Dynamic heterogeneity and facilitation in sheared granular materials: Insights from three-dimensional triaxial...

Strain localization in granular materials arises from complex microscale dynamics, including intermittent particle rearrangements and spatiotemporally correlated deformation. While dynamic heterogeneity (DH) and dynamic facilitation (DF) have been widely studied in two-dimensional amorphous materials, their prevalence in three-dimensional (3D) granular systems remains unclear. Here, we performed a 3D triaxial compression test with in-situ x-ray computed tomography to track particle-scale kinematics across small and large strain increments. We analyzed deviatoric strain, volumetric strain, and nonaffine motion fields, computed four-point spatial dynamic correlation functions to probe DH, quantified DF through a facilitation ratio, and assessed the temporal persistence of local dynamics using four-point temporal dynamic correlations. Across large strain increments, DH and DF emerge strongly in the transition regime between the initially elastic response and the critical state regime, but weaken or become statistically insignificant within the shear band at the critical state, indicating a qualitative change in collective deformation dynamics upon localization. In contrast, under small increments, both measures are suppressed across all regimes. These results demonstrate that correlated dynamics depend strongly on both strain increment and deformation regime. This work provides a comprehensive investigation of DH and DF in 3D granular materials and highlights their strain-increment- and regime-dependent behaviors, establishing a connection to glassy dynamics in amorphous solids.