Chirality destroys oriented active solids

We construct a hydrodynamic theory of the effect of chiral and active force densities on three-dimensional uniaxial solids. We show that in a fixed background medium active chiral force densities—that arise at lower order in gradients than odd elasticity—generically destabilise the solid state. We further show this active instability also affects isotropic chiral solids in an anisotropic medium, a situation that is relevant for cell clusters moving through the extracellular matrix. Interestingly, the instability is eliminated in a higher-symmetry solid, known as the polar elastomer; indeed, we show that chirality does not affect the leading-order mechanics of such materials. We further demonstrate that momentum-conserving polar active solids have two chiral odd elasticities in contrast to the one discussed for two-dimensional solids. However, we again find that the higher symmetry of polar elastomers eliminates one of these with the remaining one being equivalent to the two-dimensional odd elastic force density. Our results should apply to numerous biological and condensed matter systems.