Complete mathematical theory of the jamming transition: A perspective
arXiv:2410.21439 · doi:10.1063/5.0245684
Abstract
The jamming transition of frictionless athermal particles is a paradigm to understand the mechanics of amorphous materials at the atomic scale. Concepts related to the jamming transition and the mechanical response of jammed packings have cross-fertilized into other areas such as atomistic descriptions of the elasticity and plasticity of glasses. In this perspective article, the microscopic mathematical theory of the jamming transition is reviewed from first-principles. The starting point of the derivation is a microscopically-reversible particle-bath Hamiltonian from which the governing equation of motion for the grains under an external deformation is derived. From this equation of motion, microscopic expressions are obtained for both the shear modulus and the viscosity as a function of the distance from the jamming transition (respectively, above and below the transition). Regarding the vanishing of the shear modulus at the unjamming transition, this theory, as originally demonstrated in [Zaccone & Scossa-Romano, Phys. Rev. B 83, 184205 (2011)], is currently the only quantitative microscopic theory in parameter-free agreement with numerical simulations of [O'Hern et al. Phys. Rev. E 68, 011306 (2003)] for jammed packings. The divergence of the viscosity upon approaching the jamming transition from below is derived here, for the first time, from the same microscopic Hamiltonian. The quantitative microscopic prediction of the diverging viscosity is shown to be in fair agreement with numerical results of sheared 2D soft disks from [Olsson & Teitel, Phys. Rev. Lett. 99, 178001 (2007)].
Invited Perspective. Accepted for publication
References in corpus (99)
- Dynamics of Viscoplastic Deformation in Amorphous Solids
- Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder
- Is Random Close Packing of Spheres Well Defined?
- Jamming, Force Chains and Fragile Matter
- A density-independent glass transition in biological tissues
- Jammed Hard-Particle Packings: From Kepler to Bernal and Beyond
- Motility-driven glass and jamming transitions in biological tissues
- Mean field theory of hard sphere glasses and jamming
- Jamming of Soft Particles: Geometry, Mechanics, Scaling and Isostaticity
- Random Packings of Frictionless Particles
- Critical Scaling of Shear Viscosity at the Jamming Transition
- Effects of compression on the vibrational modes of marginally jammed solids
- Glass and Jamming Transitions: From Exact Results to Finite-Dimensional Descriptions
- Approximate analytical description of the nonaffine response of amorphous solids
- Influence of Particle Size Distribution on Random Close Packing
- Force chains and contact network topology in packings of elongated particles
- Why is Random Close Packing Reproducible?
- Universal Spectrum of Normal Modes in Low-Temperature Glasses: an Exact Solution
- Network Analysis of Particles and Grains
- Onset of Irreversibility and Chaos in Amorphous Solids Under Periodic Shear
- Flow of wet granular materials
- A unified framework for non-Brownian suspension flows and soft amorphous solids
- Mechanical and microscopic properties of the reversible plastic regime in a 2D jammed material
- Floppy modes and non-affine deformations in random fiber networks
- Critical scaling near jamming transition for frictional granular particles
- Theory of activated-rate processes under shear with application to shear-induced aggregation of colloids
- Basic Understanding of Condensed Phases of Matter via Packing Models
- Iterative Reconstruction of Memory Kernels
- Interatomic repulsion softness directly controls the fragility of supercooled metallic melts
- Non-affine response: jammed packings versus spring networks
- Disorder-assisted melting and the glass transition in amorphous solids
- Multiscaling at Point J: Jamming is a Critical Phenomenon
- Scaling properties of granular rheology near the jamming transition
- A first-order phase transition at the random close packing of hard spheres
- Relaxations and rheology near jamming
- Randomly Crosslinked Macromolecular Systems: Vulcanisation Transition to and Properties of the Amorphous Solid State
- Creep motion of an intruder within a granular glass close to jamming
- Microscopic theory of the jamming transition of harmonic spheres
- Nonequilibrium continuous phase transition in colloidal gelation with short-range attraction
- Plasticity in amorphous solids is mediated by topological defects in the displacement field
- The jamming transition and new percolation universality classes in particulate systems with attraction
- Active glasses
- Emergence of rigidity at the structural glass transition: a first principle computation
