Three-dimensional crack bridging model of biological materials with twisted Bouligand structures

Abstract Twisted fiber-reinforced structures that resemble plywood, also called Bouligand structures, are widely observed biological materials in organisms such as lobsters, crabs, mantis shrimp and scorpions, where they exhibit outstanding fracture toughness and damage resistance. In this paper, we develop a three-dimensional crack twisted-bridging model to correlate fracture toughness with Bouligand microstructures and reveal the underlying toughening mechanisms. Depending on their orientation, some nanofibers bridge the crack surfaces in a twisting arrangement within the fracture process zone at the crack tip. The crack resistance of the structures assembled by soft biopolymers and physical cross-links is parameterized in terms of the nanofiber pitch angle and interfacial properties. Bouligand structures exhibit high and direction-independent fracture toughness in the nanofiber rotating plane, a notable advantage that endows material with superior load-bearing capacity in all directions. The crack resistance of Bouligand structures increases with the pitch angle of nanofibers, and the highest value is achieved at 90 degrees. Within a reasonable structural motif, an increase in the nanofiber length or interfacial strength results in an enhancement of the fracture toughness. Compared with the finite deformation of biopolymers, the facile formation and reformation mechanism of physical cross-links at the interfaces is a more efficient toughening strategy for materials with network-like structures of nanofibers. Our theoretical predictions agree well with relevant experimental measurements. This work can aid in designing biomimetic structural materials with high performance.