On the critical exponents of the yielding transition of amorphous solids

Abstract

We investigate numerically the yielding transition of a two dimensional model amorphous solid under external shear. We use a scalar model in terms of values of the total local strain, that we derive from the full (tensorial) description of the elastic interactions in the system, in which plastic deformations are accounted for by introducing a stochastic "plastic disorder" potential. This scalar model is seen to be equivalent to a collection of Prandtl-Tomlinson particles, which are coupled through an Eshelby quadrupolar kernel. Numerical simulations of this scalar model reveal that the strain rate vs stress curve, close to the critical stress, is of the form $\dot{\gamma }\sim (\sigma -{\sigma }_c{)}^{\beta }$. Remarkably, we find that the value of $\beta$ depends on details of the microscopic plastic potential used, confirming and giving additional support to results previously obtained with the full tensorial model. %\cite{Jagla_Yiel}. To rationalize this result, we argue that the Eshelby interaction in the scalar model can be treated to a good approximation in a sort of "dynamical" mean field, which corresponds to a Prandtl-Tomlinson particle that is driven by the applied strain rate in the presence of a stochastic noise generated by all other particles. The dynamics of this Prandtl-Tomlinson particle displays different values of the $\beta$ exponent depending on the analytical properties of the microscopic potential, thus giving support to the results of the numerical simulations. Moreover, we find that other critical exponents that depend on details of the dynamics show also a dependence with the form of the disorder, while static exponents are independent of the details of the disorder. Finally, we show how our scalar model relates to other elastoplastic models and to the widely used mean field version known as the Hébraud-Lequeux model.

13 pages, 12 figures

References in corpus (4)

• Plastic Response of a 2D Lennard-Jones amorphous solid: Detailed analysis of the local rearrangements at very slow strain-rate
• Microscopic processes controlling the Herschel-Bulkley exponent
• Different universality classes at the yielding transition of amorphous systems
• The Prandtl-Tomlinson model of friction with stochastic driving

Cited by in corpus (21)

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• Scaling Description of Dynamical Heterogeneity and Avalanches of Relaxation in Glass-Forming Liquids
• Aging in a mean field elastoplastic model of amorphous solids
• The yielding of amorphous solids at finite temperatures
• Elastic interfaces on disordered substrates: From mean-field depinning to yielding
• Properties of the density of shear transformations in driven amorphous solids
• Modeling plasticity of amorphous composites: Scalar is not enough
• On the critical region of long-range depinning transitions
• Criticality at finite strain rate in fluidized soft glassy materials
• Signatures of the spatial extent of plastic events in the yielding transition in amorphous solids
• Mechanical excitation and marginal triggering during avalanches in sheared amorphous solids
• Coarse-graining amorphous plasticity: impact of rejuvenation and disorder
• Ductile and brittle yielding of athermal amorphous solids: a mean-field paradigm beyond the random field Ising model
• Thermally activated intermittent flow in amorphous solids
• Discontinuous yielding transition of amorphous materials with low bulk modulus
• The Fate of Shear-Oscillated Amorphous Solids
• Residual stress distributions in athermally deformed amorphous solids from atomistic simulations
• Dynamic phase diagram of plastically deformed amorphous solids at finite temperature
• Emergence of a random field at the yielding transition of a mean-field Elasto-Plastic model
• Soil creep facilitated by cyclic variations of environmental conditions
• Volume-shear coupling in a mesoscopic model of amorphous materials