Hostname: page-component-54dcc4c588-b5cpw Total loading time: 0 Render date: 2025-09-12T17:00:44.107Z Has data issue: false hasContentIssue false
  • English
  • Français

Mechanical Principles of a Self-Similar Hierarchical Structure

Published online by Cambridge University Press:  31 January 2011

Huajian Gao
Huajian Gao*
Affiliation:
huajian_gao@brown.edu
Get access

Abstract

Natural materials such as bone, shell, tendon and the attachment system of gecko exhibit multi-scale hierarchical structures. Here we summarize some recent studies on an idealized self-similar hierarchical model of bone and bone-like materials, and discuss mechanical principles of self-similar hierarchy, in particular to show how the characteristic length, aspect ratio and density at each hierarchical level can be selected to achieve flaw tolerance and superior stiffness and toughness across scale.Tel.: (401) 863-2626; Email address:

Keywords

biomimetic (assembly)fracturecomposite

Information

Type
Research Article
Information
MRS Online Proceedings Library (OPL) , Volume 1188: Symposium LL – Architectured Multifunctional Materials , 2009 , 1188-LL01-01
Copyright
Copyright © Materials Research Society 2009

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

1 Currey, J.D., 1977. Mechanical properties of mother of pearl in tension. Proc. R. Soc. Lond. B 196, 443–463.Google Scholar
2 Currey, J.D., 1984. The Mechanical Adaptations of Bones. Princeton University Press, Princeton, NJ, pp. 24–37.10.1515/9781400853724Google Scholar
3 Jäger, I., Fratzl, P., 2000. Mineralized collagen fibrils: a mechanical model with a staggered arrangement of mineral particles. Biophys. J. 79, 1737–1746.10.1016/S0006-3495(00)76426-5Google Scholar
4 Fratzl, P., Burgert, I., Gupta, H.S., 2004a. On the role of interface polymers for the mechanics of natural polymeric composites. Phys. Chem. Chem. Phys. 6, 5575–5579.10.1039/b411986jGoogle Scholar
5 Fratzl, P., Gupta, H.S., Paschalis, E.P., Roschger, P., 2004b. Structure and mechanical quality of the collagen-mineral nano-composite in bone. J. Mater. Chem. 14, 2115–2123.10.1039/B402005GGoogle Scholar
6 Gao, H., 2006. Application of fracture mechanics concepts to hierarchical biomechanics of bone and bon-like materials. Int. J. Fracture 138, 101–137.10.1007/s10704-006-7156-4Google Scholar
7 Autumn, K., Liang, Y.A., Hsieh, S.T., Zesch, W., Chan, W.P., Kenny, T.W., Fearing, R., and Full, R.J., 2000 Adhesive force of a single gecko foot-hair. Nature 405, 681–685.10.1038/35015073Google Scholar
8 Autumn, K., Sitti, M., Liang, Y.A., Peattie, A.M., Hansen, W.R., Sponberg, S., Kenny, T.W., Fearing, R., Israelachvili, J.N., and Full, R.J., 2002 Evidence for van der Waals adhesion in gecko seta. Proc. Natl. Acad. Sci. USA 99, 12252–12256.10.1073/pnas.192252799Google Scholar
9 Yao, H., Gao, H., 2006. Mechanics of robust and releasable adhesion in biology: bottom-up designed hierarchical structures of gecko. J. Mech. Phys. Solids 54, 1120–1146.10.1016/j.jmps.2006.01.002Google Scholar
10 Gao, H., Ji, B., Jäger, I.L., Arzt, E., Fratzl, P., 2003. Materials become insensitive to flaws at nanoscale: lessons from nature. Proc. Natl. Acad. Sci. USA 100, 5597–5600.10.1073/pnas.0631609100Google Scholar
11 Gao, H., Chen, S., 2005. Flaw tolerance in a thin strip under tension. J. App. Mech. 72, 732–737.10.1115/1.1988348Google Scholar
12 Arzt, E., Gorb, S., Spolenak, R., 2003. From micro to nano contacts in biological attachment devices. Proc. Natl. Acad. Sci. USA 100, 10603–10606.10.1073/pnas.1534701100Google Scholar
13 Gao, H., Wang, X., Yao, H., Gorb, S., Arzt, E., 2005. Mechanics of hierarchical adhesion structures of geckos. Mechanics of Materials 37, 275–285.10.1016/j.mechmat.2004.03.008Google Scholar
14 Gao, H., Yao, H., 2004. Shape insensitive optimal adhesion of nanoscale fibrillar structures. Proc. Natl. Acad. Sci. USA 101, 7851–7856.10.1073/pnas.0400757101Google Scholar
15 Yao, H. and Gao, H., 2007. Multi-scale cohesive laws in hierarchical materials, Int. J. Solids Struct., 44, 8177–8193.10.1016/j.ijsolstr.2007.06.007Google Scholar
16 Jackson, A.P., Vincent, J.F.V. and Turner, R.M., 1988. The mechanical design of nacre. Proc. Roy. Soc. Lond. B 234, 415–440.Google Scholar
