论文标题
颗粒包装的剪切响应压缩在干扰发作上方
Shear response of granular packings compressed above jamming onset
论文作者
论文摘要
我们研究了经受各向同性压缩的排斥，无摩擦球形颗粒的堵塞包装的机械响应。软性粒子模型的先前模拟，其中排斥相互作用的尺度是在粒子室内的幂律与指数$α$重叠，发现合奏平均的剪切模量$ \ langle g \ rangle g \ rangle $随压力$ p $ a as $ \ as $ \ sim p^{（α-3/2）/（α-3/2）/（α-1）}}}}}}。但是，缺乏对这种缩放行为的深刻理论理解。我们表明，球形颗粒的无摩擦填充堆积的剪切模量具有两个关键的贡献：1）连续变化是沿几何家族压力的函数，在压缩过程中，粒子间接触网络不变，2）不连续的跳跃，这是由于接触网络的变化而引起的。我们表明，可以将第一个用于封装包装的第一个几何家族的剪切模式折叠到主曲线上：$ g^{（1）}/g_0 =（p/p_0）^{（α-2）/（α-2）/（α-1）/（α-1）/（α-1）} - p/p_0 $，其中$ p_0 \ sim n^sim n^sparitiation sparitiation sparitiation spariatiatiation spariation spariation和$ g_0 \ sim n^{ - 2（α-3/2）} $。当接触网络的变化接近变化时，可能会发生与这种形式的偏差。 We further show that $\langle G (P)\rangle$ is not simply a sum of two power-laws, but $\langle G \rangle \sim (P/P_c)^a$, where $a \approx (α-2)/(α-1)$ in the $P \rightarrow 0$ limit and $\langle G \rangle \sim (P/P_c)^b$, where $b \ gtrsim（α-3/2）/（α-1）$高于特征压力$ p_c $。此外，几何家族对$ \ langle g \ rangle $的两种贡献的幅度以及接触网络的变化在$ p> p_c $的大型系统限制中仍然可以比较。
We investigate the mechanical response of jammed packings of repulsive, frictionless spherical particles undergoing isotropic compression. Prior simulations of the soft-particle model, where the repulsive interactions scale as a power-law in the interparticle overlap with exponent $α$, have found that the ensemble-averaged shear modulus $\langle G \rangle$ increases with pressure $P$ as $\sim P^{(α-3/2)/(α-1)}$ at large pressures. However, a deep theoretical understanding of this scaling behavior is lacking. We show that the shear modulus of jammed packings of frictionless, spherical particles has two key contributions: 1) continuous variations as a function of pressure along geometrical families, for which the interparticle contact network does not change, and 2) discontinuous jumps during compression that arise from changes in the contact network. We show that the shear modulus of the first geometrical family for jammed packings can be collapsed onto a master curve: $G^{(1)}/G_0 = (P/P_0)^{(α-2)/(α-1)} - P/P_0$, where $P_0 \sim N^{-2(α-1)}$ is a characteristic pressure that separates the two power-law scaling regions and $G_0 \sim N^{-2(α-3/2)}$. Deviations from this form can occur when there is significant non-affine particle motion near changes in the contact network. We further show that $\langle G (P)\rangle$ is not simply a sum of two power-laws, but $\langle G \rangle \sim (P/P_c)^a$, where $a \approx (α-2)/(α-1)$ in the $P \rightarrow 0$ limit and $\langle G \rangle \sim (P/P_c)^b$, where $b \gtrsim (α-3/2)/(α-1)$ above a characteristic pressure $P_c$. In addition, the magnitudes of both contributions to $\langle G\rangle$ from geometrical families and changes in the contact network remain comparable in the large-system limit for $P >P_c$.
