Influence of Frozen Degrees of Freedom on Rheology of Sheared, Jammed Granular Systems

We investigate the rheology of jammed, granular systems through simulations of a two-dimensional bi-disperse mixture of purely repulsive harmonic disks. These disks undergo simple shear between rough walls. While parameters such as applied stress and packing fraction are well-established factors influencing jamming, our study also considers frozen degrees of freedom, which we refer to as "pins." We find that the distribution of D2min values, which signify particle rearrangements, is influenced by proximity to pins. This also extends to regions near walls, where it arises as a byproduct of changes in particle density and flow induced by the pins. As the density of pins increases, D2min decreases in the bulk but increases near the shearing wall. This pattern correlates with local stress dependence on proximity to the walls. For pressures close to the jamming threshold, stress versus strain curves reveal an increasing trend in the shear modulus as a function of pin density, while the yield stress decreases, indicating an increase in the material’s plasticity. The length scale over which the transverse velocity deviates from an affine profile is captured by a single parameter on the order of the separation between pins, “a.” Additionally, the distance “a/2” may play a key role as the spacing between a rough wall and the first layer of pins. Finally, we study transient behaviours, such as the propagation of velocity in the direction of shear or compression, and its dependence on pin density.