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Korchinski DJ, Rottler J. Thermally activated intermittent flow in amorphous solids. SOFT MATTER 2024; 20:7891-7913. [PMID: 39318269 DOI: 10.1039/d4sm00619d] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 09/26/2024]
Abstract
Using mean field theory and a mesoscale elastoplastic model, we analyze the steady state shear rheology of thermally activated amorphous solids. At sufficiently high temperature and driving rates, flow is continuous and described by well-established rheological flow laws such as Herschel-Bulkley and logarithmic rate dependence. However, we find that these flow laws change in the regime of intermittent flow, where collective events no longer overlap and serrated flow becomes pronounced. In this regime, we identify a thermal activation stress scale, xa(T,), that wholly captures the effect of driving rate and temperature T on average flow stress, stress drop (avalanche) size and correlation lengths. Different rheological regimes are summarized in a dynamic phase diagram for the amorphous yielding transition. Theoretical predictions call for a need to re-examine the rheology of very slowly sheared amorphous matter much below the glass transition.
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Affiliation(s)
- Daniel James Korchinski
- Department of Physics and Astronomy and Quantum Matter Institute, University of British Columbia, 2355 East Mall, Vancouver, BC V6T 1Z1, Canada.
| | - Jörg Rottler
- Department of Physics and Astronomy and Quantum Matter Institute, University of British Columbia, 2355 East Mall, Vancouver, BC V6T 1Z1, Canada.
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Richard D, Elgailani A, Vandembroucq D, Manning ML, Maloney CE. Mechanical excitation and marginal triggering during avalanches in sheared amorphous solids. Phys Rev E 2023; 107:034902. [PMID: 37072969 DOI: 10.1103/physreve.107.034902] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/04/2022] [Accepted: 02/26/2023] [Indexed: 04/20/2023]
Abstract
We study plastic strain during individual avalanches in overdamped particle-scale molecular dynamics (MD) and mesoscale elastoplastic models (EPM) for amorphous solids sheared in the athermal quasistatic limit. We show that the spatial correlations in plastic activity exhibit a short length scale that grows as t^{3/4} in MD and ballistically in EPM, which is generated by mechanical excitation of nearby sites not necessarily close to their stability thresholds, and a longer lengthscale that grows diffusively for both models and is associated with remote marginally stable sites. These similarities in spatial correlations explain why simple EPMs accurately capture the size distribution of avalanches observed in MD, though the temporal profiles and dynamical critical exponents are quite different.
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Affiliation(s)
- D Richard
- Institute for Theoretical Physics, University of Amsterdam, Science Park 904, Amsterdam, Netherlands
- Department of Physics and BioInspired Institute, Syracuse University, Syracuse, New York 13244, USA
- Univiversité Grenoble Alpes, CNRS, LIPhy, 38000 Grenoble, France
| | - A Elgailani
- Northeastern University, Boston, Massachusetts 02115, USA
| | - D Vandembroucq
- PMMH, CNRS UMR 7636, ESPCI Paris, PSL University, Sorbonne Université, Université de Paris, F-75005 Paris, France
| | - M L Manning
- Department of Physics and BioInspired Institute, Syracuse University, Syracuse, New York 13244, USA
| | - C E Maloney
- Northeastern University, Boston, Massachusetts 02115, USA
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Khirallah K, Tyukodi B, Vandembroucq D, Maloney CE. Yielding in an Integer Automaton Model for Amorphous Solids under Cyclic Shear. PHYSICAL REVIEW LETTERS 2021; 126:218005. [PMID: 34114864 DOI: 10.1103/physrevlett.126.218005] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 08/11/2020] [Accepted: 04/06/2021] [Indexed: 06/12/2023]
Abstract
We present results on an automaton model of an amorphous solid under cyclic shear. After a transient, the steady state falls into one of three cases in order of increasing strain amplitude: (i) pure elastic behavior with no plastic activity, (ii) limit cycles where the state recurs after an integer period of strain cycles, and (iii) irreversible plasticity with longtime diffusion. The number of cycles N required for the system to reach a periodic orbit diverges as the amplitude approaches the yielding transition between regimes (ii) and (iii) from below, while the effective diffusivity D of the plastic strain field vanishes on approach from above. Both of these divergences can be described by a power law. We further show that the average period T of the limit cycles increases on approach to yielding.
