Avalanches in Strained Amorphous Solids: Does Inertia Destroy Critical Behavior?

Salerno, K. Michael; Maloney, Craig; Robbins, Mark O.

doi:10.1103/physrevlett.109.105703

Cited by 149 publications

(206 citation statements)

References 38 publications

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“…21 where the critical scaling of avalanches in quasistatic shear of disordered systems is discussed . They showed that Γ c = 0.1 (τ = 10) is a critical damping rate separating the overdamped (larger Γ) and underdamped (smaller Γ) regimes which are characterized by different scaling behavior.…”

Section: Discussionmentioning

confidence: 99%

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Time-dependent elastic response to a local shear transformation in amorphous solids

Puosi

Rottler

2014

Phys. Rev. E

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The elastic response of a two-dimensional amorphous solid to induced local shear transformations, which mimic the elementary plastic events occurring in deformed glasses, is investigated via Molecular Dynamics simulations. We show that for different spatial realizations of the transformation, despite relative fluctuations of order one, the long time equilibrium response averages out to the prediction of the Eshelby inclusion problem for a continuum elastic medium. We characterize the effects of the underlying dynamics on the propagation of the elastic signal. A crossover from a propagative transmission in the case of weakly-damped dynamics to a diffusive transmission for strong damping is evidenced. In the latter case, the full time dependent elastic response is in agreement with the theoretical prediction, obtained by solving the diffusion equation for the displacement field in an elastic medium.

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Section: Discussionmentioning

confidence: 99%

“…In order to investigate how inertia affects the response, different conditions of the underlying dynamics, from overdamped to underdamped, are considered. This is motivated by recent work by Salerno et al [21] where the role of inertia on the critical behavior of avalanches in strained amorphous solids is discussed.…”

Section: Introductionmentioning

confidence: 99%

Time-dependent elastic response to a local shear transformation in amorphous solids

Puosi

Rottler

2014

Phys. Rev. E

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“…The comparison between these two phenomena has led to the proposition that the yielding transition is in the universality class of mean-field depinning (33, 34). However, experiments find a reological exponent β > 1 against the β ≤ 1 predicted for elastic depinning, and numerical simulations display intriguing finite size effects that differ from depinning (9,10,(35)(36)(37).Formally, elasto-plastic models are very similar to automaton models known to capture the depinning transition well (17); the key difference lies in the interaction kernel G, long-ranged and of variable sign for elasto-plastic models while essentially a Laplacian for depinning with short-range elasticity. We recently showed (20) that in the presence of long-ranged interaction with variable sign, the distribution of shear transformations at a distance x from instability, P(x), is singular with P(x) ∼ x θ , unlike in depinning for which θ = 0.…”

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confidence: 99%

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Scaling description of the yielding transition in soft amorphous solids at zero temperature

Lin

Lerner

Rosso

et al. 2014

Proc. Natl. Acad. Sci. U.S.A.

252

370

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Yield stress materials flow if a sufficiently large shear stress is applied. Although such materials are ubiquitous and relevant for industry, there is no accepted microscopic description of how they yield, even in the simplest situations in which temperature is negligible and in which flow inhomogeneities such as shear bands or fractures are absent. Here we propose a scaling description of the yielding transition in amorphous solids made of soft particles at zero temperature. Our description makes a connection between the Herschel-Bulkley exponent characterizing the singularity of the flow curve near the yield stress Σ c , the extension and duration of the avalanches of plasticity observed at threshold, and the density P(x) of soft spots, or shear transformation zones, as a function of the stress increment x beyond which they yield. We argue that the critical exponents of the yielding transition may be expressed in terms of three independent exponents, θ, d f , and z, characterizing, respectively, the density of soft spots, the fractal dimension of the avalanches, and their duration. Our description shares some similarity with the depinning transition that occurs when an elastic manifold is driven through a random potential, but also presents some striking differences. We test our arguments in an elastoplastic model, an automaton model similar to those used in depinning, but with a different interaction kernel, and find satisfying agreement with our predictions in both two and three dimensions. M any solids will flow and behave as fluids if a sufficiently large shear stress is applied. In crystals, plasticity is governed by the motion of dislocations (1, 2). In amorphous solids, there is no order, and conserved defects cannot be defined. However, as noticed by Argon (3), plasticity consists of elementary events localized in space, called shear transformations, in which a few particles rearrange. This observation supports that there are special locations in the sample, called shear transformation zones (STZs) (4), in which the system lies close to an elastic instability. Several theoretical approaches of plasticity, such as STZ theory (4) or soft glassy rheology (5), assume that such zones relax independently or are coupled to each other via an effective temperature. However, at zero temperature and small applied strain rate _ γ, computer experiments (6-11) and very recent experiments (12, 13) indicate that local rearrangements are not independent: plasticity occurs via avalanches in which many shear transformations are involved, forming elongated structures in which plasticity localizes. If conditions are such that flow is homogeneous (as may occur, for example, in foams or emulsions), one finds that the flow curves are singular at small strain rate and follow a Herschel-Bulkley law Σ − Σ c ∼ _ γ 1=β (14, 15). These features are reproduced qualitatively by elasto-plastic models (16)(17)(18)(19)(20) in which space is discretized. In these models, a site that yields plastically affects the stress in its surroundi...

