Critical scaling near the yielding transition in granular media.
Critical scaling near the yielding transition in granular media.
复制标题
颗粒介质中屈服转变附近的临界缩放。
作者：
A. Clark;Jacob D. Thompson;M. Shattuck;N. Ouellette;C. O’Hern
我们发现，颗粒介质中的屈服转变显示二阶临界点标度行为。我们进行离散元模拟的低惯性数限制摩擦，纯排斥球形颗粒进行简单的剪切在固定的无量纲剪切应力在两个和三个空间维度。为了找到一种能支持外加应变的机械稳定（MS）堆积，尺寸为L的各向同性制备态必须经历一个总应变γ_{ms}（ε，L）。MS堆积的数密度（<$γ_{ms}^{-1}）在长度尺度为<$m的临界标度形式下，当<$m><$c}<$0.11时为零|联系我们|^{-ν}，其中ν为1.7-1.8。在屈服应力以上（ε> ε_{c}），在大系统极限L/ε_{c} 1中不存在能支持ε_{c}的MS填料。通过剪切产生的MS填料具有各向异性力和接触网络，这表明，在这些网络可以变形的程度的上限，这些网络可以远离各向同性填料。
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.