Why is Structural Hierarchy So Prevalent in Biological Materials?
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Structural hierarchy, in which materials possess distinct features on multiple length scales, is ubiquitous in nature. Many biological materials, such as bone, cellulose, and muscle, have as many as ten hierarchical levels. While structural hierarchy confers many mechanical advantages, including improved toughness and economy of material, it also presents a problem as each hierarchical level substantially increases the amount of information necessary for proper assembly. This seems to conflict with the broad prevalence of naturally occurring hierarchical structures. At the present, there is no general framework for understanding the interplay between structures on disparate length scales; such a framework is a critical tool for accounting for the robustness of hierarchical materials to defects. Here, we use simulations and experiments to validate a generalized model for the tensile stiffness of hierarchical, stretching-stabilized networks with a nested, dilute hexagonal lattice structure, and demonstrate that the stiffness of such networks becomes less sensitive to errors in assembly with additional levels of hierarchy. Following seminal work by Maxwell and others on criteria for stiff frames, we extend the concept of connectivity in network mechanics, and find a similar dependence of material stiffness upon each hierarchical level. More broadly, this work helps account for the success of hierarchical, filamentous materials in biology and materials design, and offers a heuristic for ensuring that desired material properties are achieved within the required tolerance.
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