Critical scaling near the yielding transition in granular media

Physical Review. E
Abram H ClarkCorey S O'Hern

Abstract

We show that the yielding transition in granular media displays second-order critical-point scaling behavior. We carry out discrete element simulations in the low-inertial-number limit for frictionless, purely repulsive spherical grains undergoing simple shear at fixed nondimensional shear stress Σ in two and three spatial dimensions. To find a mechanically stable (MS) packing that can support the applied Σ, isotropically prepared states with size L must undergo a total strain γ_{ms}(Σ,L). The number density of MS packings (∝γ_{ms}^{-1}) vanishes for Σ>Σ_{c}≈0.11 according to a critical scaling form with a length scale ξ∝|Σ-Σ_{c}|^{-ν}, where ν≈1.7-1.8. Above the yield stress (Σ>Σ_{c}), no MS packings that can support Σ exist in the large-system limit L/ξ≫1. MS packings generated via shear possess anisotropic force and contact networks, suggesting that Σ_{c} is associated with an upper limit in the degree to which these networks can be deformed away from those for isotropic packings.

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Citations

Feb 16, 2019·Physical Review Letters·Ishan SrivastavaJeremy B Lechman
May 31, 2019·Physical Review Letters·Kuniyasu Saitoh, Brian P Tighe
May 21, 2021·The European Physical Journal. E, Soft Matter·Michio Otsuki, Hisao Hayakawa
Jun 22, 2021·Physical Review Letters·Hugo PerrinYoël Forterre
Oct 26, 2021·Soft Matter·Carlos Villarroel, Gustavo Düring
Nov 4, 2021·The European Physical Journal. E, Soft Matter·Stanislav ParezEinat Aharonov

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