Hypostatic jammed packings of frictionless nonspherical particles.
Hypostatic jammed packings of frictionless nonspherical particles.
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DOI：
10.1103/physreve.97.012909
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发表时间：
2018-01
期刊：
影响因子：
--
通讯作者：
O'Hern CS
中科院分区：
文献类型：
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作者：
VanderWerf K;Jin W;Shattuck MD;O'Hern CS
我们对各种非球形粒子的静态堆积进行了计算研究，包括圆形线，圆形多边形，椭圆，不对称二聚体，哑铃等，以确定哪些形状形成的堆积具有比自由度更少的接触（实体填料），并且具有相同数量的接触和自由度（等静压填料），并理解为什么实体包装的非球形颗粒可以是机械稳定的，尽管有更少的接触比从天真的约束计数预测。为了生成高度精确的力和扭矩平衡的包装circulo线和圆多边形，我们开发了一个粒子间的潜力，使连续的力和扭矩作为粒子坐标的函数。我们表明，包装分数和协调数在干扰发病服从masterlike的形式，我们研究的所有非球形颗粒包装时，绘制与颗粒的非球面性，这是成比例的平方周长的比例的颗粒的面积。此外，不同的颗粒形状的包装的动力学矩阵的本征值谱崩溃时，绘制在相同的非球形颗粒的实体包装，我们验证的“四次”模式的数量沿着的势能增加作为扰动振幅的四次方匹配的数量丢失的接触相对于均衡值。我们表明，在四次模式的方向上的总势能的四阶导数保持非零的填料的压力减少到零。此外，我们计算的不等式约束的圆形线包装中的每个接触的主曲率，并确定特定类型的接触具有凸曲率的不等式约束。这些接触可以限制多个自由度，并允许非球形颗粒的实体包装机械稳定。
We perform computational studies of static packings of a variety of nonspherical particles including circulo-lines, circulo-polygons, ellipses, asymmetric dimers, dumbbells, and others to determine which shapes form packings with fewer contacts than degrees of freedom (hypostatic packings) and which have equal numbers of contacts and degrees of freedom (isostatic packings), and to understand why hypostatic packings of nonspherical particles can be mechanically stable despite having fewer contacts than that predicted from naive constraint counting. To generate highly accurate force- and torque-balanced packings of circulo-lines and cir-polygons, we developed an interparticle potential that gives continuous forces and torques as a function of the particle coordinates. We show that the packing fraction and coordination number at jamming onset obey a masterlike form for all of the nonspherical particle packings we studied when plotted versus the particle asphericity which is proportional to the ratio of the squared perimeter to the area of the particle. Further, the eigenvalue spectra of the dynamical matrix for packings of different particle shapes collapse when plotted at the same For hypostatic packings of nonspherical particles, we verify that the number of “quartic” modes along which the potential energy increases as the fourth power of the perturbation amplitude matches the number of missing contacts relative to the isostatic value. We show that the fourth derivatives of the total potential energy in the directions of the quartic modes remain nonzero as the pressure of the packings is decreased to zero. In addition, we calculate the principal curvatures of the inequality constraints for each contact in circulo-line packings and identify specific types of contacts with inequality constraints that possess convex curvature. These contacts can constrain multiple degrees of freedom and allow hypostatic packings of nonspherical particles to be mechanically stable.