Mechanical interlocking enables materials whose components remain associated while retaining internal mobility. Such assemblies can undergo large rearrangements without losing cohesion, yet resist deformation when contacts restrict further motion. Understanding this behavior requires connecting the motions of individual components to the collective mechanics of the materials. In this talk, I will discuss polycatenated architected materials and entangled helical weaves as model systems for connecting local motion to the collective mechanics of the assembly. I will describe how these architectures form and what prevents their components from separating, then examine the sliding and rotation that remain possible within them. Reconfigurable knot chains and swellable architectures will illustrate how changes in geometry alter these motions and the resulting material response. I will close with our progress toward nanoscale interlocked assemblies, where thermal motion raises questions about the lifetime and relaxation of interlocked states and how these processes affect collective phase behavior.

“Architectured” materials and structures constructed from building blocks with specific shapes and arrangements can give rise to unique and attractive mechanisms. For example, in nacre-like brick-and-mortar materials and topologically interlocked panels, the interplay between stiff and strong elements, geometry and weaker interfaces gives rise to nonlinear deformations and toughness in otherwise all-brittle materials. Our explorations of these designs have recently intersected the field of granular mechanics. Our playground still includes geometry, mechanics and structural properties, but our building blocks are now individual grains or particles, and we use vibrations as an assembly tool. In this talk I will discuss two of these “engineered” granular materials. The first one is fully dense granular crystals made of space-filling polyhedral grains. These “macroscale” crystals are 10 times stronger than traditional granular materials, and they display a rich set of mechanisms: Nonlinear deformations, crystal plasticity reminiscent of atomistic mechanisms, geometric strain hardening, micro-buckling. The second example is engineered entangled matter made of particles with barbs and hooks. We capture entanglement mechanisms at multiple length scales using discrete element models, Monte Carlo simulations and Markov probability, and we use these models to design particle shapes that maximize entanglement. Entangled bundles made from these optimized particles are flexible, but also surprisingly strong and tough in tension. Granular crystals and entangled matter provide new combinations of strength, toughness and recyclability, making them attractive for a broad range of structural applications.