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“…[15,20] showed that disordered solids undergoing underdamped dynamics enter a nontrivial universality class, where τ appears to show a crossover from ∼ 1.3 to ∼ 1.6 when it is estimated through the stress drops. This exponent crossover together with the qualitative features (hump) of the universal scaling function and the steady-state average stress consistent decrease, all resemble the behavior of our model.…”

Section: Consistency With Microscopic Molecular Dynamics Simulationsmentioning

confidence: 99%

Shearing a glass and the role of pinning delay in models of interface depinning

Papanikolaou

2016

Phys. Rev. E

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When a disordered solid is sheared, yielding is followed by the onset of intermittent response that is characterized by slip in local regions usually labeled shear-transformation zones (STZ). Such intermittent response resembles the behavior of earthquakes or contact depinning, where a welldefined landscape of pinning disorder prohibits the deformation of an elastic medium. Nevertheless, a disordered solid is evidently different in that pinning barriers of particles are due to neighbors that are also subject to motion. Microscopic yielding leads to destruction of the local microstructure and local heating. It is natural to assume that locally a liquid emerges for a finite timescale before cooling down to a transformed configuration. For including this characteristic transient in glass depinning models, we propose a general mechanism that involves a "pin-delay" time T pd , during which each region that slipped evolves as a fluid. The new timescale can be as small as a single avalanche timestep. We demonstrate that the inclusion of this mechanism causes a drift of the critical exponents towards higher values for the slip sizes τ , until a transition to permanent shear-banding behavior happens causing almost oscillatory, stick-slip response. Moreover, it leads to a proliferation of large events that are highly inhomogeneous and resemble sharp slip band formation. Our model appears to be qualitatively consistent with recent experiments and simulations of disordered solids under shear.Extreme phenomena in nature appear in a wide range of scales, from the abrupt nano-deformation of materials to earthquake faults that extend several miles. At all scales, avoiding such phenomena requires a deep understanding of the disparate timescales leading to separate as well as collections of events. Material plastic deformation displays characteristic intermittency in a wide range of systems: single crystals [1], bulk metallic glasses (BMG) [2-4], disordered granular solids [5,6], colloids [7], frictional contacts [8,9]. While numerical simulations of materials can be very detailed at short timescales, the detailed study of a collection of abrupt events remains still out of reach. The theoretical intuition for such systems comes from the thorough study of interface depinning: a d-dimensional elastic string travelling on a landscape of quenched disorder in d+1 dimensions under the help of a uniform external force [10]. In complex disordered solids, though, while the assumption of an elastic medium appears reasonable, the one related to quenched disorder should be placed under scrutiny: the pinning disorder for every particle originates in the actual interface that attempts to depin (other nearby particles); a disordered solid pins itself during deformation. A basic consequence is that local glass depinning is not immediately followed by re-pinning; instead, in short-time transients (compared to typical avalanche durations), the system behaves locally as a fluid of finite viscosity η; In the context of depinning models we call this ...

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Avalanches in Strained Amorphous Solids: Does Inertia Destroy Critical Behavior?

Cited by 149 publications

References 38 publications

Time-dependent elastic response to a local shear transformation in amorphous solids

Time-dependent elastic response to a local shear transformation in amorphous solids

Scaling description of the yielding transition in soft amorphous solids at zero temperature

Shearing a glass and the role of pinning delay in models of interface depinning

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