Shear wave filtering in naturally-occurring Bouligand structures

Abstract

Wave propagation was investigated in the Bouligand-like structure from within the dactyl club of the stomatopod, a crustacean that is known to smash their heavily shelled preys with high accelerations. We incorporate the layered nature in a unitary material cell through the propagator matrix formalism while the periodic nature of the material is considered via Bloch boundary conditions as applied in the theory of solid state physics. Our results show that these materials exhibit bandgaps at frequencies related to the stress pulse generated by the impact of the dactyl club to its prey, and therefore exhibiting wave filtering in addition to the already known mechanisms of macroscopic isotropic behavior and toughness.

A Sinusoidally Architected Helicoidal Biocomposite

“…[22][23][24] In fact, the continuation of fibrous pore canal tubules from the periodic region into the impact region likely plays a role in strengthening this interface, which can experience shear and tensile stress due to wave propagation upon impact. [19] Similar tubular Submitted to 6 structures such as those found in bone, teeth and horns have been found to enhance toughness through mechanisms such as crack deflection and resistance to microbuckling. [25,26] A schematic depicting the intersecting rotating fiber and pore canal tubule architecture is shown in Figure 2E.…”

Structure and mechanical properties of selected protective systems in marine organisms

“…In this region, cracks propagate in a helicoidal pattern, creating a larger crack surface area, and are stopped quickly when traversing the helicoid trajectory by an oscillation in stiffness [205]. In addition, this structure has been shown to effectively disperse the stress pulse waves generated during impact [207]. Combining a hard outer layer with an inner, energy dispersive matrix is reminiscent of human-made impact resistant armor.…”

Structural Orientation and Anisotropy in Biological Materials: Functional Designs and Mechanics

“…The twisted plywood structure, termed the Bouligand structure, is another excellent prototype of intricate orientations in nature . It features a helicoidally stacking arrangement of unidirectional fiber layers in a periodic fashion and is found in a range of biological materials, including the exoskeletons of crustaceans and insects, fish scales, bone osteons (Figure ), and the dactyl clubs of mantis shrimps (Figure b) . Such a structure is particularly effective in resisting damage or impact along the orthogonal direction of layers.…”

“…[54,[56][57][58]70,102,110,[156][157][158][159][160][161][162][163][164] It features a helicoidally stacking arrangement of unidirectional fiber layers in a periodic fashion and is found in a range of biological materials, including the exoskeletons of crustaceans and insects, [54,102,159,160,164] fish scales, [58,157] bone osteons (Figure 4), [70,110] and the dactyl clubs of mantis shrimps (Figure 6b). [56,57,158,161] Such a structure is particularly effective in resisting damage or impact along the orthogonal direction of layers. In the more brittle Bouligand structures, as seen in the exoskeletons of crustaceans, cracks are directed to twist continuously along the out-of-plane contours as they grow, [91,92] as shown in Figure 6b.…”

“…The effective mode I stress intensity at the crack tip and crack driving force represented by the strain energy release rate with crack extension can also be decr eased, [91,92,162,163] as shown in Figure 6c. Additionally, the Bouligand structure is capable of dissipating mechanical energy by filtering the shear stress waves in the case of dynamic loading, [161] thereby endowing materials with enhanced impact resistance.…”