Structural hierarchy confers error tolerance in biological materials
Structural hierarchy confers error tolerance in biological materials
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DOI：
10.1073/pnas.1813801116
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发表时间：
2018-08
期刊：
影响因子：
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通讯作者：
Jonathan Michel;P. Yunker
中科院分区：
文献类型：
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作者：
Jonathan Michel;P. Yunker
结构层次在自然界中普遍存在，是工程材料的一个新兴趋势。尽管有许多优点，但分层材料也增加了复杂性，并大大增加了组装中出现随机错误的机会。尽管如此，高度等级化的组织在不同的谱系中已经进化了许多次;这种普遍性表明了机械鲁棒性的共同来源。在这项工作中，我们引入了一个听话的，模型层次格与可控属性的每个长度尺度。我们发现，与直觉相反，增加额外的结构层次实际上减少了机械性能的相对变化，尽管装配误差增加。这一发现告诉我们的分层结构的生物材料的出现的理解，同时也提供了一个实用的启发式材料设计。结构层次是指材料在不同长度尺度上具有不同的特征，在自然界中普遍存在。不同的生物材料，如骨骼、纤维素和肌肉，有多达10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，它也带来了一个问题：每个层次都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丝状网络的拉伸刚度与嵌套，稀释三角形晶格结构。继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，并发现了材料刚度对每个层次的类似依赖性。使用这个模型，我们发现，刚度变得不太敏感的错误，在装配与额外的层次结构，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，从而可能独立于模型。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。
Significance Structural hierarchy is ubiquitous in nature and an emerging trend in engineered materials. Despite their many virtues, hierarchical materials also add complexity and dramatically increase the opportunities for random errors in assembly. Nonetheless, highly hierarchical tissues have evolved many times in diverse lineages; this prevalence suggests a common source of mechanical robustness. In this work, we introduce a tractable, model hierarchical lattice with controllable attributes on each length scale. We find, contrary to intuition, that adding additional levels of structure actually reduces the relative variation in mechanical properties, despite an increase in assembly errors. This finding informs our understanding of the emergence of hierarchically structured biological materials, while also offering a practical heuristic in materials design. 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 10 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 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 similar dependence of material stiffness upon each hierarchical level. Using this model, we find that stiffness becomes less sensitive to errors in assembly with additional levels of hierarchy; although surprising, we show that this result is analytically predictable from first principles and thus potentially 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.