Ductile and brittle yielding of athermal amorphous solids: a mean-field paradigm beyond the random field Ising model
arXiv:2310.07843 · doi:10.1103/PhysRevE.110.045002
Abstract
Developing a unified theory describing both ductile and brittle yielding constitutes a fundamental challenge of non-equilibrium statistical physics. Recently, it has been proposed that the nature of the yielding transition is controlled by physics akin to that of the quasistatically driven Random field Ising model (RFIM), which has served as the paradigm for understanding the effect of quenched disorder in slowly driven systems with short-ranged interactions. However, this theoretical picture neglects both the dynamics of, and the elasticity-induced long-ranged interactions between, the mesoscopic material constituents. Here, we address these two aspects and provide a unified theory building on the Hébraud-Lequeux elastoplastic description. The first aspect is crucial to understanding the competition between the imposed deformation rate and the finite timescale of plastic rearrangements: we provide a dynamical description of the macroscopic stress drop and predictions for the divergence of the peak susceptibility with inverse shear rate. The second is essential in order to capture properly the behaviour in the limit of quasistatic driving, where avalanches of plasticity diverge with system size at any value of the strain. We fully characterise the avalanche behaviour, which is radically different to that of the RFIM. In the quasistatic, infinite size limit, we find that both models have mean-field Landau exponents, obscuring the effect of the interactions. We show, however, that the latter profoundly affect the behaviour of finite systems approaching the spinodal-like brittle yield point, where we recover qualitatively the finite-size trends found in particle simulations, and modify the nature of the random critical point separating ductile and brittle yielding, where we predict critical behaviour on top of the marginality present at any value of the strain.
arXiv comment40 pages, 43 figures
References in corpus (73)
- Theoretical perspective on the glass transition and amorphous materials
- Crackling Noise
- Yield Stress Materials in Soft Condensed Matter
- Amorphous Systems in Athermal, Quasistatic Shear
- Statistical Models of Fracture
- Persistence and First-Passage Properties in Non-equilibrium Systems
- A kinetic theory of plastic flow in soft glassy materials
- Models and algorithms for the next generation of glass transition studies
- A random critical point separates brittle and ductile yielding transitions in amorphous materials
- Scaling description of the yielding transition in soft amorphous solids at zero temperature
- Subextensive Scaling in the Athermal, Quasistatic Limit of Amorphous Matter in Plastic Shear Flow
- Hysteresis, Avalanches, and Disorder Induced Critical Scaling: A Renormalization Group Approach
- First-Order Transition in the Breakdown of Disordered Media
- Plastic Response of a 2D Lennard-Jones amorphous solid: Detailed analysis of the local rearrangements at very slow strain-rate
- A mode-coupling theory for the pasty rheology of soft glassy materials
- Elastic consequences of a single plastic event : a step towards the microscopic modeling of the flow of yield stress fluids
- Predicting plasticity in disordered solids from structural indicators
- Marginal Stability in Structural, Spin and Electron Glasses
- Driving rate dependence of avalanche statistics and shapes at the yielding transition
- Microscopic Mechanism of Shear Bands in Amorphous Solids
- Avalanches in Breakdown and Fracture Processes
- Shear-Induced Stress Relaxation in a Two-Dimensional Wet Foam
- Self-organized criticality in the hysteresis of the Sherrington - Kirkpatrick model
- Local yield stress statistics in model amorphous solids
- Following the evolution of glassy states under external perturbations: compression and shear-strain
- Universality of Avalanche Exponents in Plastic Deformation of Disordered Solids
- Theory of collective opinion shifts: from smooth trends to abrupt swings
- Avalanche localization and crossover scaling in amorphous plasticity
- Elasto-plastic description of brittle failure in amorphous materials
- Local and global avalanches in a 2D sheared granular medium
- Shear yielding and shear jamming of dense hard sphere glasses
- Finite Size Scaling analysis of the avalanches in the 3d Gaussian Random Field Ising Model with metastable dynamics
- Ductile and brittle yielding in thermal and athermal amorphous materials
- Time dependent elastic response to a local shear transformation in amorphous solids
- Experimental measurements of stress redistribution in flowing emulsions
- Life and Death in a Cage and at the Edge of a Cliff
- On the relevance of disorder in athermal amorphous materials under shear
- Elastic avalanches reveal marginal behaviour in amorphous solids
- Following the evolution of glassy states under external perturbations: the full replica symmetry breaking solution
- Rejuvenation and Shear-Banding in model amorphous solids
- Criticality in elastoplastic models of amorphous solids with stress-dependent yielding rates
- Elasticity, Facilitation and Dynamic Heterogeneity in Glass-Forming liquids
- Brittle yielding of amorphous solids at finite shear rates
- Spinodals with Disorder: from Avalanches in Random Magnets to Glassy Dynamics
- Anomalous Elasticity and Screening in Amorphous Solids
- Density controls the kinetic stability of ultrastable glasses
- Probing relevant ingredients in mean-field approaches for the athermal rheology of yield stress materials
- Elastoplasticity Mediates Dynamical Heterogeneity Below the Mode-Coupling Temperature
- Relevance of Shear Transformations in the Relaxation of Supercooled Liquids
- Role of fluctuations in the yielding transition of two-dimensional glasses
- An elasto-plastic approach based on microscopic insights for the steady state and transient dynamics of sheared disordered solids
- On the critical exponents of the yielding transition of amorphous solids
- Microscopic processes controlling the Herschel-Bulkley exponent
- Scaling Description of Dynamical Heterogeneity and Avalanches of Relaxation in Glass-Forming Liquids
- Yielding, shear banding and brittle failure of amorphous materials
- Finite-disorder critical point in the yielding transition of elasto-plastic models
- Mechanical Failure in Amorphous Solids: Scale Free Spinodal Criticality
- Aging in a mean field elastoplastic model of amorphous solids
- Nontrivial rheological exponents in sheared yield stress fluids
- Scaling description of creep flow in amorphous solids
- Avalanche size distributions in mean field plastic yielding models
- Elastic interfaces on disordered substrates: From mean-field depinning to yielding
- Rare events and disorder control the brittle yielding of well-annealed amorphous solids
- Anomalous mean-field behavior of the fully connected Ising model
- Properties of the density of shear transformations in driven amorphous solids
- Finite-size scaling of the random-field Ising model above the upper critical dimension
- Instantaneous Normal Modes Reveal Structural Signatures for the Herschel-Bulkley Rheology in Sheared Glasses
- Aging and linear response in the Hébraud-Lequeux model for amorphous rheology
- Spontaneous instabilities and stick-slip motion in a generalized Hebraud-Lequeux model
- Far-from-equilibrium criticality in the Random Field Ising Model with Eshelby Interactions
- Mechanical excitation and marginal triggering during avalanches in sheared amorphous solids
- Gaps between avalanches in 1D Random Field Ising Models
- Universal mechanical instabilities in the energy landscape of amorphous solids: evidence from athermal quasistatic expansion