Scale-Rich Network-Based Metamaterials

TL;DR

This paper introduces Scale-Rich metamaterials, a novel design framework embedding multiscale heterogeneity into mechanical metamaterials, enabling highly tunable and multifunctional properties through network-inspired structural diversity.

Contribution

It presents a new network science-inspired approach to design metamaterials with broad scale variability, surpassing traditional homogeneous unit cell constraints.

Findings

Exhibit highly tunable elastic anisotropy

Show delocalized nonlinear deformation with high energy absorption

Enable programmable acoustic wave control

Abstract

Materials, at their essence, are networks defined by homogeneity: uniform bonds, fixed thicknesses, and discrete length scales. Mechanical metamaterials, while representing structurally more diverse microstructures, remain defined by the homogeneity of their unit cells, pore sizes, or repeating features. In contrast, as network science has revealed, real-world and biological systems -- from the Internet to the brain -- derive their function from broad, multiscale variability in connectivity and link length. Here, we introduce Scale-Rich (SR) metamaterials, a design framework that embeds network heterogeneity into mechanical metamaterials, achieving order-of-magnitude heterogeneity in ligament lengths, thicknesses, and connectivity. Governed by only two parameters, SR networks span orders of magnitude in structural features, overcoming prior constraints in metamaterial design. Translating these network models into physically realizable materials, we use simulations and experiments to show that SR metamaterials exhibit properties inaccessible to traditional single-scale systems, including highly tunable elastic anisotropy, delocalized nonlinear deformation with high energy absorption, and programmable acoustic wave control. This network-science-based paradigm establishes a minimal yet universal framework for engineering multifunctional materials whose mechanical and acoustic behavior emerge directly from scale diversity itself.