Beaded metamaterials

Beaded materials occupy an interesting place in material science between granular matter and textiles. In this context, beads appear as discrete, rigid, volumetric elements in contact with one another, while being embedded topologically in a network of compliant thread.

Bead-weaving patterns provide a means to prescribe order to the networks. In this research, we focus on angle weave, a technique in which intersecting loops of $n$ beads form tiling patterns. Angle weaves thus offer a sophisticated approach to programming shape through strategic manipulation of valency. For instance, 12 loops of 5 beads will close a dodecahedron, a tiling of 7 beads forms a hyperbolic surface, and so on.

Beyond shape programming, beaded textiles tend to exhibit greater stiffness than most conventional textiles. While this enhanced stiffness logically stems from the rigidity of individual beads, the precise mechanisms underlying this property become the subject of the study.

We approach the problem via a model experiment comprising six interlaced building blocks made of five-bead rings. When the thread ends are pulled, the model comes out-of-plane to form a shell. We study the shell’s stiffness by measuring the resulting force as it’s compressed, which in many cases reveals a linear dependency on pretension. Sometimes the choice of thread material, pretension, and loading scheme can lead to locked, superjammed configurations, supporting even greater loads. We rationalize our results using simple theory and additional experiments that seek to isolate the roles of geometry and friction between beads and thread.

Further work

In our Nature Communications paper, we show that large bead networks tend to develop some characteristic slack. This makes the material floppy for small local deformations and stiff for larger ones as slack is exhausted. Meanwhile, the thread is subject to significant capstan friction as excess length is requested by sliding or stretching through a tortuous network, of which a free end is not well defined.

Some additional questions arise from considering these effects. The pages below (works in progress) elaborate on the following points:

1. The beaded catenary problem: If slack is present, how does gravity contribute to the softening or stiffening of a simple beaded structure?

2. How do we characterize the stiffness of large bead networks, where friction, slack, and elasticity dominate?