Zhang Jerry, VanderWerf Kyle, Li Chengling, Zhang Shiyun, Shattuck Mark D, O'Hern Corey S
Department of Mechanical Engineering and Materials Science, Yale University, New Haven, Connecticut 06520, USA.
Department of Physics, Yale University, New Haven, Connecticut 06520, USA.
Phys Rev E. 2021 Jul;104(1-1):014901. doi: 10.1103/PhysRevE.104.014901.
We investigate the mechanical response of jammed packings of circulo-lines in two spatial dimensions, interacting via purely repulsive, linear spring forces, as a function of pressure P during athermal, quasistatic isotropic compression. The surface of a circulo-line is defined as the collection of points that is equidistant to a line; circulo-lines are composed of a rectangular central shaft with two semicircular end caps. Prior work has shown that the ensemble-averaged shear modulus for jammed disk packings scales as a power law, 〈G(P)〉∼P^{β}, with β∼0.5, over a wide range of pressure. For packings of circulo-lines, we also find robust power-law scaling of 〈G(P)〉 over the same range of pressure for aspect ratios R≳1.2. However, the power-law scaling exponent β∼0.8-0.9 is much larger than that for jammed disk packings. To understand the origin of this behavior, we decompose 〈G〉 into separate contributions from geometrical families, G_{f}, and from changes in the interparticle contact network, G_{r}, such that 〈G〉=〈G_{f}〉+〈G_{r}〉. We show that the shear modulus for low-pressure geometrical families for jammed packings of circulo-lines can both increase and decrease with pressure, whereas the shear modulus for low-pressure geometrical families for jammed disk packings only decreases with pressure. For this reason, the geometrical family contribution 〈G_{f}〉 is much larger for jammed packings of circulo-lines than for jammed disk packings at finite pressure, causing the increase in the power-law scaling exponent for 〈G(P)〉.
我们研究了二维空间中圆形线状体紧密堆积的力学响应，这些圆形线状体通过纯排斥性的线性弹簧力相互作用，作为无热、准静态各向同性压缩过程中压力(P)的函数。圆形线状体的表面定义为与一条直线等距的点的集合；圆形线状体由一个带有两个半圆形端盖的矩形中心轴组成。先前的研究表明，在很宽的压力范围内，紧密堆积的圆盘的系综平均剪切模量按幂律缩放，即(\langle G(P)\rangle\sim P^{\beta})，其中(\beta\sim0.5)。对于圆形线状体的堆积，在相同的压力范围内，对于纵横比(R\gtrsim1.2)，我们也发现了(\langle G(P)\rangle)的稳健幂律缩放。然而，幂律缩放指数(\beta\sim0.8 - 0.9)比紧密堆积的圆盘的指数大得多。为了理解这种行为的起源，我们将(\langle G\rangle)分解为来自几何族的单独贡献(G_f)和来自粒子间接触网络变化的贡献(G_r)，使得(\langle G\rangle=\langle G_f\rangle+\langle G_r\rangle)。我们表明，对于圆形线状体紧密堆积的低压几何族，其剪切模量会随着压力的增加而增加或减小，而对于紧密堆积的圆盘的低压几何族，其剪切模量仅随压力减小。因此，在有限压力下，对于圆形线状体紧密堆积，几何族贡献(\langle G_f\rangle)比紧密堆积的圆盘大得多，导致(\langle G(P)\rangle)的幂律缩放指数增加。
