Floppiness, cutting, and freezing: Dynamic critical scaling near isostaticity
arXiv:1203.3411 · doi:10.1103/PhysRevLett.109.168303
Abstract
The isostatic state plays a central role in organizing the response of many amorphous materials. We demonstrate the existence of a dynamic critical length scale in nearly isostatic spring networks that is valid both above and below isostaticity and at finite frequencies, and use scaling arguments to relate the length scale to viscoelastic response. We predict theoretically and verify numerically how proximity to isostaticity controls the viscosity, shear modulus, and creep of random networks.
arXiv comment5 pages, 3 figures
References in corpus (21)
- Jamming of Soft Particles: Geometry, Mechanics, Scaling and Isostaticity
- Critical Scaling of Shear Viscosity at the Jamming Transition
- Vibrations and diverging length scales near the unjamming transition
- Geometric origin of excess low-frequency vibrational modes in amorphous solids
- Criticality and isostaticity in fiber networks
- A coordination-based approach to elasticity of floppy and stiff random networks
- Critical scaling in linear response of frictionless granular packings near jamming
- Stress Propagation through Frictionless Granular Material
- A unified framework for non-Brownian suspension flows and soft amorphous solids
- Nonaffine Correlations in Random Elastic Media
- Cross-link governed dynamics of biopolymer networks
- Model for the Scaling of Stresses and Fluctuations in Flows near Jamming
- Scaling of phononic transport with connectivity in amorphous solids
- Non-affine response: jammed packings versus spring networks
- Relaxations and rheology near jamming
- Stiff Polymers, Foams and Fiber Networks
- Shear flow of non-Brownian suspensions close to jamming
- Nonlinear effective medium theory of disordered spring networks
- Growing length and time scales in a suspension of athermal particles
- Exact mean field inference in asymmetric kinetic Ising systems
- Nonlinear elastic stress response in granular packings
Cited by in corpus (22)
- Modeling semiflexible polymer networks
- A minimal-length approach unifies rigidity in under-constrained materials
- Shear dilatancy in marginal solids
- Viscous forces and bulk viscoelasticity near jamming
- Stability of jammed packings I: the rigidity length scale
- Scaling theory for mechanical critical behavior in fiber networks
- Atomic-scale origin of dynamic viscoelastic response and creep in disordered solids
- Beyond linear elasticity: Jammed solids at finite shear strain and rate
- Dynamical behavior of disordered spring networks
- Stress relaxation above and below the jamming transition
- Coarsening and mechanics in the bubble model for wet foams
- Non-affine deformation of semiflexible polymer and fiber networks
- Jamming graphs: A local approach to global mechanical rigidity
- Normal stresses, contraction, and stiffening in sheared elastic networks
- Finite temperature mechanical instability in disordered lattices
- Rheology near jamming - the influence of lubrication forces
- Local and global measures of the shear moduli of jammed disk packings
- Strain-controlled critical slowing down in the rheology of disordered networks
- Disordered Contact Networks in Jammed Packings of Frictionless Disks
- Correlations of strain and plasticity in flowing foam
- Unearthing the anticrystal: criticality in the linear response of disordered solids
- Viscoelastic scaling regimes for marginally-rigid fractal spring networks