Mean-Field Description of Plastic Flow in Amorphous Solids
Failure and flow of amorphous materials are central to various phenomena including earthquakes and landslides. There is accumulating evidence that the yielding transition between a flowing and an arrested phase is a critical phenomenon, but the associated exponents are not understood, even at a mean...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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American Physical Society
2016-01-01
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| Series: | Physical Review X |
| Online Access: | http://doi.org/10.1103/PhysRevX.6.011005 |
| _version_ | 1819010330956660736 |
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| author | Jie Lin Matthieu Wyart |
| author_facet | Jie Lin Matthieu Wyart |
| author_sort | Jie Lin |
| collection | DOAJ |
| description | Failure and flow of amorphous materials are central to various phenomena including earthquakes and landslides. There is accumulating evidence that the yielding transition between a flowing and an arrested phase is a critical phenomenon, but the associated exponents are not understood, even at a mean-field level where the validity of popular models is debated. Here, we solve a mean-field model that captures the broad distribution of the mechanical noise generated by plasticity, whose behavior is related to biased Lévy flights near an absorbing boundary. We compute the exponent θ characterizing the density of shear transformation P(x)∼x^{θ}, where x is the stress increment beyond which they yield. We find that after an isotropic thermal quench, θ=1/2. However, θ depends continuously on the applied shear stress; this dependence is not monotonic, and its value at the yield stress is not universal. The model rationalizes previously unexplained observations and captures reasonably well the value of exponents in three dimensions. Values of exponents in four dimensions are accurately predicted. These results support the fact that it is the true mean-field model that applies in large dimensions, and they raise fundamental questions about the nature of the yielding transition. |
| first_indexed | 2024-12-21T01:10:33Z |
| format | Article |
| id | doaj.art-fd4be8d0667542a081655b7a339553ad |
| institution | Directory Open Access Journal |
| issn | 2160-3308 |
| language | English |
| last_indexed | 2024-12-21T01:10:33Z |
| publishDate | 2016-01-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review X |
| spelling | doaj.art-fd4be8d0667542a081655b7a339553ad2022-12-21T19:20:56ZengAmerican Physical SocietyPhysical Review X2160-33082016-01-016101100510.1103/PhysRevX.6.011005Mean-Field Description of Plastic Flow in Amorphous SolidsJie LinMatthieu WyartFailure and flow of amorphous materials are central to various phenomena including earthquakes and landslides. There is accumulating evidence that the yielding transition between a flowing and an arrested phase is a critical phenomenon, but the associated exponents are not understood, even at a mean-field level where the validity of popular models is debated. Here, we solve a mean-field model that captures the broad distribution of the mechanical noise generated by plasticity, whose behavior is related to biased Lévy flights near an absorbing boundary. We compute the exponent θ characterizing the density of shear transformation P(x)∼x^{θ}, where x is the stress increment beyond which they yield. We find that after an isotropic thermal quench, θ=1/2. However, θ depends continuously on the applied shear stress; this dependence is not monotonic, and its value at the yield stress is not universal. The model rationalizes previously unexplained observations and captures reasonably well the value of exponents in three dimensions. Values of exponents in four dimensions are accurately predicted. These results support the fact that it is the true mean-field model that applies in large dimensions, and they raise fundamental questions about the nature of the yielding transition.http://doi.org/10.1103/PhysRevX.6.011005 |
| spellingShingle | Jie Lin Matthieu Wyart Mean-Field Description of Plastic Flow in Amorphous Solids Physical Review X |
| title | Mean-Field Description of Plastic Flow in Amorphous Solids |
| title_full | Mean-Field Description of Plastic Flow in Amorphous Solids |
| title_fullStr | Mean-Field Description of Plastic Flow in Amorphous Solids |
| title_full_unstemmed | Mean-Field Description of Plastic Flow in Amorphous Solids |
| title_short | Mean-Field Description of Plastic Flow in Amorphous Solids |
| title_sort | mean field description of plastic flow in amorphous solids |
| url | http://doi.org/10.1103/PhysRevX.6.011005 |
| work_keys_str_mv | AT jielin meanfielddescriptionofplasticflowinamorphoussolids AT matthieuwyart meanfielddescriptionofplasticflowinamorphoussolids |