Local buckling analysis of biological nanocomposites based on a beam-spring model

Biological materials such as bone, tooth, and nacre are load-bearing nanocomposites composed of mineral and protein. Since the mineral crystals often have slender geometry, the nanocomposites are susceptible to buckle under the compressive load. In this paper, we analyze the local buckling behaviors of the nanocomposite structure of the biological materials using a beam-spring model by which we can consider plenty of mineral crystals and their interaction in our analysis compared with existing studies. We show that there is a transition of the buckling behaviors from a local buckling mode to a global one when we continuously increase the aspect ratio of mineral, leading to an increase of the buckling strength which levels off to the strength of the composites reinforced with continuous crystals. We find that the contact condition at the mineral tips has a striking effect on the local buckling mode at small aspect ratio, but the effect diminishes when the aspect ratio is large. Our analyses also show that the staggered arrangement of mineral plays a central role in the stability of the biological nanocomposites.