Theory of rigidity and numerical analysis of density of states of two-dimensional amorphous solids with dispersed frictional grains in the linear response regime
arXiv:2207.06632 · doi:10.1103/PhysRevE.107.054902
Abstract
Using the Jacobian matrix, we obtain theoretical expression of rigidity and the density of states of two-dimensional amorphous solids consisting of frictional grains in the linear response to an infinitesimal strain, in which we ignore the dynamical friction caused by the slip processes of contact points. The theoretical rigidity agrees with that obtained by molecular dynamics simulations. We confirm that the rigidity is smoothly connected to the value in the frictionless limit. For the density of states, we find that there are two modes in the density of states for sufficiently small , which is the ratio of the tangential to normal stiffness. Rotational modes exist at low frequencies or small eigenvalues, whereas translational modes exist at high frequencies or large eigenvalues. The location of the rotational band shifts to the high-frequency region with an increase in and becomes indistinguishable from the translational band for large . The rigidity determined by the translational modes agrees with that obtained by the molecular dynamics simulations, whereas the contribution of the rotational modes is almost zero for small .
arXiv comment28 pages, 16 figures
References in corpus (53)
- Jamming at Zero Temperature and Zero Applied Stress: the Epitome of Disorder
- A model for collisions in granular gases
- Amorphous Systems in Athermal, Quasistatic Shear
- The Jamming Transition in Granular Systems
- Vibrational modes identify soft spots in a sheared disordered packing
- Geometric origin of excess low-frequency vibrational modes in amorphous solids
- Jamming transition in emulsions and granular materials
- On the Rigidity of Amorphous Solids
- Approximate analytical description of the nonaffine response of amorphous solids
- A random critical point separates brittle and ductile yielding transitions in amorphous materials
- Force distributions near the jamming and glass transitions
- Continuum limit of the vibrational properties of amorphous solids
- Universal Breakdown of Elasticity at the Onset of Material Failure
- Statistics and properties of low-frequency vibrational modes in structural glasses
- Critical scaling in linear response of frictionless granular packings near jamming
- The yielding transition in amorphous solids under oscillatory shear deformation
- Low-frequency vibrational modes of stable glasses
- Critical and non-critical jamming of frictional grains
- Critical scaling near jamming transition for frictional granular particles
- Jamming in Systems Composed of Frictionless Ellipse-Shaped Particles
- Macroscopic yielding in jammed solids is accompanied by a non-equilibrium first-order transition in particle trajectories
- A microscopic view of the yielding transition in concentrated emulsions
- The distribution of forces affects vibrational properties in hard sphere glasses
- Global Equation of State of two-dimensional hard sphere systems
- Jamming phase diagram for frictional particles
- Isostaticity at Frictional Jamming
- Critical Scaling of Shearing Rheology at the Jamming Transition of Soft Core Frictionless Disks
- Excitations of Ellipsoid Packings near Jamming
- Universality of jamming of non-spherical particles
- Critical jamming of frictional grains in the generalized isostaticity picture
- Nonlinear plastic modes in disordered solids
- Constraints and vibrations in static packings of ellipsoidal particles
- Softening and Yielding of Soft Glassy Materials
- Brittle yielding of amorphous solids at finite shear rates
- Critical scaling near the yielding transition in granular media
- Universality of the Plastic Instability in Strained Amorphous Solids
- Elastic Moduli and Vibrational Modes in Jammed Particulate Packings
- Elementary plastic events in amorphous silica
- Rotational and Translational Phonon Modes in Glasses Composed of Ellipsoidal Particles
- Oscillatory Instabilities in Frictional Granular Matter
- Sponge-like rigid structures in frictional granular packings
- Bridging particle deformability and collective response in soft solids
- Discontinuous change of shear modulus for frictional jammed granular materials
- Rotational sound in disordered granular materials
- Jamming with tunable roughness
- Origin of reversible and irreversible atomic-scale rearrangements in a model two-dimensional network glass
- Scaling laws for frictional granular materials confined by constant pressure under oscillatory shear
- Softening and residual loss modulus of jammed grains under oscillatory shear in an absorbing state
- Giant Amplification of Small Perturbations in Frictional Amorphous Solid
- Noise Amplification in Frictional Systems: Oscillatory Instabilities
- Vibrational properties of two-dimensional dimer packings near the jamming transition
- Eigenvalue analysis of stress-strain curve of two-dimensional amorphous solids of dispersed frictional grains with finite shear strain
- Testing mean-field theory for jamming of non-spherical particles: Contact number, gap distribution, and vibrational density of states