SPECIAL ISSUE EDITORS: Christian Hellmich and Dinesh Katti
May 1, 2009

Analytical Studies on a Crack in Layered Structures Mimicking Nacre

Publication: Journal of Engineering Mechanics
Volume 135, Issue 5

Abstract

In this paper, we study a model layered structure mimicking nacre. We start from an elastic energy appropriate for the model. We formulate how to obtain stress and strain distributions for this special elastic theory and explicitly derive a solution to a certain boundary condition. This solution predicts a reduction of the stress concentration around the crack tip, which proves the strength of the model structure.

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Acknowledgments

This work is supported by KAKENHI from MEXT, Japan.

References

Barthelat, F., Tang, H., Zavattieri, P. D., Li, C.-M., Espinosa, H. D. J. (2007). “On the mechanics of mother-of-pearl: A key feature in the material hierarchical structure.” J. Mech. Phys. Solids, 55, 306.
Currey, J. D. (1977). “Mechanical properties of mother of pearl in tension.” Proc. R. Soc. London, Ser. B, 196, 443.
Deville, S., Saiz, E., Nalla, R. K., and Tomsia, A. P. (2006). “Freezing as a path to build complex composites.” Science, 311, 515.
Evans, A. G., Suo, Z., Wang, R. Z., Aksay, I. A., He, M. Y., and Hutchinson, J. W. (2001). “Model for the robust mechanical behavior of nacre.” J. Mater. Res., 16, 2475.
Fratzl, P., Gupta, H. S., Paschalis, E. P., and Roschger, P. (2004). “Structure and mechanical quality of the collagen-mineral nano-composite in bone.” J. Mater. Chem., 14, 2115.
Gao, H. J., Ji, B. H., Jager, I. L., Artz, E., and Fratzl, P. (2003). “Materials become insensitive to flaws at nanoscale: Lessons from nature.” Proc. Natl. Acad. Sci. U.S.A., 100, 5597.
Hamamoto, Y., and Okumura, K. (2008). “Analytical solution to a fracture problem in a tough layered structure.” Phys. Rev. E, 78, 026118.
Hellmich, Ch., and Ulm, F.-J. (2002). “Are mineralized tissues open crystal foams reinforced by crosslinked collagen? Some energy arguments.” J. Biomech., 35, 1199.
Jackson, A. P., Vincent, J. F. V., and Turner, R. M. (1988). “The mechanical design of nacre.” Proc. R. Soc. London, Ser. B, 234, 415.
Ji, B., and Gao, H. (2004). “Mechanical properties of nanostructure of biological materials.” J. Mech. Phys. Solids, 52, 1963.
Kamat, S., Su, X., Ballarini, R., and Heuer, A. H. (2000). “Structural basis for the fracture toughness of the shell of the conch Strombus gigas.” Nature (London), 405, 1036.
Katti, D. R., Katti, K. S., Sopp, J., and Sarikaya, M. (2001). “3D finite element modeling of mechanical response in nacre-based hybrid nanocomposites.” Comput. Theor. Polym. Sci., 11, 397.
Kotha, S. P., Li, Y., and Guzelsu, N. (2001). “Micromechanical model of nacre tested in tension.” J. Mater. Sci., 36, 2001-2008.
Li, X., Chang, W.-C., Chao, Y. J., Wang, R., and Chang, M. (2004). “Nanoscale structural and mechanical characterization of a natural nanocomposite material: The shell of red abalone.” Nano Lett., 4, 613.
Mayer, G. (2005). “Rigid biological systems as models for synthetic composites.” Science, 310, 1144.
Nukala, P. K. V. V., and Šimunović, S. (2005) “Statistical physics models for nacre fracture simulation.” Phys. Rev. E, 72, 041919.
Okumura, K. (2002). “Why is nacre strong? II: Remaining mechanical weakness for cracks propagating along the sheets.” Eur. Phys. J. E, 7, 303.
Okumura, K. (2003). “Enhanced energy of parallel fractures in nacre-like composite materials.” Europhys. Lett., 63, 701.
Okumura, K. (2004). “Toughness of double elastic networks.” Europhys. Lett., 67, 470.
Okumura, K. (2005). “Fracture strength of biomimetic composites: Scaling views on nacre.” J. Phys.: Condens. Matter, 17, S2879.
Okumura, K., and De Gennes, P.-G. (2001). “Why is nacre strong? Elastic theory and fracture mechanics for biocomposites with stratified structures.” Eur. Phys. J. E, 4, 121.
Rao, M. P., Sanchez-Herencia, A. J., Beltz, G. E., McMeeking, R. M., and Lange, F. F. (1999). “Laminar ceramics that exhibit a threshold strength.” Science, 286, 102.
Sarikaya, M., and Aksay, I. A. (1995). “Nacre: Properties, crystallography, morphology, and formation.” Biomimetics: Design and processing of materials, AIP, New York, 35–90.
Smith, B. L., et al. (1999). “Molecular mechanistic origin of the toughness of natural adhesives, fibres and composites.” Nature (London), 399, 761.
Song, F., and Bai, Y. L. (2003). “Effects of nanostructures on the fracture strength of the interfaces in nacre.” J. Mater. Res., 18, 1741.

Information & Authors

Information

Published In

Go to Journal of Engineering Mechanics
Journal of Engineering Mechanics
Volume 135Issue 5May 2009
Pages: 461 - 467

History

Received: Jul 5, 2007
Accepted: Jul 23, 2008
Published online: May 1, 2009
Published in print: May 2009

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Notes

Note. Associate Editor: Christian Hellmich

Authors

Affiliations

Yukari Hamamoto
Master Student, Dept. of Physics, Graduate School of Humanities and Sciences, Ochanomizu Univ., 2-1-1 Otsuka, Bunkyo-ku, Tokyo 112-8610, Japan.
Professor, Dept. of Physics, Graduate School of Humanities and Sciences, Ochanomizu Univ., 2-1-1 Otsuka, Bunkyo-ku, Tokyo 112-8610, Japan (corresponding author). E-mail: [email protected]

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