Coarse-Grained Equivalent Stiffness: A Structure-Plasticity Indicator across the Order-Disorder Spectrum

Predicting plastic deformation across the spectrum of structural order, from crystalline to amorphous solids, remains a grand challenge. Coarse-grained equivalent stiffness (CGES), derived from the local dynamical matrix, is introduced as a broadly applicable parameter for mechanical stability. Its spatial variation effectively pinpoints "soft zones'' susceptible to plastic rearrangements. Across six systems ranging from single crystals with dislocations to disordered polycrystals, quasicrystals, and amorphous solids, CGES spatially correlate with local plastic rearrangements, accurately capturing dislocation cores, grain boundaries, and shear transformation zones (STZs). In single crystals, CGES gradients deterministically pinpoint dislocation cores where plasticity is fully localized. For the four disordered systems, quantitative analysis shows that plastic events are statistically concentrated within CGES-identified soft zones, with occurrence probabilities 3--7 times higher than in the bulk. Moreover, local eigenvectors align with plastic rearrangements directions, elucidating microscopic deformation pathways. CGES thus offers a unified, efficient framework for predicting plasticity without prior load, advancing the understanding of failure mechanisms in diverse solids.