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Affiliation(s)
| | - Botond Tyukodi
- Northeastern University, Boston, Massachusetts 02115, USA
- Department of Physics, Brandeis University, Waltham, Massachusetts 02454, USA
| | - Damien Vandembroucq
- PMMH, CNRS, ESPCI Paris, Université PSL, Sorbonne Université, Université de Paris, F-75005 Paris, France
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Clemmer JT, Salerno KM, Robbins MO. Criticality in sheared, disordered solids. I. Rate effects in stress and diffusion. Phys Rev E 2021; 103:042605. [PMID: 34005889 DOI: 10.1103/physreve.103.042605] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/30/2020] [Accepted: 03/16/2021] [Indexed: 11/07/2022]
Abstract
Rate effects in sheared disordered solids are studied using molecular dynamics simulations of binary Lennard-Jones glasses in two and three dimensions. In the quasistatic (QS) regime, systems exhibit critical behavior: the magnitudes of avalanches are power-law distributed with a maximum cutoff that diverges with increasing system size L. With increasing rate, systems move away from the critical yielding point and the average flow stress rises as a power of the strain rate with exponent 1/β, the Herschel-Bulkley exponent. Finite-size scaling collapses of the stress are used to measure β as well as the exponent ν which characterizes the divergence of the correlation length. The stress and kinetic energy per particle experience fluctuations with strain that scale as L^{-d/2}. As the largest avalanche in a system scales as L^{α}, this implies α<d/2. The diffusion rate of particles diverges as a power of decreasing rate before saturating in the QS regime. A scaling theory for the diffusion is derived using the QS avalanche rate distribution and generalized to the finite strain rate regime. This theory is used to collapse curves for different system sizes and confirm β/ν.
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Affiliation(s)
- Joel T Clemmer
- Sandia National Laboratories, Albuquerque, New Mexico 87123, USA
| | | | - Mark O Robbins
- Department of Physics and Astronomy, Johns Hopkins University, Baltimore, Maryland 21218, USA
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Investigation of the Time-Dependent Transitions Between the Time-Fractional and Standard Diffusion in a Hierarchical Porous Material. Transp Porous Media 2020. [DOI: 10.1007/s11242-020-01435-8] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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Karimi K. Self-diffusion in plastic flow of amorphous solids. Phys Rev E 2019; 100:063003. [PMID: 31962436 DOI: 10.1103/physreve.100.063003] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/15/2019] [Indexed: 06/10/2023]
Abstract
We report on a particle-based numerical study of sheared amorphous solids in the dense slow flow regime. In this framework, deformation and flow are accompanied by critical fluctuation patterns associated with the macroscopic plastic response. The former is commonly attributed to the collective slip patterns that relax internal stresses within the bulk material and give rise to an effective mechanical noise governing the latter particle-level process. In this paper, the avalanche-type dynamics between plastic events is shown to have a strong relevance on the self-diffusion of tracer particles in the Fickian regime. As a consequence, strong size effects emerge in the effective diffusion coefficient that is rationalized in terms of avalanche size distributions and the relevant temporal occurrence.
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Affiliation(s)
- Kamran Karimi
- Department of Physics and Astronomy, University of Calgary, 2500 University Drive NW, Calgary, Alberta, Canada T2N 1N4
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Tyukodi B, Vandembroucq D, Maloney CE. Avalanches, thresholds, and diffusion in mesoscale amorphous plasticity. Phys Rev E 2019; 100:043003. [PMID: 31770912 DOI: 10.1103/physreve.100.043003] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/29/2019] [Indexed: 06/10/2023]
Abstract
We present results on a mesoscale model for amorphous matter in athermal, quasistatic (a-AQS), steady-state shear flow. In particular, we perform a careful analysis of the scaling with the lateral system size L of (i) statistics of individual relaxation events in terms of stress relaxation S, and individual event mean-squared displacement M, and the subsequent load increments Δγ, required to initiate the next event; (ii) static properties of the system encoded by x=σ_{y}-σ, the distance of local stress values from threshold; and (iii) long-time correlations and the emergence of diffusive behavior. For the event statistics, we find that the distribution of S is similar to, but distinct from, the distribution of M. We find a strong correlation between S and M for any particular event, with S∼M^{q} with q≈0.65. The exponent q completely determines the scaling exponents for P(M) given those for P(S). For the distribution of local thresholds, we find P(x) is analytic at x=0, and has a value P(x)|_{x=0}=p_{0} which scales with lateral system length as p_{0}∝L^{-0.6}. The size dependence of the average load increment 〈Δγ〉 appears to be asymptotically controlled by the plateau behavior of P(x) rather than by a subsequent apparent power-law behavior. Extreme value statistics arguments lead thus to a scaling relation between the exponents governing P(x) and those governing P(S). Finally, we study the long-time correlations via single-particle tracer statistics. The value of the diffusion coefficient is completely determined by 〈Δγ〉 and the scaling properties of P(M) (in particular from 〈M〉) rather than directly from P(S) as one might have naively guessed. Our results (i) further define the a-AQS universality class, (ii) clarify the relation between avalanches of stress relaxation and diffusive behavior, and (iii) clarify the relation between local threshold distributions and event statistics.
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Affiliation(s)
- Botond Tyukodi
- Department of Mechanical and Industrial Engineering, Northeastern University, Boston, Massachusetts 02115, USA
| | - Damien Vandembroucq
- PMMH, CNRS, ESPCI Paris, PSL University, Sorbonne Université, Université de Paris, F-75005 Paris, France
| | - Craig E Maloney
- Department of Mechanical and Industrial Engineering, Northeastern University, Boston, Massachusetts 02115, USA
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