Abstract
The effective interactions between the constituents of driven soft matter generically defy Newton's third law. Combining theory and numerical simulations, we establish that six classes of mechanics with no counterparts in equilibrium systems emerge in elastic crystals challenged by nonreciprocal interactions. Going beyond linear deformations, we reveal that interactions violating Newton's third law generically turn otherwise quiescent dislocations into motile singularities which steadily glide though periodic lattices.
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