Abstract

Non-reciprocal interactions in active elastic media cause work cycles and wave propagation forbidden in equilibrium. These linear phenomena offer a route to designing autonomous materials that spontaneously crawl, roll or swim. Yet these same phenomena also render non-reciprocal materials hard to design, and force us to reckon with active elastodynamics beyond the linear regime.

In this talk I will describe our current work on rationally designing non-reciprocal materials made of robots, and modelling their collective dynamics. First I will show that odd elasticity, the continuum hallmark of microscopic non-reciprocity, emerges in a broad range of lattices made of non-reciprocal springs. Strikingly however, we find that the strength of odd response strongly depends on the precise lattice geometry. Hyperstatic lattices are needlessly hard to actuate, leading to sub-optimal odd response. By contrast, we find that in overly floppy lattices, zero modes couple to microscopic non-reciprocity, destroying odd moduli entirely. By avoiding these pitfalls, we identify optimal design principles for building odd lattices.

After connecting microscale non-reciprocity to macroscale elasticity, I will then present a continuum model of nonlinear odd elasticity, benchmarked against microscopic simulation and table-top experiments. Combining non-reciprocity and non-linearity in momentum-conserving materials yields long-wavelength instabilities and travelling nonlinear patterns. Strikingly, momentum conservation causes these emergent patterns to coarsen over time. As a result, these active metamaterials spontaneously rid themselves of disorder in favour of coherent motion. We then explore how this coarsening can respond to environmental stimuli, leading to a toolkit of distinct patterns for designing locomotion and actuation.