Optimal elasticity of biological networks

TL;DR

This paper models and analyzes the optimal design of biological elastic networks, revealing how natural venation structures maximize rigidity and efficiency, and applying these principles to create bio-inspired metamaterials.

Contribution

It introduces a model of hierarchical beam networks that explains leaf venation optimization and demonstrates how natural design principles can inform the fabrication of elastic metamaterials.

Findings

Optimal networks reproduce real leaf venation features

Hierarchical reticulated topology enhances rigidity and resource efficiency

Guidelines for designing elastic structures based on natural principles

Abstract

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.