Critical scaling for yield is independent of distance to isostaticity

Granular materials, suspensions, foams, and emulsions can form amorphous jammed states. These states can yield when subjected to a shear stress τ. When μ = τ/p, where p is the system pressure, exceeds a critical value μ_c, jammed states become inaccessible and flow persists indefinitely. Near μ = μ_c, long-range cooperative effects become dominant, as shown by the success of recent nonlocal rheological models. Long-range cooperativity in these systems is often framed in terms of the isostatic jamming point, which occurs at p = 0. The relationship between isostatic jamming and yielding is not fully understood. Here, using simulations of quasi-statically sheared soft sphere packings, we observe critical behavior near μ=μ_c, with a diverging length scale ξ ~ |μ - μ_c |^-ν, that is independent of distance to isostaticity over a wide range of p. The critical scaling functions and values of the scaling exponents are nearly independent of distance to isostaticity despite the large range of p. Our results demonstrate that yielding of jammed systems represents a critical transition that is distinct from the isostatic point. Our results may also be useful in deriving and improving nonlocal rheological models.