Properties of the density of shear transformations in driven amorphous solids

Abstract

The strain load $\Delta \gamma$ that triggers consecutive avalanches is a key observable in the slow deformation of amorphous solids. Its temporally averaged value $⟨\Delta \gamma ⟩$ displays a non-trivial system-size dependence that constitutes one of the distinguishing features of the yielding transition. Details of this dependence are not yet fully understood. We address this problem by means of theoretical analysis and simulations of elastoplastic models for amorphous solids. An accurate determination of the size dependence of $⟨\Delta \gamma ⟩$ leads to a precise evaluation of the steady-state distribution of local distances to instability $x$. We find that the usually assumed form $P(x)\sim x^{\theta }$ (with $\theta$ being the so-called pseudo-gap exponent) is not accurate at low $x$ and that in general $P(x)$ tends to a system-size-dependent \textit{finite} limit as $x\to 0$. We work out the consequences of this finite-size dependence standing on exact results for random-walks and disclosing an alternative interpretation of the mechanical noise felt by a reference site. We test our predictions in two- and three-dimensional elastoplastic models, showing the crucial influence of the saturation of $P(x)$ at small $x$ on the size dependence of $⟨\Delta \gamma ⟩$ and related scalings.

16 pages, 13 figures

References in corpus (7)

• Scaling description of the yielding transition in soft amorphous solids at zero temperature
• Inertia and universality of avalanche statistics: The case of slowly deformed amorphous solids
• On the relevance of disorder in athermal amorphous materials under shear
• Microscopic processes controlling the Herschel-Bulkley exponent
• Aging in a mean field elastoplastic model of amorphous solids
• The Prandtl-Tomlinson model of friction with stochastic driving
• Interplay of rearrangements, strain, and local structure during avalanche propagation

Cited by in corpus (8)

• Unified View of Avalanche Criticality in Sheared Glasses
• Scaling Description of Dynamical Heterogeneity and Avalanches of Relaxation in Glass-Forming Liquids
• Yielding and plasticity in amorphous solids
• The yielding of amorphous solids at finite temperatures
• Signatures of the spatial extent of plastic events in the yielding transition in amorphous solids
• Ductile and brittle yielding of athermal amorphous solids: a mean-field paradigm beyond the random field Ising model
• The Fate of Shear-Oscillated Amorphous Solids
• Dynamic phase diagram of plastically deformed amorphous solids at finite temperature