17 Menig, R., Meyers, M.H., Meyers, M.A. and Vecchio, K.S., 2000. Quasi-static and dynamic mechanical response of Haliotis rufescens (abalone) shells. Acta Mat. 48, 2383–2398.10.1016/S1359-6454(99)00443-7Google Scholar
18 Menig, R., Meyers, M.H., Meyers, M.A. and Vecchio, K.S., 2001. Quasi-static and dynamic mechanical response of Strombus gigas (conch) shells. Mat. Sci. Eng. A 297, 203–211.10.1016/S0921-5093(00)01228-4Google Scholar
19 Landis, W.J., 1995. The strength of a calcified tissue depends in part on the molecular structure and organization of its constituent mineral crystals in their organic matrix. Bone 16, 533–544.10.1016/8756-3282(95)00076-PGoogle Scholar
20 Landis, W.J., Hodgens, K.J., Song, M.J., Arena, J., Kiyonaga, S., Marko, M., Owen, C. and McEwen, B.F., 1996. Mineralization of collagen may occur on fibril surfaces: evidence from conventional and high voltage electron microscopy and three dimensional imaging. J. Struct. Biol. 117, 24–35.10.1006/jsbi.1996.0066Google Scholar
21 Rho, J.Y., Kuhn-Spearing, L. and Zioupos, P., 1998. Mechanical properties and the hierarchical structure of bone. Med. Eng. & Phys. 20, 92–102.10.1016/S1350-4533(98)00007-1Google Scholar
22 Weiner, S. and Wagner, H.D., 1998. The material bone: structure-mechanical function relations. Annual Review of Materials Science 28, 271–298.10.1146/annurev.matsci.28.1.271Google Scholar
23 Warshawsky, H., 1989. Organization of crystals in enamel. Anat. Rec. 224, 242–262.10.1002/ar.1092240214Google Scholar
24 Tesch, W., Eidelman, N., Roschger, P., Goldenberg, F., Klaushofer, K. and Fratzl, P., 2001. Graded microstructure and mechanical properties of human crown dentin. Calc. Tissue Int. 69, 147–157.10.1007/s00223-001-2012-zGoogle Scholar
25 Jiang, H.D., Liu, X.Y., Lim, C.T. and Hsu, C.Y., 2005. Ordering of self-assembled nanobiominerals in correlation to mechanical properties of hard tissues. Appl. Phys. Lett. 86, 163901.10.1063/1.1906295Google Scholar
26 Wang, R.Z., Suo, Z., Evans, A.G., Yao, N., and Aksay, I.A., 2001. Deformation mechanisms in nacre. J. Mat. Res. 16, 2485–2493.10.1557/JMR.2001.0340Google Scholar
27 Buehler, M.J., Keten, S., Ackbarow, T., 2008. Theoretical and computational hierarchical nanomechanics of protein materials: Deformation and fracture. Prog. Mat. Sci. 53, 1101–1241.10.1016/j.pmatsci.2008.06.002Google Scholar
28 Puxkandl, R., Zizak, I., Paris, O., Keckes, J., Tesch, W., Bernstorff, S., Purslow, P., Fratzl, P., 2001. Viscoelastic properties of collagen: synchrotron radiation investigations and structural model. Phil. Trans. Roy. Soc. Lond. B, 357, 191–197.10.1098/rstb.2001.1033Google Scholar
29 Ji, B. and Gao, H., 2004. Mechanical properties of nanostructure of biological materials. J. Mech. Phys. Solids 52, 1963–1990.10.1016/j.jmps.2004.03.006Google Scholar
30 Chen, B., Wu, P.D. and Gao, H., 2009. A characteristic length for stress transfer in the nanostructure of biological composites. Comp. Sci. Tech. 69, 1160–1164.10.1016/j.compscitech.2009.02.012Google Scholar
31 Cox, H.L., 1952. The elasticity and strength of paper and other fibrous materials. Brit. J. appl. Phys. 3, 72–9.10.1088/0508-3443/3/3/302Google Scholar
32 Hutchinson, J.W. and Jensen, H.M., 1990. Model of fiber debonding and pullout in brittle composites with friction, Mech. Mater. 9:139–163.10.1016/0167-6636(90)90037-GGoogle Scholar
33 Nairn, J.A., 1997. On the use of shear-lag methods for analysis of stress transfer in unidirectional composites, Mech. Mater. 26:63–80.10.1016/S0167-6636(97)00023-9Google Scholar
34 Tucker, C.L. III and Liang, E., 1999. Stiffness predictions for unidirectional short fiber composites: review and evaluation, Compos. Sci. Technol. 59:655–671.10.1016/S0266-3538(98)00120-1Google Scholar
35 Buehler, M.J., 2007. Nature designs tough collagen: Explaining the nanostructure of collagen fibrils. Proc. Natl. Acad. Sci. USA 103, 12285–12290.10.1073/pnas.0603216103Google Scholar
36 Guo, X. and Gao, H., 2005. Bio-inspired material design and optimization. IUTAM Symposium on topological design optimization of structures, machines and materials - status and perspectives, October 26-29, 2005, Rungstedgaard, Copenhagen, Denmark.Google Scholar