- Explicit Analytical Solution for Random Close Packing in d=2 and d=3
- Perspective: Inverse methods for material design
- Shear modulus of simulated glass-forming model systems: Effects of boundary condition, temperature and sampling time
- Replica theory of the rigidity of structural glasses
- Rigid cluster decomposition reveals criticality in frictional jamming
- Generalized Langevin equation and fluctuation-dissipation theorem for particle-bath systems in external oscillating fields
- Compression stiffening of fibrous networks with stiff inclusions
- Shear-driven solidification of dilute colloidal suspensions
- Turning intractable counting into sampling: computing the configurational entropy of three-dimensional jammed packings
- Topology of vibrational modes predict plastic events in glasses
- Cavity and replica methods for the spectral density of sparse symmetric random matrices
- Jamming in two-dimensional packings
- Deformations, relaxation and broken symmetries in liquids, solids and glasses: a unified topological field theory
- Atomic-scale origin of dynamic viscoelastic response and creep in disordered solids
- Theory of harmonic dissipation in disordered solids
- Jamming of semiflexible polymers
- Spatial Distributions of Local Elastic Moduli Near the Jamming Transition
- Estimating random close packing in polydisperse and bidisperse hard spheres via an equilibrium model of crowding
- Relaxation and vibrational properties in metal alloys and other disordered systems
- Mean-field model for the density of states of jammed soft spheres
- Low-frequency vibrations of jammed packings in large spatial dimensions
- Atomic theory of viscoelastic response and memory effects in metallic glasses
- A review on shear jamming
- Local structure controls shear and bulk moduli in disordered solids
- Perspective on Reversible to Irreversible Transitions in Periodic Driven Many Body Systems and Future Directions For Classical and Quantum Systems
- Jamming in Systems With Quenched Disorder
- Theory of elastic constants of athermal amorphous solids with internal stresses
- Vibrational density of states and specific heat in glasses from random matrix theory
- Stress relaxation above and below the jamming transition
- Frictional rigidity percolation and minimal rigidity proliferation: From a new universality class to superuniversality
- Pinning Susceptibility: The effect of dilute, quenched disorder on jamming
- General theory of the viscosity of liquids and solids from nonaffine particle motions
- Hyperuniformity of Maximally Random Jammed Packings of Hyperspheres Across Spatial Dimensions
- Identifying non-affine softening modes in glassy polymer networks: A pathway to chemical design
- A unifying model for random matrix theory in arbitrary space dimensions
- Vibrational spectroscopy via the Caldeira-Leggett model with anharmonic system potentials
- Experimental and Numerical Verification of Anomalous Screening Theory in Granular Matter
- Generalized Langevin equation with shear flow and its fluctuation-dissipation theorems derived from a Caldeira-Leggett Hamiltonian
- Elasticity-Controlled Jamming Criticality in Soft Composite Solids
- Nonaffine lattice dynamics with the Ewald method reveals strongly nonaffine elasticity of α-quartz
- Clustering of negative topological charge precedes plastic failure in 3D glasses
- Micromechanical description of the compaction of soft pentagon assemblies
- A geometric probabilistic approach to random packing of hard disks in a plane
- Equivalence of fluctuation-dissipation and Edwards' temperature in cyclically sheared granular systems
- Softening and residual loss modulus of jammed grains under oscillatory shear in an absorbing state
- Jamming and replica symmetry breaking of weakly disordered crystals
- Hyperballistic transport in dense systems of charged particles under ac electric fields
- Eigenvalue analysis of stress-strain curve of two-dimensional amorphous solids of dispersed frictional grains with finite shear strain
- Timescale bridging in atomistic simulations of epoxy polymer mechanics using non-affine deformation theory
- Shear hardening in frictionless amorphous solids near the jamming transition
- Vibrational density of states of jammed packing: mean-field theory
- Understanding spin glass transition as a dynamic phenomenon
- Soft modes in jammed hard spheres (I): Mean field theory of the isostatic transition
- Theory of heavy-quarks contribution to the quark-gluon plasma viscosity
- Proof of a conjecture on the infinite dimension limit of a unifying model for random matrix theory
- Theory of rigidity and numerical analysis of density of states of two-dimensional amorphous solids with dispersed frictional grains in the linear response regime