  It is accepted that stress and structure self-organize cooperatively during
quasi-static dynamics of granular systems, but the consequences of this
self-organization are not fully understood. 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 quasi-statically by two
different procedures. We define cells, cell orders, cell orientations, and cell
stresses and report the following. 1. The mean ratio of cell principal stresses
decreases with cell order and increases with friction. 2. The ratio
distributions collapse onto a single curve under a simple scaling, for all
packing protocols and friction coefficients. 3. Cells orient along the local
stress major principal axes. 4. A simple first-principles model explains the
correlations between the local cell and stress principal axis orientations. 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 re-organization upon
application of external stress, suggests that current stress theories of
granular matter need to be revisited.
