Hyperelastic phase-field fracture mechanics modeling of the toughening induced by Bouligand structures in natural materials

Abstract

Bouligand structures are widely observed in natural materials; elasmoid fish scales and the exoskeleton of arthropods, such as lobsters, crabs, mantis shrimp and insects, are prime examples. In fish scales, such as those of the Arapaima gigas, the tough inner core beneath the harder surface of the scale displays a Bouligand structure comprising a layered arrangement of collagen fibrils with an orthogonal or twisted staircase (or plywood) architecture. A much rarer variation of this structure, the double-twisted Bouligand structure, has been discovered in the primitive elasmoid scales of the coelacanth fish; this architecture is quite distinct from "modern" elasmoid fish scales yet provides extraordinary resistance to deformation and fracture. Here we examine the toughening mechanisms created by the double-twisted Bouligand structure in comparison to those generated by the more common single Bouligand structures. Specifically, we have developed an orientationdependent, hyperelastic, phase-field fracture mechanics method to computationally examine the relative fracture toughness of elasmoid fish scales comprising single vs. double-twisted Bouligand structures of fibrils. The model demonstrates the critical role played by the extra inter-bundle fibrils found in coelacanth fish scales in enhancing the toughness of Bouligand-type structures. Synthesis and fracture tests of 3-D printed Bouligand-type materials are presented to support the modeling and complement our understanding of the fracture mechanisms in Bouligandtype structures.

Nested helicoids in biological microstructures

“…The BLU fracture toughness has been previously investigated by crack propagation analysis 12,[16][17][18][19] . However, the effect of tilting and off-axis twisting on the laminate fracture toughness should be assessed by further research.…”

“…The intricate conformation of the Bouligand laminate unit (BLU) has captured the interest of scientists and engineers, particularly because of its resemblance to laminated composites and its potential for inspiring even stronger, stiffer and tougher synthetic structures [6][7][8][9][10][11][12][13][14][15] . The potential mechanical properties of BLUs have been analyzed by laminate theory 11,12 and fracture mechanics 12,[16][17][18][19] , and by building and testing macroscale models [19][20][21][22][23] . Reproducing BLUs at the microscale, the scale typically found in nature, is still an open ongoing challenge.…”

“…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 example [12][13][14]19,24 ). Mathematically, this means that at any point along the twisting rotation axis, the helicoid will appear exactly the same 25 .…”

Discontinuous fibrous Bouligand architecture enabling formidable fracture resistance with crack orientation insensitivity

“…Recent investigations revealed that crack twisting mode significantly enhances fracture toughness in the Bouligand architecture where a crack plane propagates following the twisted fiber orientation (27)(28)(29)(30)(31)(32)(33). This amplifies the crack surface area and reorients fibers orientation in response to external loadings (27)(28)(29)33), e.g., tension, bending, or impact loads. The resultant modulus oscillation in the Bouligand structure is also proposed to promote the crack twisting (30).…”

3D Printing of Bioinspired Biomaterials for Tissue Regeneration

“…Bouligand structure is composed of superimposed layers of parallel aligned fibers with special angle deviation, which widely exists in the “weapon” or “armor” of animals such as the claws of crab, [ 145,146 ] fish scales, [ 147,148 ] beetle wings, [ 149,150 ] and Mantis shrimp. [ 151 ] Crack propagation paths of Bouligand structure would be longer than “brick‐and‐mortar” structure due to the larger interfacial area perunit crack length, leading to more energy dissipation and a high damage tolerance.…”