Coordinated stress-structure self-organization in granular packing

During quasistatic dynamics of granular systems, the stress and structure self-organize, but there is currently no quantitative measure or understanding of this phenomenon. Such an understanding is essential because local structural properties of the settled material are then correlated with the local stress, which calls into question existing linear theories of stress transmission in granular media. A method to quantify the local stress-structure correlations is necessary for addressing this issue and we present here such a method for planar systems. We then use it to analyze numerically several different systems, compressed quasistatically by two different procedures. We define cells, cell orders, cell orientations, and cell stresses and report the following results. (i) Cells orient along the local stress major principal axes. (ii) The mean ratio of cell principal stresses decreases with cell order and increases with friction. (iii) The ratio distributions collapse onto a single curve under a simple scaling, for all packing protocols and friction coefficients. (iv) A constructed model explains the correlations between the local cell and stress principal axis orientations. (v) The collapse of the stress ratios onto a Weibull distribution is modeled theoretically. Our results quantify the cooperative stress-structure self-organization and provide a way to relate quantitatively the stress-structure coupling to different process parameters and particle characteristics. Significantly, the strong stress-structure correlation, driven by structural reorganization upon application of external stress, suggests that current stress theories of granular matter need to be revisited.