Pressure-dependent shear response of jammed packings of 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 $⟨G-G_0⟩$ scales with $p^{\alpha }$, where $\alpha \approx 1$, but above a characteristic pressure $p^{\ast \ast }$, $⟨G-G_0⟩\sim p^{\beta }$, where $\beta \approx 0.5$. 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 $p>p^{\ast \ast }$, 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 $\alpha$ and $\beta$. We also demonstrate the phenomenon of {\it compression unjamming}, where a jammed packing can unjam via isotropic compression.

arXiv comment6 pages, 4 pages

References in corpus (23)

• Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder
• Jammed Hard-Particle Packings: From Kepler to Bernal and Beyond
• The Jamming Transition in Granular Systems
• Packing of Compressible Granular Materials
• Jamming transition in emulsions and granular materials
• Jamming of frictional spheres and random loose packing
• Hypoconstrained Jammed Packings of Nonspherical Hard Particles: Ellipses and Ellipsoids
• Geometric origin of mechanical properties of granular materials
• Finite-Size Scaling at the Jamming Transition
• Stress Propagation through Frictionless Granular Material
• Critical and non-critical jamming of frictional grains
• Random close packing revisited: How many ways can we pack frictionless disks?
• Memory of jamming - multiscale models for soft and granular matter
• Structural signatures of the unjamming transition at zero temperature
• A stability-reversibility map unifies elasticity, plasticity, yielding and jamming in hard sphere glasses
• Hypostatic jammed packings of frictionless nonspherical particles
• Experimental study of forces between quasi-two-dimensional emulsion droplets near jamming
• Critical jamming of frictional grains in the generalized isostaticity picture
• Universality of jamming of non-spherical particles
• Protocol dependence of the jamming transition
• The role of deformability in determining the structural and mechanical properties of bubbles and emulsions
• Stress anisotropy in shear-jammed packings of frictionless disks
• The response of jammed packings to thermal fluctuations

Cited by in corpus (18)

• Shear-driven solidification and nonlinear elasticity in epithelial tissues
• The structural, vibrational, and mechanical properties of jammed packings of deformable particles in three dimensions
• Bridging particle deformability and collective response in soft solids
• Shear response of granular packings compressed above jamming onset
• Jamming below upper critical dimension
• Contact network changes in ordered and disordered disk packings
• Local and global measures of the shear moduli of jammed disk packings
• Tessellated granular metamaterials with tunable elastic moduli
• Disorder Perturbation Expansion for Athermal Crystals
• Mechanical and Vibrational Properties of Three-Dimensional Dimer Packings Near the Jamming Transition
• Designing the pressure-dependent shear modulus using tessellated granular metamaterials
• Mechanical response of packings of non-spherical particles: A case study of 2D packings of circulo-lines
• Active Jamming at Criticality
• Athermal fluctuations in three dimensional disordered crystals
• Microscopic Reversibility and Emergent Elasticity in Ultrastable Granular Systems
• Control parameter dependence of fluctuation near jamming
• Bulk modulus of soft particle assemblies under compression
• Preserving elastic anisotropy with tessellations of granular packings