On optimal hierarchy of load-bearing biological materials

Load-bearing biological materials such as shell, mineralized tendon and bone exhibit two to seven levels of structural hierarchy based on constituent materials (biominerals and proteins) of relatively poor mechanical properties. A key question that remains unanswered is what determines the number of hierarchical levels in these materials. Here we develop a quasi-self-similar hierarchical model to show that, depending on the mineral content, there exists an optimal level of structural hierarchy for maximal toughness of biocomposites. The predicted optimal levels of hierarchy and cooperative deformation across multiple structural levels are in excellent agreement with experimental observations.