scholarly journals Aging in a mean field elastoplastic model of amorphous solids

2020 ◽  
Vol 32 (12) ◽  
pp. 127104
Author(s):  
Jack T. Parley ◽  
Suzanne M. Fielding ◽  
Peter Sollich
Keyword(s):  
Mean Field ◽  
Amorphous Solids ◽  
Elastoplastic Model

scholarly journals Continuum limit of the vibrational properties of amorphous solids

2017 ◽  
Vol 114 (46) ◽  
pp. E9767-E9774 ◽  
Author(s):  
Hideyuki Mizuno ◽  
Hayato Shiba ◽  
Atsushi Ikeda
Keyword(s):  
Large Scale ◽  
Continuum Limit ◽  
Scaling Law ◽  
Mean Field ◽  
Low Frequency ◽  
Amorphous Solids ◽  
Mode Analysis ◽  
Vibrational Modes ◽  
Phonon Modes ◽  
The Continuum

The low-frequency vibrational and low-temperature thermal properties of amorphous solids are markedly different from those of crystalline solids. This situation is counterintuitive because all solid materials are expected to behave as a homogeneous elastic body in the continuum limit, in which vibrational modes are phonons that follow the Debye law. A number of phenomenological explanations for this situation have been proposed, which assume elastic heterogeneities, soft localized vibrations, and so on. Microscopic mean-field theories have recently been developed to predict the universal non-Debye scaling law. Considering these theoretical arguments, it is absolutely necessary to directly observe the nature of the low-frequency vibrations of amorphous solids and determine the laws that such vibrations obey. Herein, we perform an extremely large-scale vibrational mode analysis of a model amorphous solid. We find that the scaling law predicted by the mean-field theory is violated at low frequency, and in the continuum limit, the vibrational modes converge to a mixture of phonon modes that follow the Debye law and soft localized modes that follow another universal non-Debye scaling law.

scholarly journals Criticality in elastoplastic models of amorphous solids with stress-dependent yielding rates

Soft Matter ◽  
2019 ◽  
Vol 15 (44) ◽  
pp. 9041-9055 ◽  
Author(s):  
E. E. Ferrero ◽  
E. A. Jagla
Keyword(s):  
Critical Exponents ◽  
Mean Field ◽  
Amorphous Solids ◽  
Stress Dependent ◽  
Local Yielding

Elastoplastic models are analyzed at the yielding transition. Universality and critical exponents are discussed. The flowcurve exponent happens to be sensitive to the local yielding rule. An alternative mean-field description of yielding is explained.

scholarly journals Impact of jamming criticality on low-temperature anomalies in structural glasses

2019 ◽  
Vol 116 (28) ◽  
pp. 13768-13773 ◽  
Author(s):  
Silvio Franz ◽  
Thibaud Maimbourg ◽  
Giorgio Parisi ◽  
Antonello Scardicchio
Keyword(s):  
Low Temperature ◽  
Specific Heat ◽  
Field Model ◽  
Analytic Solution ◽  
Mean Field ◽  
Universality Class ◽  
Amorphous Solids ◽  
Anomalous Behavior ◽  
Marginal Stability ◽  
Mean Field Model

We present a mechanism for the anomalous behavior of the specific heat in low-temperature amorphous solids. The analytic solution of a mean-field model belonging to the same universality class as high-dimensional glasses, the spherical perceptron, suggests that there exists a cross-over temperature above which the specific heat scales linearly with temperature, while below it, a cubic scaling is displayed. This relies on two crucial features of the phase diagram: (i) the marginal stability of the free-energy landscape, which induces a gapless phase responsible for the emergence of a power-law scaling; and (ii) the vicinity of the classical jamming critical point, as the cross-over temperature gets lowered when approaching it. This scenario arises from a direct study of the thermodynamics of the system in the quantum regime, where we show that, contrary to crystals, the Debye approximation does not hold.

scholarly journals Elastic avalanches reveal marginal behavior in amorphous solids

2019 ◽  
Vol 117 (1) ◽  
pp. 86-92 ◽  
Author(s):  
Baoshuang Shang ◽  
Pengfei Guan ◽  
Jean-Louis Barrat
Keyword(s):  
Complex Structure ◽  
Mean Field ◽  
System Size ◽  
Amorphous Solids ◽  
Marginal Stability ◽  
Small Perturbations ◽  
Scale Free ◽  
Glass Forming ◽  
Quasistatic Regime ◽  
Nonlinear Elastic

Mechanical deformation of amorphous solids can be described as consisting of an elastic part in which the stress increases linearly with strain, up to a yield point at which the solid either fractures or starts deforming plastically. It is well established, however, that the apparent linearity of stress with strain is actually a proxy for a much more complex behavior, with a microscopic plasticity that is reflected in diverging nonlinear elastic coefficients. Very generally, the complex structure of the energy landscape is expected to induce a singular response to small perturbations. In the athermal quasistatic regime, this response manifests itself in the form of a scale-free plastic activity. The distribution of the corresponding avalanches should reflect, according to theoretical mean-field calculations [S. Franz and S. Spigler,Phys. Rev. E95, 022139 (2017)], the geometry of phase space in the vicinity of a typical local minimum. In this work, we characterize this distribution for simple models of glass-forming systems, and we find that its scaling is compatible with the mean-field predictions for systems above the jamming transition. These systems exhibit marginal stability, and scaling relations that hold in the stationary state are examined and confirmed in the elastic regime. By studying the respective influence of system size and age, we suggest that marginal stability is systematic in the thermodynamic limit.

ELASTIC DEFORMATIONS IN COVALENT AMORPHOUS SOLIDS

2013 ◽  
Vol 27 (05) ◽  
pp. 1330002 ◽  
Author(s):  
ALESSIO ZACCONE
Keyword(s):  
Mechanical Response ◽  
Mechanical Stability ◽  
Electronic Materials ◽  
Mean Field ◽  
Structural Disorder ◽  
Amorphous Solids ◽  
Amorphous Semiconductors ◽  
Atomic Displacements ◽  
Rigidity Percolation ◽  
Potential Applications

Structural disorder has a dramatic impact on the mechanical response and stability of solids. On the one hand, rigidity percolation shows that the limit of mechanical stability coincides with the emergence of floppy modes. On the other hand, the rigidity of solids is also lowered by nonaffine atomic displacements, i.e. additional motions caused by the disorder on top of the affine displacements dictated by the strain. These two frameworks have offered alternative descriptions of the elasticity of disordered solids with central-force bonds, but the relationship between rigidity percolation and nonaffinity has remained unclear. As such, a unifying theory of real materials, i.e. those with covalent (noncentral) bonds, such as amorphous semiconductors, has been elusive. After briefly reviewing these theories, we present a mean-field argument which attempts to provide the unifying link between rigidity percolation and non-affinity. This framework yields analytical predictions of the shear modulus of covalent amorphous solids with potential applications to amorphous semiconductors and disordered carbon electronic materials.

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