Mechanical excitation and marginal triggering during avalanches in sheared amorphous solids.

We study plastic strain during individual avalanches in overdamped particle-scale molecular dynamics (MD) and mesoscale elastoplastic models (EPM) for amorphous solids sheared in the athermal quasistatic limit. We show that the spatial correlations in plastic activity exhibit a short length scale that grows as t^{3/4} in MD and ballistically in EPM, which is generated by mechanical excitation of nearby sites not necessarily close to their stability thresholds, and a longer lengthscale that grows diffusively for both models and is associated with remote marginally stable sites. These similarities in spatial correlations explain why simple EPMs accurately capture the size distribution of avalanches observed in MD, though the temporal profiles and dynamical critical exponents are quite different.

Mapping out the glassy landscape of a mesoscopic elastoplastic model.

We develop a mesoscopic model to study the plastic behavior of an amorphous material under cyclic loading. The model is depinning-like and driven by a disordered thresholds dynamics that is coupled by long-range elastic interactions. We propose a simple protocol of "glass preparation" that allows us to mimic thermalization at high temperatures as well as aging at vanishing temperature. Various levels of glass stabilities (from brittle to ductile) can be achieved by tuning the aging duration. The aged glasses are then immersed into a quenched disorder landscape and serve as initial configurations for various protocols of mechanical loading by shearing. The dependence of the plastic behavior upon monotonous loading is recovered. The behavior under cyclic loading is studied for different ages and system sizes. The size and age dependence of the irreversibility transition is discussed. A thorough characterization of the disorder-landscape is achieved through the analysis of the transition graphs, which describe the plastic deformation pathways under athermal quasi-static shear. In particular, the analysis of the stability ranges of the strongly connected components of the transition graphs reveals the emergence of a phase-separation like process associated with the aging of the glass. Increasing the age and, hence, the stability of the initial glass results in a gradual break-up of the landscape of dynamically accessible stable states into three distinct regions: one region centered around the initially prepared glass phase and two additional regions characterized by well-separated ranges of positive and negative plastic strains, each of which is accessible only from the initial glass phase by passing through the stress peak in the forward and backward, respectively, shearing directions.

Inferring elastic properties of an fcc crystal from displacement correlations: subspace projection and statistical artifacts.

We compute the effective dispersion and vibrational density of states (DOS) of two-dimensional subregions of three-dimensional face-centered-cubic crystals using both a direct projection-inversion technique and a Monte Carlo simulation based on a common underlying Hamiltonian. We study both a (111) and (100) plane. We show that for any given direction of wave vector, both (111) and (100) show an anomalous ω(2)∼q regime at low q where ω(2) is the energy associated with the given mode and q is its wave number. The ω(2)∼q scaling should be expected to give rise to an anomalous DOS, D(ω), at low ω: D(ω)∼ω(3) rather than the conventional Debye result: D(ω)∼ω(2). The DOS for (100) looks to be consistent with D(ω)∼ω(3), while (111) shows something closer to the conventional Debye result at the smallest frequencies. In addition to the direct projection-inversion calculation, we perform Monte Carlo simulations to study the effects of finite sampling statistics. We show that finite sampling artifacts act as an effective disorder and bias D(ω), giving a behavior closer to D(ω)∼ω(2) than D(ω)∼ω(3). These results should have an important impact on the interpretation of recent studies of colloidal solids where the two-point displacement correlations can be obtained directly in real-space via microscopy.

Density invariant vibrational modes in disordered colloidal crystals.

We experimentally measure the density of states (DOS) and dynamical structure factor (DSF) arising from the thermal fluctuations in a colloidal crystal composed of thermally sensitive micron-sized hydrogel particles at several different particle volume fractions, ϕ's. Particle positions are tracked over long times using optical microscopy and particle tracking algorithms in a single two-dimensional (2D) [111] plane of a 3D face-centered-cubic single crystal. The dynamical fluctuations are spatially heterogeneous while the lattice itself is highly ordered. At all ϕ's, the DOS exhibits an excess of low frequency modes, a so-called boson peak (BP), and the DSF exhibits a cross-over from propagating to nonpropagating behavior, a so-called Ioffe-Regel crossover, at a frequency somewhat below the BP for both longitudinal and transverse modes. As we tune ϕ from 0.64 to 0.56, the Lindemann parameter grows from ~3% to ~8%; however, the shape of the DOS and DSF remain largely unchanged when rescaled by the Debye level. This invariance indicates that the effective degree of disorder remains essentially constant even in the vicinity of melting.

Local anisotropy in globally isotropic granular packings.

We report on two-dimensional computer simulations of frictionless granular packings at various area fractions φ above the jamming point φ(c). We measure the anisotropy in coarse-grained stress ε(s) and shear modulus ε(m) as functions of coarse-graining scale, R. ε(s) can be collapsed onto a master curve after rescaling R by a characteristic length scale ξ and ε(s) by an anisotropy magnitude A. Both A and ξ accelerate as φ→φ(c) from above, consistent with a divergence at φ(c). ε(m) shows no characteristic length scale and has a nontrivial power-law form, ε(m)~R(-0.62), over almost the entire range of R at all φ. These results suggest that the force chains present in the spatial structure of the quenched stress may be governed by different physics than the anomalous elastic response near jamming.

Normal modes and density of states of disordered colloidal solids.

The normal modes and the density of states (DOS) of any material provide a basis for understanding its thermal and mechanical transport properties. In perfect crystals, normal modes are plane waves, but they can be complex in disordered systems. We have experimentally measured normal modes and the DOS in a disordered colloidal crystal. The DOS shows Debye-like behavior at low energies and an excess of modes, or Boson peak, at higher energies. The normal modes take the form of plane waves hybridized with localized short wavelength features in the Debye regime but lose both longitudinal and transverse plane-wave character at a common energy near the Boson peak.

Anisotropic power law strain correlations in sheared amorphous 2D solids.

The local deformation of steadily sheared two-dimensional Lennard-Jones glasses is studied via computer simulations at zero temperature. In the quasistatic limit, spatial correlations in the incremental strain field are highly anisotropic. The data show power law behavior with a strong angular dependence of the scaling exponent, and the strongest correlations along the directions of maximal shear stress. These results support the notion that the jamming transition at the onset of flow is critical, but suggest unusual critical behavior. The predicted behavior is testable through experiments on sheared amorphous materials such as bubble rafts, foams, emulsions, granular packings, and other systems where particle displacements can be tracked.

Correlations in the elastic response of dense random packings.

Results are presented for the autocorrelation function of the vortexlike nonaffine piece of the linear elastic displacement field in dense random bidisperse packings of harmonically repulsive disks in 2D. The autocorrelation function is shown to scale precisely with the length of the simulation cell in systems ranging from 20 to 100 particles across. It is shown that, to first order, the displacement fields can be thought to arise from the action of uncorrelated local random forcing of a homogeneous elastic sheet, and a theory is presented which gives excellent quantitative agreement with the form of the correlation functions. These results suggest measurements to be made in many types of densely packed, random materials where the elastic displacement fields are accessible experimentally such as granular materials, dense emulsions, colloidal suspensions, etc.