Pressure Dependent Shear Response of Jammed Packings of Frictionless Spherical Particles

Abstract

The mechanical response of packings of purely repulsive, spherical particles to athermal, quasistatic simple shear near jamming onset is highly nonlinear. Previous studies have shown that, at small pressure p, the ensemble-averaged static shear modulus G − G0 scales with p α , where α ≈ 1, but above a characteristic pressure p * * , G − G0 ∼ p β , where β ≈ 0.5. However, we find that the shear modulus G i for an individual packing typically decreases linearly with p along a geometrical family where the contact network does not change. We resolve this discrepancy by showing that, while the shear modulus does decrease linearly within geometrical families, G also depends on a contribution from discontinuous jumps in G that occur at the transitions between geometrical families. For p > p * * , geometrical-family and rearrangement contributions to G are of opposite signs and remain comparable for all system sizes. G can be described by a scaling function that smoothly transitions between the two power-law exponents α and β. We also demonstrate the phenomenon of compression unjamming, where a jammed packing can unjam via isotropic compression.arXiv:1908.09435v1 [cond-mat.soft]

Mechanical response of packings of non-spherical particles: A case study of 2D packings of circulo-lines

“…Several previous experimental studies of compressed emulsions [18,19] and packings of thin granular cylinders [20] have also found power-law scaling of the contact number and shear modulus with pressure during isotropic compression. In previous computational studies of packings of frictionless, spherical particles [21], we showed that there are two important contributions to the ensemble-averaged shear modulus: G f from geometrical families and G r from changes in the interparticle contact network during compression. For isotropic compression, jammed packings within a geometrical family are mechanically stable packings with different pressures that are related to each other by continuous, quasistatic changes in packing fraction with no changes in the interparticle contact network.…”

“…Numerous prior studies have shown that the ensembleaveraged shear modulus G for packings of frictionless, spherical particles increases as a power-law in pressure when P > P * * [12,17], where P * * ∼ N −2 decreases with increasing system size. For finite-sized systems, we have used the following scaling form for the ensemble-averaged shear modulus [21]:…”

“…To explain the increase in the power-law scaling exponent for packings of circulo-lines, we decompose the ensemble-averaged shear modulus G into contributions from geometrical families, G f , and from discontinuous jumps caused by changes in the interparticle contact network, G r : G = G f + G r [21,24]. In Fig.…”

“…For frictionless, spherical particles, the shear modulus along a geometrical family decreases with increasing pressure during isotropic compression (and no shearing of the boundaries). For systems with purely repulsive linear spring interactions, G f decreases roughly linearly with pressure, G f (P )/G 0 ∼ 1 − P/P 0 , where G 0 is the shear modulus at P = 0 and P 0 is the pressure at which G f (P ) = 0, although there are deviations from this simple form as the system approaches contact network changes [21,24]. Thus, the increase in the ensembleaveraged shear modulus, G , with pressure for packings of spherical particles arises from G r , where changes in the contact network cause discontinuous upward jumps in the shear modulus.…”

Bulk modulus of soft particle assemblies under compression

“…By means of smoothed interaction laws between bodies, simulations may reproduce some elasticity due to a virtual contact deflection, although the bodies themselves do not undergo strains. Using this approach, the elastic properties of particle assemblies have been studied, however restricting considerations of the small-strain domain of deformations [1][2][3][4]. More recently, the development of more advanced methods coupling discrete and finite elements [5][6][7][8][9][10] or meshless methods [11,12] have permitted to explore the compression behavior of soft granular media beyond jamming.…”