Long-Range Correlations in Elastic Moduli and Local Stresses at the Unjamming Transition
arXiv:2405.19908 · doi:10.1039/d4sm00328d
Abstract
We explore the behavior of spatially heterogeneous elastic moduli as well as the correlations between local moduli in model solids with short-range repulsive potentials. We show through numerical simulations that local elastic moduli exhibit long-range correlations, similar to correlations in the local stresses. Specifically, the correlations in local shear moduli exhibit anisotropic behavior at large lengthscales characterized by pinch-point singularities in Fourier space, displaying a structural pattern akin to shear stress correlations. Focussing on two-dimensional jammed solids approaching the unjamming transition, we show that stress correlations exhibit universal properties, characterized by a quadratic dependence of the correlations as the pressure approaches zero, independent of the details of the model. In contrast, the modulus correlations exhibit a power-law dependence with different exponents depending on the specific interaction potential. Furthermore, we illustrate that while affine responses lack long-range correlations, the total modulus, which encompasses non-affine behavior, exhibits long-range correlations.
References in corpus (51)
- Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder
- Jamming, Force Chains and Fragile Matter
- Random Packings of Frictionless Particles
- Fractal free energy landscapes in structural glasses
- Irreversible reorganization in a supercooled liquid originates from localised soft modes
- Universal nature of particle displacements close to glass and jamming transitions
- Vibrational modes identify soft spots in a sheared disordered packing
- Packing of Compressible Granular Materials
- Vibrations and diverging length scales near the unjamming transition
- Geometric origin of excess low-frequency vibrational modes in amorphous solids
- Unified study of glass and jamming rheology in soft particle systems
- Continuum limit of amorphous elastic bodies (III): Three dimensional systems
- Critical scaling in linear response of frictionless granular packings near jamming
- Inhomogeneous elastic response of silica glass
- Finite-Size Scaling at the Jamming Transition
- Statistics of the contact network in frictional and frictionless granular packings
- Stability at Random Close Packing
- A statistical mechanics framework for static granular matter
- Anomalous properties of the acoustic excitations in glasses on the mesoscopic length-scale
- Entropy and Temperature of a Static Granular Assembly
- Measuring Spatial Distribution of Local Elastic Modulus in Glasses
- Do Athermal Amorphous Solids Exist?
- Relaxing in foam
- Jammed frictionless discs: connecting local and global response
- Heat transport in model jammed solids
- Observation of the onset of strong scattering on high frequency acoustic phonons in densified silica glass
- Emergence of rigidity at the structural glass transition: a first principle computation
- Acoustic excitations and elastic heterogeneities in disordered solids
- Pinch Point Singularities of Tensor Spin Liquids
- Phonon transport and vibrational excitations in amorphous solids
- Elastic heterogeneity, vibrational states, and thermal conductivity across an amorphisation transition
- The Jamming Perspective on Wet Foams
- Emergent Elasticity in Amorphous Solids
- Connecting shear localization with the long-range correlated polarized stress fields in granular materials
- Elastic Moduli and Vibrational Modes in Jammed Particulate Packings
- Spatial Distributions of Local Elastic Moduli Near the Jamming Transition
- Field theory for amorphous solids
- Relation of vibrational excitations and thermal conductivity to elastic heterogeneities in disordered solids
- Local structure controls shear and bulk moduli in disordered solids
- Stress-stress Correlations Reveal Force Chains in Gels
- Tensor Electromagnetism and Emergent Elasticity in Jammed Solids
- Eshelby inclusions in granular matter: theory and simulations
- Tracking the connection between disorder and energy landscape in glasses using geologically hyperaged amber
- Scaling Theory for the Frictionless Unjamming Transition
- Emergence of linear isotropic elasticity in amorphous and polycrystalline materials
- Anomalous Stress Fluctuations in Athermal Two Dimensional Amorphous Solids
- Local and global measures of the shear moduli of jammed disk packings
- Analytical prediction of logarithmic Rayleigh scattering in amorphous solids from tensorial heterogeneous elasticity with power-law disorder
- Note: Simple argument for emergent anisotropic stress correlations in disordered solids
- On elastic constants of zero-temperature amorphous solids
- Vibrational density of states of amorphous solids with long-ranged power-law correlated disorder in elasticity