Subextensive Scaling in the Athermal, Quasistatic Limit of Amorphous Matter in Plastic Shear Flow

We present the results of numerical simulations of an atomistic system undergoing plastic shear flow in the athermal, quasistatic limit. The system is shown to undergo cascades of local rearrangements, associated with quadrupolar energy fluctuations, which induce system-spanning events organized into lines of slip oriented along the Bravais axes of the simulation cell. A finite size scaling analysis reveals subextensive scaling of the energy drops and participation numbers, linear in the length of the simulation cell, in good agreement with the observed real-space structure of the plastic events.Comment: 4 pages, 6 figure

Avalanches, thresholds, and diffusion in meso-scale amorphous plasticity

We present results on a meso-scale model for amorphous matter in athermal, quasi-static (a-AQS), steady state shear flow. In particular, we perform a careful analysis of the scaling with the lateral system size, $L$, of: i) statistics of individual relaxation events in terms of stress relaxation, $S$, and individual event mean-squared displacement, $M$, and the subsequent load increments, $\Delta \gamma$, required to initiate the next event; ii) static properties of the system encoded by $x=\sigma_y-\sigma$, the distance of local stress values from threshold; and iii) long-time correlations and the emergence of diffusive behavior. For the event statistics, we find that the distribution of $S$ is similar to, but distinct from, the distribution of $M$. We find a strong correlation between $S$ and $M$ for any particular event, with $S\sim M^{q}$ with $q\approx 0.65$. $q$ completely determines the scaling exponents for $P(M)$ given those for $P(S)$. For the distribution of local thresholds, we find $P(x)$ is analytic at $x=0$, and has a value $\left. P(x)\right|_{x=0}=p_0$ which scales with lateral system length as $p_0\sim L^{-0.6}$. Extreme value statistics arguments lead to a scaling relation between the exponents governing $P(x)$ and those governing $P(S)$. Finally, we study the long-time correlations via single-particle tracer statistics. The value of the diffusion coefficient is completely determined by $\langle \Delta \gamma \rangle$ and the scaling properties of $P(M)$ (in particular from $\langle M \rangle$) rather than directly from $P(S)$ as one might have naively guessed. Our results: i) further define the a-AQS universality class, ii) clarify the relation between avalanches of stress relaxation and diffusive behavior, iii) clarify the relation between local threshold distributions and event statistics

Emergent lengthscales in the quenched stresses and elastic response of soft particle packings near jamming

We study stress correlations and elastic response in large-scale computer simulations of two-dimensional particle packings near jamming. We show that there are characteristic lengths in both the stresses and elastic response that diverge in similar ways as the confining pressure approaches zero from above. For the case of the stress field, we show that the power spectrum of the hydrostatic pressure and shear stress agrees with a field-theoretic framework proposed by Henkes and Chakraborty at short to intermediate wavelengths (where the power is flat in Fourier space), but contains significant excess power at wavelengths larger than ~ 50‑100 particle diameters, with the specific crossover point going to larger wavelength at decreasing pressure, consistent with a divergence at p = 0. For the case of the elastic response, we probe the system in three ways: (i) point forcing; (ii) “constrained” homogeneous deformation where the system is driven with no-slip boundary conditions; and (iii) “free periodic” homogeneous deformation. For the point force, we see distinct characteristic lengths for longitudinal and transverse modes each of which diverges in a different way with decreasing pressure with ξT ~ P –0.25 and ξL ~ P –0.4 respectively. For the constrained homogeneous deformation we see a scaling of the local shear modulus with the size of the probing region consistent with ξ ~ P –0.5 similar to the ξL ~ P –0.4 observed in the longitudinal component of the point-response and in perfect agreement with the rigidity length discussed in recently proposed scenarios for jamming. Finally, we show that the transverse and longitudinal contributions to the strain field in response to unconstrained deformation (either volumetric or shear) have markedly different behavior. The transverse contribution is surprisingly invariant with respect to p with localized shear transformations dominating the response down to surprisingly small pressures. The longitudinal contribution develops a feature at small wavelength that intensifies with decreasing p but does not show any appreciable change in length. We interpret this pressure-invariant length as the characteristic shear zone size

Evolution of displacements and strains in sheared amorphous solids

The local deformation of two-dimensional Lennard-Jones glasses under imposed shear strain is studied via computer simulations. Both the mean squared displacement and mean squared strain rise linearly with the length of the strain interval $\Delta \gamma$ over which they are measured. However, the increase in displacement does not represent single-particle diffusion. There are long-range spatial correlations in displacement associated with slip lines with an amplitude of order the particle size. Strong dependence on system size is also observed. The probability distributions of displacement and strain are very different. For small $\Delta \gamma$ the distribution of displacement has a plateau followed by an exponential tail. The distribution becomes Gaussian as $\Delta \gamma$ increases to about .03. The strain distributions consist of sharp central peaks associated with elastic regions, and long exponential tails associated with plastic regions. The latter persist to the largest $\Delta \gamma$ studied.Comment: Submitted to J. Phys. Cond. Mat. special volume for PITP Conference on Mechanical Behavior of Glassy Materials. 16 Pages, 8 figure

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 which are coupled by long-range elastic interactions. We propose a simple protocol of "glass preparation" which allows us to mimic thermalisation at high temperature, 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 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, respectively, backward shearing directions.Comment: 20 pages, 12 figures, including supplemental materia