Funded Grants

A network approach to multi-scale materials

Many engineered and biological materials are "metamaterials" built from smaller components. A cathedral is a pile of stones, a sweater is knit from yarn, and a jellyfish is a collection of cells. Such metamaterials are inherently tunable based on how the building blocks are assembled. Some properties are inherited from the building blocks – yarn is more flexible than stone – and other properties arise cooperatively. Although made of metal, chainmail nonetheless drapes like a sweater: the flexibility arises from the rotation of links. If you removed links from the chainmail or stones from the cathedral one by one, you would cross a threshold beyond which you had no coherent structure: cooperativity has its limits.

Thus, the properties of the building blocks, the interactions between them, and their geometric configurations all play a role in determining the properties of metamaterials. The network of connections between the blocks not only controls whether the material is stable, but also the flow of energy, fluids, or electricity. A great boon in design would arise from having tools to create materials with an optimal mix of rigidity/flexibility, or a particular connectivity of pores. Ultra- light building materials would optimize rigidity, fabrics for smart clothing would optimize drape without loss of electrically conducting paths, and energy-harvesting nanomaterials would tune the vibrational modes. However, design principles permitting scalability from the choice of building blocks to the full behavior of the system remain poorly understood. Classically, descriptions have focused on average or maximum behavior, rather than on exploiting structures at multiple length scales. Naturally-occurring and self-organized systems illustrate an alternative approach: exploiting properties which exist on many scales. The hierarchy of connections which exist in social, neurological, ecological, epidemiological, and economic networks provide efficiency and robustness to the system as a whole.

This proposal aims to develop network science tools as a means to advance our understanding of complex metamaterials. To make this connection, we write a mathematical representation of a material as a network. The building blocks are the nodes of the network, and the specific configuration provides the connections between those nodes. Such representations allow for sophisticated analyses which partition the material into connected “communities” and pinpoint key nodes/edges which control the behavior of the system. Because networks associated with materials are spatially-embedded (building blocks connect to neighboring blocks), their properties provide an interesting contrast with those studied in social/biological contexts.

My group is poised to make advances by combining expertise in granular materials, network theory, and nonlinear dynamics. This proposal describes controlled laboratory measurements mapping out the network of connections within real materials, with the aim of developing new network tools to predict the complex, cooperative response. Our experiments will focus on granular materials (optical measurements provide the contact forces) and 3D printed foams with the contact network known in advance. Building on recent successes which use networks to quantify rigidity and transport properties in granular materials, we aim to provide a new framework for design of multiscale materials to meet engineering goals.