Nested helicoids in biological microstructures

Abstract

Helicoidal formations often appear in natural microstructures such as bones and arthropods exoskeletons. Named Bouligands after their discoverer, these structures are angle-ply laminates that assemble from laminae of chitin or collagen fibers embedded in a proteinaceous matrix. High resolution electron microscope images of cross-sections through scorpion claws are presented here, uncovering structural features that are different than so-far assumed. These include in-plane twisting of laminae around their corners rather than through their centers, and a second orthogonal rotation angle which gradually tilts the laminae out-of-plane. The resulting Bouligand laminate unit (BLU) is highly warped, such that neighboring BLUs are intricately intertwined, tightly nested and mechanically interlocked. Using classical laminate analysis extended to laminae tilting, it is shown that tilting significantly enhances the laminate flexural stiffness and strength, and may improve toughness by diverting crack propagation. These observations may be extended to diverse biological species and potentially applied to synthetic structures.