Limits...
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

Mean energy drops.The mean energy drop  as a function of the maximal strain amplitude Γ for the largest system size. Note the distinct cusp at the irreversibility point.
© Copyright Policy - open-access
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC4660054&req=5

f4: Mean energy drops.The mean energy drop as a function of the maximal strain amplitude Γ for the largest system size. Note the distinct cusp at the irreversibility point.

Mentions: To understand the role of avalanches in the transition-to-chaos/yield, we studied the avalanche statistics for different maximal strain amplitudes and system sizes. Since the simulations were athermal, we identified drops in the potential energy (Fig. 3c) with plastic rearrangement events. For each simulation, we extracted all of the energy drops in the last shear cycle (to avoid transient effects), created a histogram of the energy drops and calculated the average energy drop for each maximal strain amplitude. We observe in Fig. 4 a cusp at the point at which the irreversibility transition occurs, followed by saturation to a value that depends on the system size, at large strain amplitudes. The cusp suggests that the irreversibility transition is related to a change in the avalanche dynamics, and the system size dependence of the saturation suggests that there is a saturating correlation length. To understand the avalanche statistics in this system, we invoke a simple model31 that belongs to the same universality class as the theory of front depinning (but with long-range interactions), which was originally developed to explain the motion of an interface in random media. This motion involves parts of an interface overcoming local energy barriers due to pinning sites and neighbouring locations in the interface ‘pulling' the site back. The forward motion of the interface occurs in avalanches. In the case of long-range interactions, such as the ones that exist in elasto-plastic systems, the notion of a ‘front' becomes more abstract since sites that are far apart affect each other and the notion of locality becomes blurred (see Fig. 5 for illustration). This explains why the same equations can also describe avalanche behaviour associated with the plasticity of amorphous solids in which the dynamics involves overcoming random energy barriers and long-range interactions, even if an actual front may not exist. The equations of motion describing the time evolution of the plastic displacement field u(r,t) controlled by overdamped dynamics are31:


Reversibility and criticality in amorphous solids.

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

Mean energy drops.The mean energy drop  as a function of the maximal strain amplitude Γ for the largest system size. Note the distinct cusp at the irreversibility point.
© Copyright Policy - open-access
Related In: Results  -  Collection

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

f4: Mean energy drops.The mean energy drop as a function of the maximal strain amplitude Γ for the largest system size. Note the distinct cusp at the irreversibility point.
Mentions: To understand the role of avalanches in the transition-to-chaos/yield, we studied the avalanche statistics for different maximal strain amplitudes and system sizes. Since the simulations were athermal, we identified drops in the potential energy (Fig. 3c) with plastic rearrangement events. For each simulation, we extracted all of the energy drops in the last shear cycle (to avoid transient effects), created a histogram of the energy drops and calculated the average energy drop for each maximal strain amplitude. We observe in Fig. 4 a cusp at the point at which the irreversibility transition occurs, followed by saturation to a value that depends on the system size, at large strain amplitudes. The cusp suggests that the irreversibility transition is related to a change in the avalanche dynamics, and the system size dependence of the saturation suggests that there is a saturating correlation length. To understand the avalanche statistics in this system, we invoke a simple model31 that belongs to the same universality class as the theory of front depinning (but with long-range interactions), which was originally developed to explain the motion of an interface in random media. This motion involves parts of an interface overcoming local energy barriers due to pinning sites and neighbouring locations in the interface ‘pulling' the site back. The forward motion of the interface occurs in avalanches. In the case of long-range interactions, such as the ones that exist in elasto-plastic systems, the notion of a ‘front' becomes more abstract since sites that are far apart affect each other and the notion of locality becomes blurred (see Fig. 5 for illustration). This explains why the same equations can also describe avalanche behaviour associated with the plasticity of amorphous solids in which the dynamics involves overcoming random energy barriers and long-range interactions, even if an actual front may not exist. The equations of motion describing the time evolution of the plastic displacement field u(r,t) controlled by overdamped dynamics are31:

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