Effect of inertia on sheared disordered solids: Critical scaling of avalanches in two and three dimensions

Salerno, K. Michael; Robbins, Mark O.

doi:10.1103/physreve.88.062206

Cited by 111 publications

(207 citation statements)

References 77 publications

(160 reference statements)

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“…ΔΣ is limited by the next plastic event and thus is inversely proportional to the rate at which avalanches are triggered. Although one might think that if the system were twice as large a plastic event would occur twice as soon (implying ΔΣ ∼ 1/L d ), this is not the case, and ΔΣ depends on system size with a nontrivial exponent (9,10,35,36). As argued in refs.…”

Section: Scaling Relationsmentioning

confidence: 99%

“…The phenomenological description proposed above may apply to real materials with inertial or overdamped dynamics, as well as to elasto-plastic models, although the yielding transition in these situations may not lie in the same universality class (36,43). In what follows, we test our predictions in elasto-plastic models, implemented as in ref.…”

Section: Elasto-plastic Modelmentioning

confidence: 99%

“…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.…”

mentioning

confidence: 99%

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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.

256

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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Section: Scaling Relationsmentioning

confidence: 99%

Section: Elasto-plastic Modelmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 2 more Smart Citations

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.

256

370

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“…The effect of inertia on steadily sheared disordered solids in the athermal quasistatic limit was examined in two and three dimensions using molecular dynamics simulations [6].…”

Section: Introductionmentioning

confidence: 99%

The effect of a reversible shear transformation on plastic deformation of an amorphous solid

Priezjev¹

2015

J. Phys.: Condens. Matter

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Molecular dynamics simulations are performed to investigate the plastic response of a model glass to a local shear transformation in a quiescent system. The deformation of the material is induced by a spherical inclusion that is gradually strained into an ellipsoid of the same volume and then reverted back into the sphere. We show that the number of cage-breaking events increases with increasing strain amplitude of the shear transformation. The results of numerical simulations indicate that the density of cage jumps is larger in the cases of weak damping or slow shear transformation. Remarkably, we also found that, for a given strain amplitude, the peak value of the density profiles is a function of the ratio of the damping coefficient and the time scale of the shear transformation.

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Viscoelastic Interfaces Driven in Disordered Media

Landes

2016

Springer Theses

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Effect of inertia on sheared disordered solids: Critical scaling of avalanches in two and three dimensions

Cited by 111 publications

References 77 publications

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

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

The effect of a reversible shear transformation on plastic deformation of an amorphous solid

Viscoelastic Interfaces Driven in Disordered Media

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