Coarsening in odd elastic metamaterials

Non-reciprocal interactions in active elastic media cause work cycles and wave propagation forbidden in equilibrium. These linear phenomena yield motifs for programming robust mechanical actuation, but they also hint at a new class of non-linear emergent phenomena in active solids.

Here, we develop a continuum model of nonlinear odd elasticity, benchmarked against microscopic simulation and table-top experiments.We show that the combination of 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, this active metamaterial spontaneously rids itself of disorder in favour of coherent motion. We explore how this coarsening can respond to environmental stimuli, leading to a toolkit of distinct patterns for designing locomotion and actuation.

Our results position odd elastic solids as an illustrative example of nonlinear physics in the absence of reciprocity, and point towards applications of these animate materials towards shape change, crawling, and swimming