Criticality in elastoplastic models of amorphous solids with stress-dependent yielding rates.
Soft Matter
; 15(44): 9041-9055, 2019 Nov 28.
Article
em En
| MEDLINE
| ID: mdl-31647078
We analyze the behavior of different elastoplastic models approaching the yielding transition. We propose two kinds of rules for the local yielding events: yielding occurs above the local threshold either at a constant rate or with a rate that increases as the square root of the stress excess. We establish a family of "static" universal critical exponents which do not depend on this dynamic detail of the model rules: in particular, the exponents for the avalanche size distribution P(S) â¼S-τSf(S/Ldf) and the exponents describing the density of sites at the verge of yielding, which we find to be of the form P(x) ≃P(0) + xθ with P(0) â¼L-a controlling the extremal statistics. On the other hand, we discuss "dynamical" exponents that are sensitive to the local yielding rule. We find that, apart form the dynamical exponent z controlling the duration of avalanches, also the flowcurve's (inverse) Herschel-Bulkley exponent ß ([small gamma, Greek, dot above]â¼ (σ-σc)ß) enters in this category, and is seen to differ in ½ between the two yielding rate cases. We give analytical support to this numerical observation by calculating the exponent variation in the Hébraud-Lequeux model and finding an identical shift. We further discuss an alternative mean-field approximation to yielding only based on the so-called Hurst exponent of the accumulated mechanical noise signal, which gives good predictions for the exponents extracted from simulations of fully spatial models.
Texto completo:
1
Coleções:
01-internacional
Base de dados:
MEDLINE
Tipo de estudo:
Prognostic_studies
Idioma:
En
Revista:
Soft Matter
Ano de publicação:
2019
Tipo de documento:
Article
País de afiliação:
Argentina
País de publicação:
Reino Unido