Activated solids: spontaneous deformations, non-affine fluctuations, softening, and failure

Internal activity can fundamentally reshape the mechanical behavior of solids, yet its role in softening and failure remains incompletely understood. In this study, we investigate spontaneous deformations in activated solids via non-affine fluctuations that quantify local rearrangements relative to global strain. Using scaling analysis and numerical simulations, we show that non-affinity in crystalline solids grows quadratically with active speed and increases linearly with persistence time before saturating. Spatial correlations reveal an activity-dependent growing correlation length, while relaxation dynamics are governed by the active persistence time. With increasing activity, the distributions of local non-affinity broaden, become more skewed, and develop heavy tails, eventually forming a secondary maximum that signals coexisting small and large non-affinities; this heterogeneity precedes defect formation and two-step melting from solid to hexatic and ultimately to fluid. Finally, we demonstrate that spatially patterned activation provides a simple route to locally induce non-affinity and mechanical softening. Our predictions are experimentally testable and suggest a pathway to tunable mechanics in adaptive metamaterials, with implications for mechanical regulation in biological systems.