Why is nacre strong? Elastic theory and fracture mechanics for biocomposites with stratified structures

Nacre, stratified ceramic layers surrounded by organic matrix, is a tough material found inside certain seashells. We construct a coarse-grained elastic energy for such an anisotropic system and present an analytic solution for a notch crack normal to the stratified sheets. This analysis proves the reduction in stress concentration which was announced in our earlier work (P. G. de Gennes and K. Okumura, C. R. Acad. Sci. Paris 1, Ser. IV, 257 (2000)) and the related increase in toughness.