Optimal elasticity of biological networks

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.