结构层次赋予生物组织的容错性
Structural hierarchy confers error tolerance in biological tissues
摘要：
结构层次，其中材料在多个长度尺度上具有不同的特征，在自然界中无处不在;不同的生物材料，如骨骼，纤维素和肌肉，有多达十个层次。结构层次赋予许多机械优势，包括改进的韧性和材料的经济性。然而，它也提出了一个问题：每个层次增加了一个新的装配错误源，并大大增加了正确装配所需的信息。这似乎与自然发生的等级结构的流行相冲突，这表明可能存在等级鲁棒性的共同机械来源。然而，我们的能力，以确定这样一个统一的现象是有限的，缺乏一个一般的机械框架的结构展示组织在不同的长度尺度。在这里，我们使用模拟来证实一个广义模型的层次，拉伸稳定，丝状网络的拉伸刚度与嵌套，稀释三角形晶格结构。在麦克斯韦和其他人关于刚性框架标准的开创性工作之后，我们扩展了网络力学中的连通性概念，并发现了材料刚度在每个层次上的数学相似依赖性。使用这个模型，我们发现，这样的网络的刚度变得不那么敏感的错误与额外的层次结构的装配，虽然令人惊讶的是，我们表明，这一结果是分析预测的第一原则，因此可能独立于模型。更广泛地说，这项工作有助于解释生物学和材料设计中分层丝状材料的成功，并提供了一种启发式方法，以确保在所需的公差范围内实现所需的材料特性。
英文摘要：
Structural hierarchy, in which materials possess distinct features on multiple length scales, is ubiquitous in nature; diverse biological materials, such as bone, cellulose, and muscle, have as many as ten hierarchical levels. Structural hierarchy confers many mechanical advantages, including improved toughness and economy of material. However, it also presents a problem: each hierarchical level adds a new source of assembly errors, and substantially increases the information required for proper assembly. This seems to conflict with the prevalence of naturally occurring hierarchical structures, suggesting that a common mechanical source of hierarchical robustness may exist. However, our ability to identify such a unifying phenomenon is limited by the lack of a general mechanical framework for structures exhibiting organization on disparate length scales. Here, we use simulations to substantiate a generalized model for the tensile stiffness of hierarchical, stretching-stabilized, filamentous networks with a nested, dilute triangular lattice structure. Following seminal work by Maxwell and others on criteria for stiff frames, we extend the concept of connectivity in network mechanics, and find a mathematically similar dependence of material stiffness upon each hierarchical level. Using this model, we find that the stiffness of such networks becomes less sensitive to errors in assembly with additional levels of hierarchy; though surprising, we show that this result is analytically predictable from first principles, and thus likely model-independent. 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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