Different universality classes at the yielding transition of amorphous systems

Abstract

We study the yielding transition of a two dimensional amorphous system under shear by using a mesoscopic elasto-plastic model. The model combines a full (tensorial) description of the elastic interactions in the system, and the possibility of structural reaccommodations that are responsible for the plastic behavior. The possible structural reaccommodations are encoded in the form of a "plastic disorder" potential, which is chosen independently at each position of the sample to account for local heterogeneities. We observe that the stress must exceed a critical value ${\sigma }_c$ in order for the system to yield. In addition, when the system yields a flow curve relating stress $\sigma$ and strain rate $\dot{\gamma }$ of the form $\dot{\gamma }\sim (\sigma -{\sigma }_c{)}^{\beta }$ is obtained. Remarkably, we observe the value of $\beta$ to depend on some details of the plastic disorder potential. For smooth potentials a value of $\beta \simeq 2.0$ is obtained, whereas for potentials obtained as a concatenation of smooth pieces a value $\beta \simeq 1.5$ is observed in the simulations. This indicates a dependence of critical behavior on details of the plastic behavior that has not been pointed out before. In addition, by integrating out non-essential, harmonic degrees of freedom, we derive a simplified scalar version of the model that represents a collection of interacting Prandtl-Tomlinson particles. A mean field treatment of this interaction reproduces the difference of $\beta$ exponents for the two classes of plastic disorder potentials, and provides values of $\beta$ that compare favorably with those found in the full simulations.

13 pages, 12 figures

References in corpus (4)

• Scaling description of the yielding transition in soft amorphous solids at zero temperature
• Yielding and flow in adhesive and non-adhesive concentrated emulsions
• Slip avalanches in crystal plasticity: scaling of the avalanche cutoff
• Strain localization driven by structural relaxation in sheared amorphous solids

Cited by in corpus (14)

• Criticality in elastoplastic models of amorphous solids with stress-dependent yielding rates
• How collective asperity detachments nucleate slip at frictional interfaces
• On the critical exponents of the yielding transition of amorphous solids
• Deformation and flow of amorphous solids: An updated review of mesoscale elastoplastic models
• Microscopic processes controlling the Herschel-Bulkley exponent
• Models for the yielding behaviour of amorphous solids
• Shear-induced diffusion in non-local granular flows
• Elastic interfaces on disordered substrates: From mean-field depinning to yielding
• Soft modes and strain redistribution in continuous models of amorphous plasticity: the Eshelby paradigm, and beyond?
• The Prandtl-Tomlinson model of friction with stochastic driving
• Scaling theory for the statistics of slip at frictional interfaces
• Coarse-graining amorphous plasticity: impact of rejuvenation and disorder
• Random traction yielding transition in epithelial tissues
• Elasto-plastic models of the yielding transition with stress-dependent transition rates