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Reversibility and criticality in amorphous solids.

Regev I, Weber J, Reichhardt C, Dahmen KA, Lookman T - Nat Commun (2015)

Bottom Line: We compare this non-equilibrium critical behaviour to the prevailing concept of a 'front depinning' transition that has been used to describe steady-state avalanche behaviour in different materials.We explain why a depinning-like process can result in a transition from periodic to chaotic behaviour and why chaotic motion is not possible in pinned systems.These findings suggest that, at least for highly jammed amorphous systems, the irreversibility transition may be a side effect of depinning that occurs in systems where the disorder is not quenched.

View Article: PubMed Central - PubMed

Affiliation: School of Engineering and Applied Sciences, Harvard University, 29 Oxford Street, Cambridge, Massachusetts 02138, USA.

ABSTRACT
The physical processes governing the onset of yield, where a material changes its shape permanently under external deformation, are not yet understood for amorphous solids that are intrinsically disordered. Here, using molecular dynamics simulations and mean-field theory, we show that at a critical strain amplitude the sizes of clusters of atoms undergoing cooperative rearrangements of displacements (avalanches) diverges. We compare this non-equilibrium critical behaviour to the prevailing concept of a 'front depinning' transition that has been used to describe steady-state avalanche behaviour in different materials. We explain why a depinning-like process can result in a transition from periodic to chaotic behaviour and why chaotic motion is not possible in pinned systems. These findings suggest that, at least for highly jammed amorphous systems, the irreversibility transition may be a side effect of depinning that occurs in systems where the disorder is not quenched.

No MeSH data available.


Related in: MedlinePlus

Reversible (repetitive) Avalanches.An avalanche in a subcritical limit cycle for a system with N=16,384 particles and maximal strain amplitude Γ=0.1. Even though the avalanche spans a large part of the system, it is repeated under repeating strain cycles of identical strain amplitude. The arrows mark the displacement during the avalanche and the colours represent the magnitude of the displacement (warm—large displacement and cold—small displacement).
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f2: Reversible (repetitive) Avalanches.An avalanche in a subcritical limit cycle for a system with N=16,384 particles and maximal strain amplitude Γ=0.1. Even though the avalanche spans a large part of the system, it is repeated under repeating strain cycles of identical strain amplitude. The arrows mark the displacement during the avalanche and the colours represent the magnitude of the displacement (warm—large displacement and cold—small displacement).

Mentions: The transition from jammed to flowing behaviour in systems as diverse as earthquakes, charge density waves and disordered magnets is accompanied by the occurrence of avalanches of increasing sizes obeying power-law statistics, a signature of critical behaviour. In this work, we show using molecular dynamics simulations that in amorphous solids, at the same critical strain amplitude where irreversibility occurs, the system undergoes a non-equilibrium phase transition, which involves avalanches of diverging sizes. We analyse the avalanche statistics using a mean-field model for the depinning transition in plastic deformation that was used previously to describe plasticity in crystals and amorphous solids3031. We show that large avalanches exist even below the transition, as was also observed in ref. 32, so that the existence of avalanches alone is not sufficient to explain the irreversible behaviour (see Fig. 2 for an example of the displacement field generated by an avalanche that is repeated periodically under repeated cycles of subcritical strain). However, we show that the cause of irreversible behaviour for strain amplitudes that are larger than a critical value is rooted in the changes of the energy landscape topology at depinning, which suggests why depinning and irreversibility occur at the same point.


Reversibility and criticality in amorphous solids.

Regev I, Weber J, Reichhardt C, Dahmen KA, Lookman T - Nat Commun (2015)

Reversible (repetitive) Avalanches.An avalanche in a subcritical limit cycle for a system with N=16,384 particles and maximal strain amplitude Γ=0.1. Even though the avalanche spans a large part of the system, it is repeated under repeating strain cycles of identical strain amplitude. The arrows mark the displacement during the avalanche and the colours represent the magnitude of the displacement (warm—large displacement and cold—small displacement).
© Copyright Policy - open-access
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4660054&req=5

f2: Reversible (repetitive) Avalanches.An avalanche in a subcritical limit cycle for a system with N=16,384 particles and maximal strain amplitude Γ=0.1. Even though the avalanche spans a large part of the system, it is repeated under repeating strain cycles of identical strain amplitude. The arrows mark the displacement during the avalanche and the colours represent the magnitude of the displacement (warm—large displacement and cold—small displacement).
Mentions: The transition from jammed to flowing behaviour in systems as diverse as earthquakes, charge density waves and disordered magnets is accompanied by the occurrence of avalanches of increasing sizes obeying power-law statistics, a signature of critical behaviour. In this work, we show using molecular dynamics simulations that in amorphous solids, at the same critical strain amplitude where irreversibility occurs, the system undergoes a non-equilibrium phase transition, which involves avalanches of diverging sizes. We analyse the avalanche statistics using a mean-field model for the depinning transition in plastic deformation that was used previously to describe plasticity in crystals and amorphous solids3031. We show that large avalanches exist even below the transition, as was also observed in ref. 32, so that the existence of avalanches alone is not sufficient to explain the irreversible behaviour (see Fig. 2 for an example of the displacement field generated by an avalanche that is repeated periodically under repeated cycles of subcritical strain). However, we show that the cause of irreversible behaviour for strain amplitudes that are larger than a critical value is rooted in the changes of the energy landscape topology at depinning, which suggests why depinning and irreversibility occur at the same point.

Bottom Line: We compare this non-equilibrium critical behaviour to the prevailing concept of a 'front depinning' transition that has been used to describe steady-state avalanche behaviour in different materials.We explain why a depinning-like process can result in a transition from periodic to chaotic behaviour and why chaotic motion is not possible in pinned systems.These findings suggest that, at least for highly jammed amorphous systems, the irreversibility transition may be a side effect of depinning that occurs in systems where the disorder is not quenched.

View Article: PubMed Central - PubMed

Affiliation: School of Engineering and Applied Sciences, Harvard University, 29 Oxford Street, Cambridge, Massachusetts 02138, USA.

ABSTRACT
The physical processes governing the onset of yield, where a material changes its shape permanently under external deformation, are not yet understood for amorphous solids that are intrinsically disordered. Here, using molecular dynamics simulations and mean-field theory, we show that at a critical strain amplitude the sizes of clusters of atoms undergoing cooperative rearrangements of displacements (avalanches) diverges. We compare this non-equilibrium critical behaviour to the prevailing concept of a 'front depinning' transition that has been used to describe steady-state avalanche behaviour in different materials. We explain why a depinning-like process can result in a transition from periodic to chaotic behaviour and why chaotic motion is not possible in pinned systems. These findings suggest that, at least for highly jammed amorphous systems, the irreversibility transition may be a side effect of depinning that occurs in systems where the disorder is not quenched.

No MeSH data available.


Related in: MedlinePlus