Bridging the Gap Between Avalanche Relaxation and Yielding Rheology

Abstract: The yielding transition in amorphous materials, whether driven passively (simple shear) or actively, remains a fundamental open question in soft matter physics. While avalanche statistics at the critical point have been extensively studied, the emergence of the dynamic regime at yielding and the steady-state flow properties remain poorly understood. In particular, the significant variability observed in flow curves across different systems lacks a clear explanation. We introduce the Controlled Relaxation Time Model (CRTM), a novel simulation framework that treats relaxation time as a tunable parameter, seamlessly bridging quasistatic avalanche statistics and dynamic flow regimes. CRTM reproduces known results in both limits and enables direct analysis of the transition between them, providing precise measurements of avalanche relaxation times. Applying CRTM to different microscopic dynamics, we find that a previously proposed scaling relation connecting critical exponents holds for passive systems. However, active systems exhibit significant deviations, suggesting a missing ingredient in the current understanding of active yielding.