Why is nacre strong? II. Remaining mechanical weakness for cracks propagating along the sheets |
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Authors: | K Okumura |
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Institution: | (1) Physique de la Matière Condensée, Collège de France, 11, place Marcelin-Berthelot, 75231 Paris cedex 05, France Department of Physics, Graduate School of Humanities and Sciences, Ochanomizu University, 2-1-1, Otsuka, Bunkyo-ku, 112-8610, Japan, FR |
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Abstract: | In our previous paper (Eur. Phys. J. E 4, 121 (2001)) we proposed a coarse-grained elastic energy for nacre, or stratified structure of hard and soft layers found
in certain seashells . We then analyzed a crack running perpendicular to the layers and suggested one possible reason for
the enhanced toughness of this substance. In the present paper, we consider a crack running parallel to the layers. We propose
a new term added to the previous elastic energy, which is associated with the bending of layers. We show that there are two
regimes for the parallel-fracture solution of this elastic energy; near the fracture tip the deformation field is governed
by a parabolic differential equation while the field away from the tip follows the usual elliptic equation. Analytical results
show that the fracture tip is lenticular, as suggested in a paper on a smectic liquid crystal (P.G. de Gennes, Europhys. Lett.
13, 709 (1990)). On the contrary, away from the tip, the stress and deformation distribution recover the usual singular behaviors
( and 1/, respectively, where x is the distance from the tip). This indicates there is no enhancement in toughness in the case of parallel fracture.
Received 16 November 2001 |
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Keywords: | PACS 87 68 +z Biomaterials and biological interfaces – 46 50 +a Fracture mechanics fatigue and cracks – 81 07 -b Nanoscale materials and structures: fabrication and characterization |
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