Self-sensing metamaterials with odd micropolarity

Materials made from active, living, or robotic components can display emergent properties arising from local sensing and computation. Yet, the implications of such self-sensing and feedback on the continuum mechanics of freestanding active solids remain largely unexplored. Here, we realize a freestanding active metamaterial with piezoelectric elements and electronic feedback loops that gives rise to an odd micropolar elasticity which does not follow from a potential energy. A non-reciprocal active modulus enables bending and shearing cycles that convert electrical energy into mechanical work, and vice versa. The sign of this elastic modulus is linked to a non-Hermitian topological index that controls the localization of vibrational modes to sample boundaries. Unlike biological organisms with specialized components, our active metamaterial built out of undifferentiated cells acts as a distributed machine capable of sensing changes in its own shape and performing work in response. Aside from the design of active metabeams and other autonomous structural components, our work provides guidelines to control the elasticity of active synthetic biofilaments and membranes.