Fractal space frames and metamaterials for high mechanical efficiency

TL;DR

This paper introduces hierarchical space frame structures that significantly reduce material use for stability under compression, enabling the design of lightweight, high-strength, isotropic metamaterials with customizable shapes.

Contribution

It presents a systematic method to alter the scaling of material requirements using hierarchical space frames, optimizing structures for different load conditions.

Findings

Material volume scales as L^{3}f^{(G+1)/(G+2)} with hierarchy levels

Hierarchical structures achieve higher efficiency than solid beams

Potential for creating lightweight, high-strength isotropic materials

Abstract

A solid slender beam of length $L$, made from a material of Young's modulus $Y$ and subject to a gentle compressive force $F$, requires a volume of material proportional to $L^{3}f^{1/2}$ [where $f\equiv F/(YL^{2})\ll 1$] in order to be stable against Euler buckling. By constructing a hierarchical space frame, we are able to systematically change the scaling of required material with $f$ so that it is proportional to $L^{3}f^{(G+1)/(G+2)}$, through changing the number of hierarchical levels $G$ present in the structure. Based on simple choices for the geometry of the space frames, we provide expressions specifying in detail the optimal structures (in this class) for different values of the loading parameter $f$. These structures may then be used to create effective materials which are elastically isotropic and have the combination of low density and high crush strength. Such a material could be used to make light-weight components of arbitrary shape.