Inertia and universality of avalanche statistics: The case of slowly deformed amorphous solids

Karimi, Kamran; Ferrero, Ezequiel E.; Barrat, Jean‐Louis

doi:10.1103/physreve.95.013003

Cited by 46 publications

(68 citation statements)

References 44 publications

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“…The role of inertia has been studied recently in amorphous materials [63][64][65][66][67], where it leads to a large pseudo-gap exponent θ comparable to ours [63] (and much larger than the one present in the absence of inertia in these materials). It has been proposed that depending on the amount of damping, different universality classes could exist [64,65], but that for strongly underdamped systems the transition appears to become first order [63]. If confirmed, we speculate that the cause of the difference between amorphous solids and frictional interfaces is that avalanches are compact objects (having a fractal dimension d f > 1) only in the latter case.…”

Section: Discussionmentioning

confidence: 99%

How collective asperity detachments nucleate slip at frictional interfaces

Geus

Popović

et al. 2019

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

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Sliding at a quasi-statically loaded frictional interface can occur via macroscopic slip events, which nucleate locally before propagating as rupture fronts very similar to fracture. We introduce a novel microscopic model of a frictional interface that includes asperity-level disorder, elastic interaction between local slip events, and inertia. For a perfectly flat and homogeneously loaded interface, we find that slip is nucleated by avalanches of asperity detachments of extension larger than a critical radius Ac governed by a Griffith criterion. We find that after slip, the density of asperities at a local distance to yielding xσ presents a pseudo-gap P (xσ) ∼ (xσ) θ , where θ is a non-universal exponent that depends on the statistics of the disorder. This result makes a link between friction and the plasticity of amorphous materials where a pseudo-gap is also present. For friction, we find that a consequence is that stick-slip is an extremely slowly decaying finite size effect, while the slip nucleation radius Ac diverges as a θ-dependent power law of the system size. We discuss how these predictions can be tested experimentally. Significance statementUnderstanding how slip at a frictional interface initiates is important for a range of problems including earthquake prediction and precision engineering. The force needed to start sliding a solid object over a flat surface is classically described by a 'static friction coefficient': a constant established by measurements. It was recently questioned if such constant exists, as it was shown to be poorly reproducible. We provide a model supporting that it is stochastic even for very large system sizes: sliding is nucleated when, by chance, an avalanche of microscopic detachments reaches a critical radius, beyond which slip becomes unstable and propagates along the interface. It leads to testable predictions on key observables characterising the stability of the interface.

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Section: Discussionmentioning

confidence: 99%

How collective asperity detachments nucleate slip at frictional interfaces

Geus

Popović

et al. 2019

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

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“…This gives access to the transient elastic reponse, involving the propagation of shear waves. Exploiting this opportunity, Karimi et al (2017) analyzed the effect of inertia on the avalanche statistics and compared it with results from atomistic simulations. (Note that the effect of a delay in signal propagation had already been contemplated in an effective way by Lin et al (2014a), while, for the same purpose, Papanikolaou (2016) introduced a pinning delay in his EPM based on the depinning framework.)…”

Section: Approaches Resorting To Finite-element Methodsmentioning

confidence: 99%

Deformation and flow of amorphous solids: Insights from elastoplastic models

et al. 2018

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CONTENTSFrequently used notations 3 FIG. 1 Overview of amorphous solids. From left to right, top row : cellular phone case made of metallic glass (1); toothpaste (2); mayonnaise (3); coffee foam (4); soya beans (5). Second row : a transmission electron microscopy (TEM) image of a fractured bulk metallic glass (Cu50Zr45Ti5) by X. Tong et. al (Shanghai University, China); TEM image of blend (PLLA/PS) nanoparticles obtained by miniemulsion polymerization, from L. Becker Peres et al. (UFSC, Brazil); emulsion of water droplets in silicon oil observed with an optical microscope by N. Bremond (ESPCI Paris); a soap foam filmed in the lab by M. van Hecke (Leiden University, Netherlands); thin nylon cylinders of different diameters pictured with a camera, from T. Miller et al. (University of Sydney, Australia). The white scale bars are approximate. Just below, a chart of different amorphous materials, classified by the size and the damping regime of their elementary particles. At the bottom: some popular modeling approaches, arranged according to the length scales of the materials for which they were originally developed. STZ stands for the shear transformation zone theory of Langer (2008), and SGR for the soft glassy rheology theory of Sollich et al. (1997).

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“…We have checked that the scaling behavior does not change in a range between c = 0.03 and 3. We define the avalanche size S in terms of the stress drop through S = N |∆σ| (72). We measure the distribution P(S) for a given interval of γ to see the effect of yielding on the avalanche behavior (61,73).…”

Section: Determination Of the Stress Dropsmentioning

confidence: 99%

Random critical point separates brittle and ductile yielding transitions in amorphous materials

Ozawa

Berthier

Biroli

et al. 2018

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

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We combine an analytically solvable mean-field elasto-plastic model with molecular dynamics simulations of a generic glass former to demonstrate that, depending on their preparation protocol, amorphous materials can yield in two qualitatively distinct ways. We show that well-annealed systems yield in a discontinuous brittle way, as metallic and molecular glasses do. Yielding corresponds in this case to a first-order nonequilibrium phase transition. As the degree of annealing decreases, the first-order character becomes weaker and the transition terminates in a second-order critical point in the universality class of an Ising model in a random field. For even more poorly annealed systems, yielding becomes a smooth crossover, representative of the ductile rheological behavior generically observed in foams, emulsions, and colloidal glasses. Our results show that the variety of yielding behaviors found in amorphous materials does not necessarily result from the diversity of particle interactions or microscopic dynamics but is instead unified by carefully considering the role of the initial stability of the system.

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Inertia and universality of avalanche statistics: The case of slowly deformed amorphous solids

Cited by 46 publications

References 44 publications

How collective asperity detachments nucleate slip at frictional interfaces

How collective asperity detachments nucleate slip at frictional interfaces

Deformation and flow of amorphous solids: Insights from elastoplastic models

Random critical point separates brittle and ductile yielding transitions in amorphous materials

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