Yielding Versus Jamming: Critical Scaling of Sheared Soft-Core Disks

Using discrete element simulations, we study critical behavior for yielding of assemblies of soft-core repulsive disks over a range of dimensionless pressures P. We isotropically compress the disks in a shear-periodic (Lees-Edwards) geometry and then perform quasi-static simple shear. After each shear strain step, we relax the potential energy and dilate or compress the grains to maintain fixed pressure P and then evaluate the shear stress τ. We find that the number density of mechanically stable (MS) states and the strain between MS states obey finite-size scaling consistent with a diverging length scale ξ ~ |Σ-Σ_c|^-ν, where Σ=τ/P. We observe two distinct values of ν: one during the initial stress buildup, ν ≈ 1.7, and another characterizing the slips during steady state shear, ν ≈ 1.1. The critical stress Σ_c increases as P is decreased and approaches a constant in the low-P limit, Σ_c ≈ 0.1. However, the critical behavior (including the values of scaling exponents) is otherwise independent of P over several orders of magnitude, including well above the jamming transition. Our results show that critical scaling behavior associated with yielding is distinct from jamming, which may explain similarities among nonlocal flows of granular materials, emulsions, and other soft materials.