Eur. Phys. J. E 7, 303-310 (2002)
Why is nacre strong? II. Remaining mechanical weakness for cracks propagating along the sheetsK. Okumura
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
(Received 16 November 2001)
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 , respectively, where x is the distance from the tip). This indicates there is no enhancement in toughness in the case of parallel fracture.
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.
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag 2002