Multiscale Analysis of Local Fluctuations in Granular Materials Subject to Quasi‐Static Shear

ABSTRACT The ostensibly uniform macroscopic deformation of granular materials belies intensive fluctuations of microscopic and mesoscopic kinematics. This study employs the discrete element method to analyze the spatial characteristics of local kinematic fluctuations under different shear conditions and quantifies the consistency between multi‐scale kinematics and macroscopic behavior. With shear progression, displacement fluctuation vortices evolve from uniform small vortices into dominant large structures containing numerous small vortices, heralding shear band formation, characterized by a sequence of coherently rotating and interconnected small vortices. Within these bands, while particle displacement fluctuations are subdued, profound rotational motions lead to pronounced inter‐particle relative displacements, designating the shear band as an optimal energy dissipation structure. The probability density distribution forms of microscopic and mesoscopic kinematic fluctuations and their evolutionary trends are independent of the loading path. At the microscale, both particle displacement and rotation fluctuations follow ‐Gaussian distributions. Notably, prior to shear band formation, the distribution of normalized displacement fluctuations maintains its form with increasing strain, whereas the distribution characterizing particle rotation sharpens, reflecting a more pronounced peak and heavier tails. At the mesoscale, Loop volumetric strain and rotation exhibit ‐Gaussian distributions, while Loop deviatoric strain follows a Gamma distribution. The average micro‐ and mesoscopic kinematics align with macroscopic behaviors throughout shearing, regardless of loading paths.