Topological defects in non-reciprocal active solids with odd elasticity

Abstract

We study topological defects in active solids whose microscopic interactions violate Maxwell-Betti reciprocity (MBR). Broken MBR arises in active solids whenever the linear response between microscopic displacements and (non-conservative) forces is asymmetrical. In the continuum, broken MBR yields an asymmetric (or odd) elastic modulus tensor that modifies the interaction between dislocations, even reversing the stability of otherwise bound pairs. Such odd elastic moduli can also arise in reciprocal systems with conservative microscopic forces if pre-stress is present. Beyond continuum theories, isolated dislocations can also become motile due to microscopic work cycles active at dislocation cores that compete with conventional Peach-Koehler forces caused, for example, by ambient torque densities. We perform molecular dynamics simulations isolating active plastic processes and discuss their experimental relevance to solids composed of spinning particles and robotic metamaterials.