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.
Highlights
Helicoidal formations often appear in natural microstructures such as bones and arthropods exoskeletons
Transversal and longitudinal cross-sections through the tarsus of the Scorpio Maurus Palmatus were imaged by Scanning Electron Microscopy (SEM) (Fig. 1a–d)
Each Bouligand laminate unit (BLU) is separated from its neighbors in both the x and y directions by thin fibrous interfacial layers (‘intralayers’) about 100–200 nm thick (Fig. 2e, f), whose fibers are parallel to the BLU layers plane
Summary
Helicoidal formations often appear in natural microstructures such as bones and arthropods exoskeletons. The current literature describes the BLU as a laminate possessing infinite helical symmetry, with stacked laminae that are progressively twisted in-plane around an axis located at the lamina center (see for example12–14,19,24) This means that at any point along the twisting rotation axis, the helicoid will appear exactly the same. Our present study on the cuticle of the scorpion chela (pincers), using the Scorpio Maurus Palmatus as a model animal, reveals a more complex structural arrangement, which might be found in other species as well In this arrangement the twisting axis is located at the lamina corner instead of its center, and in addition the laminae are progressively tilted by an out-of-plane rotation, resulting in a warped helicoid. Parametric calculations of the stiffness and strength of the structure are presented, including analysis of its degree of isotropy and discussion of its functionality
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