Simple Model for the Toughness of a Helical Structure Inspired by the Exoskeleton of Lobsters

Nature has evolved remarkable hierarchical structures to realize tough biocomposites. The helical structure of the exoskeleton generally found in crustaceans is one such example. Recently, detailed structural and mechanical properties of the exoskeleton have been actively studied for lobsters, which has inspired artificial biomineralization. However, the superiority of the special structure giving the toughness has yet to be elucidated. Here, we develop a simple model of the structure of crustaceans via two-step coarse-graining to obtain a scaling law for fracture energy, a measure of fracture toughness. The law provides a clear physical understanding of how the simple model structure is optimized in terms of its the toughness by exploiting at least five important design principles.