Relaxations and rheology near jamming

Abstract

We determine the form of the complex shear modulus $G^{\ast }$ in soft sphere packings near jamming. Viscoelastic response at finite frequency is closely tied to a packing's intrinsic relaxational modes, which are distinct from the vibrational modes of undamped packings. We demonstrate and explain the appearance of an anomalous excess of slowly relaxing modes near jamming, reflected in a diverging relaxational density of states. From the density of states, we derive the dependence of $G^{\ast }$ on frequency and distance to the jamming transition, which is confirmed by numerics.

4 pages, 3 figures

References in corpus (7)

• Approximate analytical description of the nonaffine response of amorphous solids
• Microfluidic rheology of soft colloids above and below jamming
• Elastic wave propagation in confined granular systems
• Relaxing in foam
• Scaling properties of granular rheology near the jamming transition
• Jaming and Geometry of Two-Dimensional Foams
• Growing length and time scales in a suspension of athermal particles

Cited by in corpus (47)

• Modeling semiflexible polymer networks
• A unified framework for non-Brownian suspension flows and soft amorphous solids
• Soft Sphere Packings at Finite Pressure but Unstable to Shear
• Jamming in finite systems: stability, anisotropy, fluctuations and scaling
• Sticky Matter: Jamming and rigid cluster statistics with attractive particle interactions
• The Jamming Perspective on Wet Foams
• Shear dilatancy in marginal solids
• Softening and Yielding of Soft Glassy Materials
• Viscous forces and bulk viscoelasticity near jamming
• Uniform Shock Waves in Disordered Granular Matter
• Atomic-scale origin of dynamic viscoelastic response and creep in disordered solids
• Avalanche contribution to shear modulus of granular materials
• Beyond linear elasticity: Jammed solids at finite shear strain and rate
• Contact Changes near Jamming
• Floppiness, cutting, and freezing: Dynamic critical scaling near isostaticity
• Dynamical behavior of disordered spring networks
• Shear jamming, discontinuous shear thickening, and fragile states in dry granular materials under oscillatory shear
• Universal relaxation dynamics of sphere packings below jamming
• Stress relaxation above and below the jamming transition
• Coarsening and mechanics in the bubble model for wet foams
• Elasticity of Jammed Packings of Sticky Disks
• Disordered Solids Without Well-Defined Transverse Phonons: The Nature of Hard Sphere Glasses
• A computational study of transient shear banding in soft jammed solids
• Nonlocal elasticity near jamming
• On the Apparent Yield Stress in Non-Brownian Magnetorheological Fluids
• Shear shocks in fragile networks
• Discontinuous change of shear modulus for frictional jammed granular materials
• Critical scaling of jammed system after quench of temperature
• Normal stresses, contraction, and stiffening in sheared elastic networks
• Scaling laws for frictional granular materials confined by constant pressure under oscillatory shear
• Contact Changes of Sheared Systems: Scaling, Correlations, and Mechanisms
• Softening and residual loss modulus of jammed grains under oscillatory shear in an absorbing state
• Jamming as a Multicritical Point
• Scaling up the lattice dynamics of amorphous materials by orders of magnitude
• Complete mathematical theory of the jamming transition: A perspective
• Sound damping in frictionless granular materials: The interplay between configurational disorder and inelasticity
• Shear modulus and reversible particle trajectories of frictional granular materials under oscillatory shear
• Correlations of strain and plasticity in flowing foam
• Thermalized connectivity networks of jammed packings
• Effective medium theory for viscoelasticity of soft jammed solids
• Free volume under shear
• An exact expression of three-body system for the complex shear modulus of frictional granular materials
• Attraction-induced jamming in the flow of foam through a channel
• Unified study of viscoelasticity and sound damping in hard and soft amorphous solids
• Jamming transition and normal modes of polydispersed soft particle packing
• Unearthing the anticrystal: criticality in the linear response of disordered solids
• Relaxation dynamics and long-time tails explain shear-induced diffusion of soft athermal particles near jamming