Reinforced elastic sheets surround us in daily life, from concrete shell buildings to biological structures such as the arthropod exoskeleton or the venation network of dicotyledonous plant leaves. Natural structures are often highly optimized through evolution and natural selection, leading to the biologically and practically relevant problem of understanding and applying the principles of their design. Inspired by the hierarchically organized scaffolding networks found in plant leaves, here we model networks of bending beams that capture the discrete and nonuniform nature of natural materials. Using the principle of maximal rigidity under natural resource constraints, we show that optimal discrete beam networks reproduce the structural features of real leaf venation. Thus, in addition to its ability to efficiently transport water and nutrients, the venation network also optimizes leaf rigidity using the same hierarchical reticulated network topology. We study the phase space of optimal mechanical networks, providing concrete guidelines for the construction of elastic structures. We implement these natural design rules by fabricating efficient, biologically inspired metamaterials.

中文翻译：

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生物网络的最佳弹性

从混凝土外壳建筑到生物结构（如节肢动物外骨骼或双子叶植物叶片的通气网络），增强的弹性片材在我们的日常生活中环绕着我们。天然结构通常通过进化和自然选择进行高度优化，从而导致了在生物学和实践上相关的理解和应用其设计原理的问题。受植物叶片中分层组织的脚手架网络的启发，在这里，我们对弯曲梁的网络进行建模，以捕获天然材料的离散和非均匀性质。使用自然资源约束下的最大刚度原理，我们表明最佳离散梁网络再现了真实的叶脉结构特征。因此，除了能够有效输送水和养分之外，通风网络还使用相同的分层网状网络拓扑优化了叶片的刚度。我们研究了最佳机械网络的相空间，为构造弹性结构提供了具体指导。我们通过制造有效的，受生物启发的超材料来实现这些自然设计规则。