’s survival. According to (Chen et al. 2009) its heterogeneous and hierarchical structural organization are recognized as key factors in its superior behavior.
Figure 1: Structural organization of elk antler at the macro and micro scales. Antler has remarkable impact and fracture resistance.
Heterogeneous and functionally graded structures: In general, the type and level of irregularity have significant effects on the properties of cellular structures. Figure 2 displays three biological systems with intricate cellular structures, arguably displayed in order of increasing structural and functional complexity (from left to right). In each system, the toughness and energy absorption of the cellular organization are crucial for the organism’s function and survival. For example, cork is the outer bark of a treed, with heterogeneous cellular organization and remarkable energy absorption. Other examples of cellular biomaterials are elk antlers, banana peel and bone.
Figure 2: Cork and toucan beak have random heterogeneity, while the bamboo has a functionally graded cellular organization.
Structural hierarchy: Hierarchical structures are ubiquitous in nature and can be observed at many different scales in organic materials and biological systems (Aizenberg et al., 2005; Buehler, 2006; Espinosa et al., 2011; Fratzl and Weinkamer, 2007; Gibson et al., 2010; Lakes, 1993; Ortiz and Boyce, 2008; Qing and Mishnaevsky Jr, 2009). The hierarchical organization of these systems generally plays a key role in their properties, and hence survival (Fratzl and Weinkamer, 2007; Gibson et al., 2010). Hierarchy is also important in engineering and architectural design. Examples range from the Eiffel tower1993) and polymers with micro-level hierarchical structures (Lakes, 1993), to sandwich panels with cores made of foams or composite lattice structures (Cote et al., 2009; Fan et al., 2008; Kazemahvazi et al., 2009; Kazemahvazi and Zenkert, 2009; Kooistra et al., 2007). There, hierarchical organization can lead to superior mechanical behavior and tailorable properties, as described recently for sandwich cores with hierarchical structure (Fan et al., 2008), for hierarchical corrugated truss structures (Kooistra et al., 2007) and for fractal-appearing hierarchical honeycombs (Ajdari et al. 2012). The overall mechanical behavior of these structures is governed by the response at different length scales and levels of hierarchy; and increasing levels of structural hierarchy can result in lighter-weight and better-performing structures.
· Ajdari, A., Jahromi, B.H., Papadopoulos, J., Nayeb-Hashemi, H., Vaziri, A., 2012, Hierarchical honeycombs with tailorable properties, I J Solids and Structures, 49, 1413-1419
· Aizenberg, J., Weaver, J.C., Thanawala, M.S., Sundar, V.C., Morse, D.E., Fratzl, P., 2005. Skeleton of Euplectella sp.: Structural Hierarchy from the Nanoscale to the Macroscale. Science 309, 275-278.
· Bhat, T., Wang, T.G., Gibson, L.J., 1989. Micro-sandwich honeycomb. SAMPE 25, 43-45.
· Buehler, M.J., 2006. Nature designs tough collagen: Explaining the nanostructure of collagen fibrils. Proceedings of the National Academy of Sciences 103, 12285-12290.
· Burgueño, R., Quagliata, M.J., Mohanty, A.K., Mehta, G., Drzal, L.T., Misra, M., 2005. Hierarchical cellular designs for load-bearing biocomposite beams and plates. Materials Science and Engineering A 390, 178-187.
· Chen, P.Y., A.G. Stokes, and J. McKittrick, 2009, Comparison of the structure and mechanical properties of bovine femur bone and antler of the North American elk (Cervus elaphus canadensis). Acta Biomaterialia, 5(2): p. 693-706.
· Cote, F., Russell, B.P., Deshpande, V.S., Fleck, N.A., 2009. The Through-Thickness Compressive Strength of a Composite Sandwich Panel With a Hierarchical Square Honeycomb Sandwich Core. Journal of Applied Mechanics 76, 061004-061008.
· Espinosa, H.D., Juster, A.L., Latourte, F.J., Loh, O.Y., Gregoire, D., Zavattieri, P.D., 2011. Tablet-level origin of toughening in abalone shells and translation to synthetic composite materials. Nat Commun 2, 173.
· Fan, H.L., Jin, F.N., Fang, D.N., 2008. Mechanical properties of hierarchical cellular materials. Part I: Analysis. Composites Science and Technology 68, 3380-3387.
· Fratzl, P., Weinkamer, R., 2007. Nature's hierarchical materials. Progress in Materials Science 52, 1263-1334.
· Gibson, L.J., K.E. Easterling, and M.F. Ashby, 1981, The Structure and Mechanics of Cork. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 377(1769): p. 99-117.
· Gibson, L.J., Ashby, M.F., Harley, B.A., 2010. Cellular materials in nature and medicine. Cambridge University Press.
· Kazemahvazi, S., Tanner, D., Zenkert, D., 2009. Corrugated all-composite sandwich structures. Part 2: Failure mechanisms and experimental programme. Composites Science and Technology 69, 920-925.
· Kazemahvazi, S., Zenkert, D., 2009. Corrugated all-composite sandwich structures. Part 1: Modeling. Composites Science and Technology 69, 913-919.
· Kooistra, G.W., Deshpande, V., Wadley, H.N.G., 2007. Hierarchical Corrugated Core Sandwich Panel Concepts. Journal of Applied Mechanics 74, 259-268.
· Lakes, R., 1993. Materials with structural hierarchy. Nature 361, 511-515.
· Murphey, T., Hinkle, J., 2003. Some performance trends in hierarchical truss structures, AIAA, Norfolk, VA, p. 1903.
· Ortiz, C., Boyce, M.C., 2008. Bioinspired Structural Materials. Science 319, 1053-1054.
· Qing, H., Mishnaevsky Jr, L., 2009. 3D hierarchical computational model of wood as a cellular material with fibril reinforced, heterogeneous multiple layers. Mechanics of Materials 41, 1034-1049.
· Taylor, C.M., Smith, C.W., Miller, W., Evans, K.E., 2011. The effects of hierarchy on the in-plane elastic properties of honeycombs. International Journal of Solids and Structures 48, 1330-1339.