Analysis and simulation of fracture behavior in naturally occurring Bouligand structures

Abstract Through natural selection processes, refined biological materials could be created that adapt to various environments and exhibit specific functions. Such materials include typical Bouligand structures that can be widely observed in marine creatures that have hard shells. Consisting of a helicoidal arrangement of aligned fibrils, layered single-twisted Bouligand-type structures (SBS) display exceptional fracture and damage resistance. A much more primitive and rarer type of this formation, the double-twisted Bouligand-type structures (DBS), has been discovered in ancient fish scales, and this architecture could provide added rigidity and significantly contribute to toughness when facing fracture risk. In this work, we describe a computational modeling approach to investigating fracture behaviors and toughening mechanisms in Bouligand structures. To achieve qualitative insights into the fracture behaviors of DBS and SBS, we applied these two configurations, which were identified from corresponding biological materials, to analyze load-displacement responses during single edge notched (SEN) tensile testing; the toughening mechanism is also discussed further. The results clearly show that the arrangement of helix fibrils and interlaminar properties play a major role in the resulting fracture behaviors of Bouligand architectures. This is of interest for the future design of engineering materials and structures that require composites with enhanced toughness, and could deepen our understanding of the structure-property relationship of Bouligand-type structures in bionic design. Statement of significance In this work, a novel numerical modeling approach based on the extended finite element method (XFEM) has been established to evaluate the fracture behavior of a naturally-occurring Bouligand-type helicoidal structure subjected to the single edge notched (SEN) tensile loading. The roles of the biological features (i.e., layered arrangement of collagen fibrils and interbundle fibrils) on the fracture resistance and toughening mechanism of the Bouligand-type structures have been uncovered and analyzed quantitatively. This is of interest for future design of engineering materials and structures that require composites with enhanced toughness, and can deepen the understanding of the structure-property relationship of the Bouligand-type structure in bionic design.