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 determine, for the first time, the relationship between avalanche duration and size across the yielding transition, revealing how it evolves from quasistatic to dynamic flow regimes. This precise measurement is made using the Controlled Relaxation Time Model (CRTM), a new simulation framework that treats the relaxation time as a tunable parameter. CRTM reproduces known results in both limits and enables a direct analysis of the change of regime between them. Applying the model to different microscopic dynamics, we find that the existing scaling relation connecting critical exponents under flow holds for passive systems. However, active systems exhibit significant deviations, suggesting a missing ingredient in the current understanding of yielding.