Local and global measures of the shear moduli of jammed disk packings
Local and global measures of the shear moduli of jammed disk packings
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卡住盘填料剪切模量的局部和全局测量
DOI：
10.1103/physreve.107.054903
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发表时间：
2023
影响因子：
2.4
通讯作者：
O'Hern, Corey S.
中科院分区：
文献类型：
--
作者：
Zhang, Shiyun;Jin, Weiwei;Wang, Dong;Xu, Ding;Zhang, Jerry;Shattuck, Mark D.;O'Hern, Corey S.
应变控制的各向同性压缩引起的排斥，无摩擦的磁盘堵塞包装的积极或消极的全球剪切模量。我们进行了计算研究，了解的贡献，负剪切模量的机械响应堵塞的磁盘包装。我们首先将整体平均的整体剪切模量分解为，其中是具有负剪切模量的堵塞填料的分数，和分别是具有正模量和负模量的填料的平均值。我们表明，并遵循不同的幂律标度关系以上和以下。对于，和，其中对于排斥的线性弹簧相互作用。尽管如此，由于填料具有负剪切模量的贡献，本文提出了一种新的填料剪切模量的计算方法.我们进一步表明，概率分布的整体剪切模量collapses在固定和不同的值。我们用解析法计算出这是一个极限分布。随着偏度的增大，偏度减小，在极限值内为负偏度的偏态正态分布。我们还分区堵塞磁盘包装成子系统使用Delaunay三角形的磁盘中心计算局部剪切模量。我们发现，从相邻三角形的组定义的局部剪切模量可以是负的，即使当。局部剪切模量的空间相关函数显示出弱相关性，其中，是每个子系统内的粒子数。然而，开始发展长距离的空间相关性与四重角对称。
Strain-controlled isotropic compression gives rise to jammed packings of repulsive, frictionless disks with either positive or negative global shear moduli. We carry out computational studies to understand the contributions of the negative shear moduli to the mechanical response of jammed disk packings. We first decompose the ensemble-averaged, global shear modulus as, whereis the fraction of jammed packings with negative shear moduli andandare the average values from packings with positive and negative moduli, respectively. We show thatandobey different power-law scaling relations above and below. For, bothand, wherefor repulsive linear spring interactions. Despite this,withdue to the contributions from packings with negative shear moduli. We show further that the probability distribution of global shear modulicollapses at fixedand different values ofand. We calculate analytically thatis adistribution in thelimit. Asincreases, the skewness ofdecreases andbecomes a skew-normal distribution with negative skewness in thelimit. We also partition jammed disk packings into subsystems using Delaunay triangulation of the disk centers to calculate local shear moduli. We show that the local shear moduli defined from groups of adjacent triangles can be negative even when. The spatial correlation function of local shear modulidisplays weak correlations for, whereis the number of particles within each subsystem. However,begins to develop long-ranged spatial correlations with fourfold angular symmetry for.