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