Quantifying Rearrangement Statistics, Correlations, and Contributions to Macroscopic Strain in 3D Granular Materials Using X-ray Measurements

Local rearrangements are an essential ingredient of the quasi-static and dynamic deformation of granular materials. Various models have been proposed for relating local particle rearrangements to macroscopic plasticity in granular materials. All such models rely on assumptions regarding rearrangement strain, frequency, stress relaxation, and contributions to macroscopic deformation. Here, we examine in-situ X-ray measurements of particle-resolved structure and stress in quasi-statically deforming granular materials in various geometries to study the statistics of rearrangements, their length scales, their correlations with structure and stress, and their contribution to macroscopic strain. We first define distinct rearrangement measures that quantify local strain, non-affine motion, and relative rotation. We show that rearrangements defined by each of these measures have length scales of about three particle diameters. We use particle-resolved structure and stress measurements to examine the coupling between rearrangement measures, for instance between local volumetric and shear strain and between non-affine motion and relative particle rotation. We examine correlations between rearrangement magnitude and local stress and porosity preceding rearrangements, showing that, at the length scale of local rearrangements, structure plays at least as important of a role as stress. Finally, we study how local regions exhibiting large rearrangements contribute to macroscopic strain. Our results provide insight into the features and statistics of rearrangements in quasi-statically deforming granular media.