Yielding versus jamming: critical scaling of sheared, soft-core disks and spheres

Abstract

Using discrete element simulations, we demonstrate critical behavior for yielding of assemblies of soft-core repulsive disks (2D) and spheres (3D) over a wide range of dimensionless pressures. Assemblies are isotropically compressed, and we then perform quasi-static simple shear at fixed pressure using shear-periodic boundaries. By examining the fluctuations in the dimensionless shear stress \(\Sigma\), we observe finite-size scaling consistent with a diverging length scale \(\xi \propto |\Sigma - \Sigma_c|^{-\nu}\). We observe two distinct values of \(\nu\): \(\nu_{\rm ms} \approx 1.8\) characterizes the initial stress buildup in both 2D and 3D, and \(\nu_{\rm slip}\) characterizes slips during steady-state shear, where \(\nu_{\rm slip}\approx 1.1\) in 2D and \(\nu_{\rm slip}\approx 0.8\) in 3D. The critical stress \(\Sigma_c\) is constant for low pressure, \(\Sigma_c \approx 0.1\) in 2D and \(\Sigma_c \approx 0.11\) in 3D, but decreases for larger pressures. However, the critical behavior, including the values of scaling exponents, is otherwise unchanged over a wide range of pressures, including far from the jamming transition. Our results show that yielding is in fact a distinct phase transition from jamming, which may explain similarities between nonlocal rheological descriptions of granular materials, foams, emulsions, and other soft particulate materials.