[Paper Review] Yielding and plasticity in amorphous solids

Ludovic Berthier, Giulio Biroli+2 more|arXiv (Cornell University)|Jan 17, 2024

Material Dynamics and Properties4 citations

TL;DR

This paper presents a unified theoretical framework based on statistical mechanics to explain the universal rheological behavior of amorphous solids—from metallic glasses to active biological materials—showing that pre-yielding avalanche dynamics under shear or random forces collapse onto a single scaling law in infinite dimensions, with key implications for plasticity, yielding, and the role of activity and noise in nonequilibrium systems.

ABSTRACT

The physics of disordered media, from metallic glasses to colloidal suspensions, granular matter and biological tissues, offers difficult challenges because it often occurs far from equilibrium, in materials lacking symmetries and evolving through complex energy landscapes. Here, we review recent theoretical efforts to provide microscopic insights into the mechanical properties of amorphous media using approaches from statistical mechanics as unifying frameworks. We cover both the initial regime corresponding to small deformations, and the yielding transition marking a change between elastic response and plastic flow. We discuss the specific features arising for systems evolving near a jamming transition, and extend our discussion to recent studies of the rheology of dense biological and active materials.

Motivation & Objective

• To establish glass stability as a unifying principle for understanding the mechanical response of disordered, amorphous materials across vastly different length and time scales.
• To investigate the connection between shear-driven deformation and quenched random force fields in the pre-yielding regime, particularly in the context of infinite-dimensional systems.
• To explore how active forces and rotational noise influence the transition from elastic to plastic response, and whether such systems exhibit universal rheological behavior.
• To examine the breakdown of analogies between boundary-driven shear and random-force-driven systems at the yielding transition, especially regarding failure modes and strain localization.
• To extend the framework to dense active and biological materials, identifying common features such as jamming and glass transitions in nonequilibrium conditions.

Proposed method

• Employing statistical mechanics and mean-field theory in infinite dimensions to derive exact dynamical equations for particle systems under shear or random forces.
• Using scaling collapse techniques to show that avalanche statistics (size, local shear modulus) under shear and quenched random fields collapse onto a single curve when rescaled by the correlation length of the applied field.
• Applying numerical simulations in 2D and infinite dimensions to validate the scaling collapse and compare avalanche dynamics under different driving protocols.
• Analyzing the role of persistent active forces and small rotational noise in driving intermittent, avalanche-like relaxation events in active matter systems.
• Comparing brittle failure under shear with more gradual failure under random forces in computer glasses to probe the limits of the analogy between different loading protocols.
• Extending the framework to include active and biological materials by modeling them as systems undergoing nonequilibrium glass or jamming transitions.

Figure 1: Deformation and yielding of amorphous solids. Selected examples of mechanical loading experiments in amorphous materials spanning a broad range of time scales, length scales, and physical behaviours. (A) Compressive test in two metallic glasses produces elastic deformation followed by macr

Experimental results

Research questions

• RQ1 To what extent do the avalanche statistics of amorphous solids under shear and under quenched random forces exhibit universal scaling in infinite dimensions?
• RQ2 How does the correlation length of the applied field govern the collapse of avalanche statistics in both shear and random-force-driven systems?
• RQ3 Why does the analogy between shear and random-force driving break down at the yielding transition, particularly in terms of failure mode (e.g., shear bands vs. gradual failure)?
• RQ4 How do small amounts of rotational noise perturb the equivalence between active matter with persistent forces and sheared systems?
• RQ5 What are the quantitative differences in plastic and elastic responses between boundary-driven shear flows and random-force-driven systems in active matter?

Key findings

• Infinite-dimensional systems exhibit a complete collapse of avalanche statistics (including event sizes and local shear modulus) under shear and quenched random forces when scaled by the correlation length of the applied field.
• The scaling collapse holds in 2D simulations of jammed soft particles, indicating that the analogy between shear and random-force driving is robust beyond mean-field theory.
• As the correlation length of the random force field increases toward the system size, the scaling factor approaches unity, indicating equivalence to shear in the limit of long-range correlations.
• Under shear, computer glasses with high stability exhibit brittle failure with localized shear bands and large stress drops, whereas under random forces, the same materials fail more gradually without obvious shear bands.
• The introduction of small rotational noise in highly persistent active systems leads to intermittent, avalanche-driven dynamics that resemble sheared systems but may differ quantitatively in avalanche statistics and response characteristics.
• Theoretical and numerical results suggest that symmetries in the driving field may be necessary for brittle failure, and finite-size effects may obscure strain localization in random-force-driven systems.

Figure 2: Oscillatory strain and reversibility. (A) Stress $\sigma$ versus applied strain $\gamma$ in a colloidal glass up to some maximum value $\gamma_{\rm max}$ , at which the strain is reversed back to zero, and (B) non-affine mean-squared displacement $\Delta_{r}$ between the configurations at