Pre-yielding mechanical response near the jamming transition

Abstract

The mechanical and rheological properties of jammed packings of frictionless particles under shear strain remain poorly understood, even when the strain amplitude is very small and well below the yielding threshold. Systems above the jamming transition point φ J are known to display two anomalous mechanical behaviors with respect to the frequency ω (or time t) and the strain amplitude γ. In the linear-response regime (γ → 0), the modulus under oscillatory shear strain exhibits an algebraic scaling, G(ω) ∼ ω 1/2 (or G(t) ∼ t -1/2 in the real-time representation). In contrast, in the quasistatic limit (ω → 0), the modulus shows a nonlinear behavior, G(γ) ∼ γ -1/2 , a phenomenon referred to as softening. The ranges of ω and γ over which these algebraic scalings hold broaden as φ J is approached from above, while both G(ω) and G(γ) vanish for φ < φ J . In this study, we investigate the mechanical response when both ω and γ are nite, and thus two anomalies coexist. To this end, we perform numerical analyses using two rheological protocols: oscillatory shear and transient relaxation. Our results demonstrate that the mechanical responses are not simply described as the superposition of the two algebraic relaxations and instead exhibit rich nonlinear viscoelastic behaviors both above and below φ J .