Finite Size Analysis of Zero-Temperature Jamming Transition under Applied Shear Stress by Minimizing a Thermodynamic-Like Potential

Liu, Hao; Xie, Xiaoyi; Xu, Nanping

doi:10.1103/physrevlett.112.145502

Cited by 25 publications

(62 citation statements)

References 38 publications

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“…Thus, the packing fraction at the transition fluctuates from state to state. Several studies have focused on finite-size effects associated with this distribution of packing fractions at the onset of jamming [5,[18][19][20]. In contrast, we concentrate on finite-size scaling in bulk quantities above the transition and bypass the effects of the distribution of jamming onsets by looking at behavior as a function of pressure or, equivalently, φ − φ c , where φ c is the packing fraction at the jamming onset for a given state.…”

Section: Introduction and Conclusionmentioning

confidence: 99%

Jamming in finite systems: Stability, anisotropy, fluctuations, and scaling

et al. 2014

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Athermal packings of soft repulsive spheres exhibit a sharp jamming transition in the thermodynamic limit. Upon further compression, various structural and mechanical properties display clean power-law behavior over many decades in pressure. As with any phase transition, the rounding of such behavior in finite systems close to the transition plays an important role in understanding the nature of the transition itself. The situation for jamming is surprisingly rich: the assumption that jammed packings are isotropic is only strictly true in the large-size limit, and finite-size has a profound effect on the very meaning of jamming. Here, we provide a comprehensive numerical study of finite-size effects in sphere packings above the jamming transition, focusing on stability as well as the scaling of the contact number and the elastic response.

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Section: Introduction and Conclusionmentioning

confidence: 99%

Jamming in finite systems: Stability, anisotropy, fluctuations, and scaling

et al. 2014

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“…The simulation box is taken to have Lees-Edwards periodic boundary conditions. A similar procedure was used to generate packings at constant shear stress [25]. Note that by lowering p, we are able to approach the jamming point (since for our pair potential in Eq.…”

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confidence: 99%

Period proliferation in periodic states in cyclically sheared jammed solids

2017

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Athermal disordered systems can exhibit a remarkable response to an applied oscillatory shear: after a relatively few shearing cycles, the system falls into a configuration that had already been visited in a previous cycle. After this point the system repeats its dynamics periodically despite undergoing many particle rearrangements during each cycle. We study the behavior of orbits as we approach the jamming point in simulations of jammed particles subject to oscillatory shear at fixed pressure and zero temperature. As the pressure is lowered, we find that it becomes more common for the system to find periodic states where it takes multiple cycles before returning to a previously visited state. Thus, there is a proliferation of longer periods as the jamming point is approached.Keywords: cyclic shearing, reversibility, memory, absorbing-state phase transition, jammingOscillatory sheared athermal particle packings or suspensions can fall into periodic "absorbing states" [1] in which the system returns to a configuration previously visited during the shearing process at the same point in the cycle. Once it returns to that configuration, the dynamics repeats itself indefinitely. At low densities in the absorbing state, the particles follow the flow without ever making contact with one another so that the system moves back and forth along a flat direction in the energy landscape [2][3][4], and particles return to their original positions after a single shear cycle: T = 1. As the strain amplitude γ t increases beyond some value γ * t , particles can no longer avoid each other and the system undergoes a dynamical "absorbing state" transition from the absorbing phase to a phase in which the system continually visits new configurations. Models [3,[5][6][7][8] have linked this transition to variants of directed percolation [8][9][10], which represents a broad class of non-equilibrium phase transitions [1].Athermal glasses such as Lennard-Jones glasses, by contrast, have an extensive entropy of energy minima that are not flat [11][12][13]. At very small strain amplitudes, they exhibit elastic behavior in which they explore different configurations within the same energy minimum. As γ t increases so that the system can explore more than one minimum, one might expect the system to meander indefinitely around a hopelessly intricate energy landscape as the system is driven in an oscillatory fashion. Yet, remarkably, these systems can fall into absorbing states-they can find their way back to previously visited energy minima even as they undergo multiple particle rearrangements. Thus these systems explore many such minima [14-17] over and over again. Finally, when γ t is increased to γ * t , the system undergoes an absorbing state transition to a phase in which the system never returns to previously visited minima.In this paper we investigate the fate of absorbing states in packings of jammed spheres that can be tuned to the jamming transition, where the system loses rigidity [18,19]. Far above this transition, absorbing states...

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“…To investigate the shear stress dependence of the states obtained by the QS sampling, we just bin the shear stress using an interval ∆ and average states with the shear stress lying in (σ − ∆/2, σ + ∆/2). In order to obtain jammed states under desired shear stress σ, we start with random states and minimize the thermodynamic-like potential [7] H( r 1 , r 2 , ..…”

Section: Simulation Model and Methodsmentioning

confidence: 99%

“…In Ref. [7], we attribute it to the fact that the QS sampling tends to explore low-energy states, which is a demonstration of the historic dependence of the QS sampling. For finite size systems, the volume fraction of the jamming transition at point J is not well-defined, but broadened to a distribution with a width w due to the finite size effect [2] .…”

Section: Critical Scaling Of the Yield Stressmentioning

confidence: 99%

“…In such an approach, the shear stress is not a well-controlled quantity, while in reality shearing is mostly triggered by the shear force instead of the shear strain. Recently, we reported an efficient method to find local potential energy minima under constant shear stress by minimizing a thermodynamic-like potential [7] . This new method enables us to generate jammed solids under desired shear stress and thus study how their properties vary with the shear stress by unbiasedly sampling the potential energy landscape.…”

Section: Introductionmentioning

confidence: 99%

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Mechanical properties of jammed packings of frictionless spheres under an applied shear stress

Liu¹,

Tong²,

Xu³

2014

Chinese Phys. B

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By minimizing a thermodynamic-like potential, we unbiasedly sample the potential energy landscape of soft and frictionless spheres under constant shear stress. We obtain zero-temperature jammed states under desired shear stresses and investigate their mechanical properties as a function of the shear stress. As a comparison, we also obtain jammed states from the quasistatic-shear sampling in which the shear stress is not well-controlled. Although the yield stresses determined by both samplings show the same power-law scaling with the compression from point J, i.e. the jamming transition point at zero temperature and shear stress, for finite size systems, the quasistatic-shear sampling leads to a lower yield stress and a higher critical volume fraction of point J. The shear modulus of jammed solids decreases when increasing the shear stress. However, the shear modulus does not decay to zero at yielding. This discontinuous change of the shear modulus implies the discontinuous nature of the unjamming transition under nonzero shear stress, which is further verified by the observation of a discontinuous jump of the pressure from jammed solids to shear flows. The pressure jump decreases upon decompression and approaches zero at the critical-like point J, in analogy with well-known phase transitions under external field. The analysis of force networks in jammed solids reveals that the force distribution is more sensitive to the increase of the shear stress near point J. The force network anisotropy increases with the shear stress. Weak particle contacts near the average force and under large shear stresses exhibit asymmetric angle distribution.

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Finite Size Analysis of Zero-Temperature Jamming Transition under Applied Shear Stress by Minimizing a Thermodynamic-Like Potential

Cited by 25 publications

References 38 publications

Jamming in finite systems: Stability, anisotropy, fluctuations, and scaling

Jamming in finite systems: Stability, anisotropy, fluctuations, and scaling

Period proliferation in periodic states in cyclically sheared jammed solids

Mechanical properties of jammed packings of frictionless spheres under an applied shear stress

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