Local and global measures of the shear moduli of jammed disk packings.
Phys Rev E
; 107(5-1): 054903, 2023 May.
Article
em En
| MEDLINE
| ID: mdl-37329065
ABSTRACT
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 ãGã=(1-F_{-})ãG_{+}ã+F_{-}ãG_{-}ã, where F_{-} is the fraction of jammed packings with negative shear moduli and ãG_{+}ã and ãG_{-}ã are the average values from packings with positive and negative moduli, respectively. We show that ãG_{+}ã and ã|G_{-}|ã obey different power-law scaling relations above and below pN^{2}â¼1. For pN^{2}>1, both ãG_{+}ãN and ã|G_{-}|ãNâ¼(pN^{2})^{ß}, where ßâ¼0.5 for repulsive linear spring interactions. Despite this, ãGãNâ¼(pN^{2})^{ß^{'}} with ß^{'}â³0.5 due to the contributions from packings with negative shear moduli. We show further that the probability distribution of global shear moduli P(G) collapses at fixed pN^{2} and different values of p and N. We calculate analytically that P(G) is a Γ distribution in the pN^{2}âª1 limit. As pN^{2} increases, the skewness of P(G) decreases and P(G) becomes a skew-normal distribution with negative skewness in the pN^{2}â«1 limit. 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 G>0. The spatial correlation function of local shear moduli C(r[over â]) displays weak correlations for pn_{sub}^{2}<10^{-2}, where n_{sub} is the number of particles within each subsystem. However, C(r[over â]) begins to develop long-ranged spatial correlations with fourfold angular symmetry for pn_{sub}^{2}â³10^{-2}.
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Coleções:
01-internacional
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MEDLINE
Idioma:
En
Revista:
Phys Rev E
Ano de publicação:
2023
Tipo de documento:
Article