Session K24: Amorphous Matter at the Meso-Scale: Finite Temperatures, Finite Rates, Active Driving

Memory effects in mesoscopic elasto-plastic models of amorphou solids

Due to their out-of-equilibrium nature, materials such as amorphous solids, glasses or dense suspensions exhibit a history-dependent mechanical behavior. Thermal and mechanical annealing drastically affect the modes of deformation and failure. In recent years experiments and numerical simulations of disordered materials under cyclic loading have unveiled puzzling properties such as the convergence to reversible plastic cycles or the possibility to record and read a past state of deformation. We give a short review of such memory effects in lattice-based elastoplastic models of amorphous solids.   

Mechanical versus thermal activation in driven amorphous solids

Amorphous solids are a disparate class of materials that includes glasses, foams, emulsions, and granular packings. Surprisingly, they exhibit common behaviour in their mechanical response to loading, with an initially elastic regime giving way to a jerky flowing state characterized by intermittent bursts of activity dubbed ``avalanches’’. In the athermal and quasistatic (AQS) limit of slow driving and zero temperature, this steady-state shows the hallmarks of a dynamical phase transition, with power-law scaling for avalanche size and duration, anomalous stress flucutations, and rheological behaviour characterized by nontrivial critical exponents.

Mesoscopic elastoplastic models are ideally suited to reveal universal aspects of this fascinating behavior. In the first part of the talk, we explore how the spatial extent of plastic events affects the distribution of residual stresses, i.e. how far the system is from instability. A key result is the link between the statistical properties of the weakest sites, and the mean stress release caused by collective rearrangements called avalanches [1].

In the second part, we will discuss how finite temperature, driving rate, and finite-size effects compete to truncate avalanches and tune the system away from criticality. Using various scaling arguments and simulations of a mesoscale lattice model of amorphous plasticity equipped with a temperature dependent activation of weak sites, we derive a nonequilibrium phase diagram that captures the onset of avalanche overlap, when temperature effects are prevalent, and when finite-size effects dominate for the critical behaviour [2]. We obtain the macroscopic rheology of sheared amorphous solids with the full mesoscale model as well as a mean-field approximation, and interpret trends with temperature and shear rate in terms of the proposed dynamical phases.   

ELASTICITY, FACILITATION, AVALANCHES OF RELAXATION, AND DYNAMIC HETEROGENEITY IN GLASS-FORMING LIQUIDS

We study the role of elasticity-induced facilitation on the dynamics of glass-forming liquids by coarse-grained two-dimensional models in which local relaxation events, taking place by thermal activation, can trigger new relaxations by long-range elastically-mediated interactions. By simulations, we show that the models reproduces the main salient facts associated with dynamic heterogeneity and offers a mechanism to explain the emergence of dynamical correlations at the glass transition [1]. Moreover, we provide a theoretical description of dynamical heterogeneities, based on the premise that relaxation occurs via local rearrangements coupled by elasticity. We find that the dynamical correlation length and correlation volume are controlled by a critical point at vanishing temperature, and predict their singular behavior in terms of the distribution of local energy barriers at T=0. We  show that a  decoupling between particle diffusion and relaxation time (the so-called Stoke-Einstein violation) must occur, which diverges at T=0. Our description makes a direct connection between dynamical heterogeneities and avalanche-type response [2].   

Understanding the ductile-to-brittle transition in disordered solids using structuro-elastoplaisc models

The deformation of disordered solids is governed by a complicated interplay between elastic deformation, plastic particle rearrangements, and their underlying disordered packing structure. Pinpointing the exact influence of microscopic factors such as particle interactions and preparation history on the ductility of a solid is challenging. In this study, we use a recently developed structro-elastoplasic (StEP) framework to model the ductile-to-brittle transition of three distinctive disordered solids: (i) simulated two-dimensional repulsive disks annealed at different temperatures, (ii) experimental two-dimensional rafts of granular materials at an air-oil interface with different particle interactions and (iii) simulated three-dimensional oligomer nanopillars deformed under different temperatures. In all three systems, we used a machine learning method to develop a structural descriptor, softness, which predicts the propensity of a particle to rearrange. Microscopic interplay between softness, elasticity, and rearrangements was extracted and used to inform the StEP models, which in turn captures the shear band formation and the brittle-to-ductile transition in all three systems. Through analysis of the models, we demonstrate how the StEP model can be used to establish the pathway from the respective microscopic factors of the three systems, i.e., preparation history, particle interaction, and temperature, to their ductility upon deformation.