生物网络的最优弹性
Optimal elasticity of biological networks
摘要：
在日常生活中，从混凝土外壳建筑物到生物结构，如节肢动物外骨骼或双子叶植物叶片的脉序网络，增强弹性片材围绕着我们。自然结构通常通过进化和自然选择高度优化，导致理解和应用其设计原理的生物学和实际相关问题。受植物叶子中分层组织的脚手架网络的启发，我们在这里建立了弯曲梁网络模型，这些弯曲梁网络捕捉了自然材料的离散和非均匀性质。利用自然资源约束下的最大刚度原则，我们表明，最佳离散梁网络再现真实的叶脉的结构特征。因此，除了其有效运输水和养分的能力之外，脉序网络还使用相同的分层网状网络拓扑结构来优化叶片刚度。我们研究了最优力学网络的相空间，为弹性结构的构造提供了具体的指导。我们通过制造高效的、受生物启发的超材料来实现这些自然设计规则。
英文摘要：
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 non-uniform 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.
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