Mechanochemical feedback drives complex inertial dynamics in active solids

By combining internal driving (activity) with elasticity, active solid systems can exhibit nonequilibrium mechanics and autonomous motion. While these systems are often studied in overdamped settings, e.g., in soft materials, the role of inertia has received less attention. We propose a model of a chemically active solid that includes mechanochemical feedback. Our findings reveal that when this feedback dominates over mechanical damping, autonomous inertial dynamics can spontaneously emerge through the sustained consumption of chemical fuel. By integrating numerical simulations, analytical methods, and approaches from dynamical systems, we demonstrate how active feedback drives complex nonlinear dynamics across multiple time scales, including limit cycles and chaotic behavior. Our results suggest design principles for the development of ultrafast actuators and autonomous machines made from soft, chemically powered solids.