How do slender mineral crystals resist buckling in biological materials?

Mineral crystals in biological materials such as bone, tooth, and sea shell are susceptible to buckling under compressive loading due to their slender geometry with large aspect ratios. How does nature deal with this problem? This question is especially interesting in view of the three orders of magnitude difference in elastic modulus between protein and mineral. As a first analysis of this question, we study the stability of a single mineral platelet confined in an otherwise perfect protein-mineral nanostructure. We find that there exists a transition of buckling strength from an aspect ratio-dependent regime to a lower threshold value, independent of the crystal geometry. Typical values of the aspect ratio of mineral crystals of bone and nacre fall in this transition region. The existence of a buckling strength independent of the detailed geometrical parameters of mineral may be critically important from the point of view of structure robustness as the composite behaviour of biomaterials should not depend sensitively on small variations in crystal size and shape.