Twisting cracks in Bouligand structures

The Bouligand structure, which is found in many biological materials, is a hierarchical architecture that features uniaxial fiber layers assembled periodically into a helicoidal pattern. Many studies have highlighted the high damage-resistant performance of natural and biomimetic Bouligand structures. One particular species that utilizes the Bouligand structure to achieve outstanding mechanical performance is the smashing Mantis Shrimp, Odontodactylus Scyllarus (or stomatopod). The mantis shrimp generates high speed, high acceleration blows using its raptorial appendage to defeat highly armored preys. The load-bearing part of this appendage, the dactyl club, contains an interior region [16] that consists of a Bouligand structure. This region is capable of developing a significant amount of nested twisting microcracks without exhibiting catastrophic failure. The development and propagation of these microcracks are a source of energy dissipation and stress relaxation that ultimately contributes to the remarkable damage tolerance properties of the dactyl club. We develop a theoretical model to provide additional insights into the local stress intensity factors at the crack front of twisting cracks formed within the Bouligand structure. Our results reveal that changes in the local fracture mode at the crack front leads to a reduction of the local strain energy release rate, hence, increasing the necessary applied energy release rate to propagate the crack, which is quantified by the local toughening factor. Ancillary 3D simulations of the asymptotic crack front field were carried out using a J-integral to validate the theoretical values of the energy release rate and the local stress intensity factors.