Unified Understanding of Nonlinear Rheology near the Jamming Transition Point

When slowly sheared, jammed packings respond elastically before yielding. This linear elastic regime becomes progressively narrower as the jamming transition point is approached, and rich nonlinear rheologies such as shear softening and hardening or melting emerge. However, the physical mechanism of these nonlinear rheologies remains elusive. To clarify this, we numerically study jammed packings of athermal frictionless soft particles under quasistatic shear. We find the universal scaling behavior for the ratio of the shear stress and the pressure P, independent of the preparation protocol of the initial configurations. In particular, we reveal shear softening /P^1/2 over an unprecedentedly wide range of strain up to the yielding point, which a simple scaling argument can rationalize.