Mapping out the glassy landscape of a mesoscopic elastoplastic model

Abstract

We develop a mesoscopic model to study plastic behavior of amorphous materials under cyclic loading. The model is depinning-like and driven by a disordered thresholds dynamics coupled by long-range elastic interactions. We propose a simple protocol of ``glass preparation' which allows to mimic thermalisation at high temperature and aging at vanishing temperature. Various levels of glass stabilities (from brittle to ductile) can be achieved by tuning the aging duration. The aged glasses are immersed into a quenched disorder landscape, serving as initial configurations for various protocols of mechanical loading by shearing. The dependence of the plastic behavior upon monotonous loading is recovered. The behavior under cyclic loading is studied for different ages and system sizes. The size and age dependence of the irreversibility transition is discussed. A thorough characterization of the disorder-landscape is achieved through analysis of transition graphs, which describe plastic deformation pathways under athermal quasi-static shear. The analysis of the stability ranges of the strongly connected components of the transition graphs reveals the emergence of a phase-separation like process associated with the aging of the glass. Increasing the age and hence stability of the initial glass, results in a gradual break-up of the landscape of dynamically accessible stable states into three distinct regions: one region centered around the initially prepared glass phase, and two additional regions, characterized by well-separated ranges of positive and negative plastic strains, which are accessible only from the initial glass phase by passing through the stress peak in the forward, respectively, backward shearing directions.

Cavitation instabilities in amorphous solids via secondary mechanical perturbations

“…3(c) at different densities. The power law observed in the works of Kumar et al [41], τ rel ∼ (γ irr − γ) −2.8 here too serves as a good guide to the eye; γ irr is the estimated yield threshold under cyclic shear.…”

“…Or, it can be due to the formation of a cavity. We observe that for smaller γ max , the system eventually reaches a limit cycle [37,[39][40][41] where either the energy decreases to a constant value or oscillates between two or more different values. Examples of limit cycles with a period greater than one are shown in the Supplementary Information.…”

Modeling amorphous materials: from hydrogel packings to mesoscale models

“…i) Here all systems were prepared in an initial rapid quench. The issue of thermal annealing, or zero temperature aging [100], of the samples before subjecting them to shearing should be investigated. ii) We have used a simple single-amplitude cycling protocol.…”

“…In terms of the ER->RPR and RPR->DR transitions, most previous work, including our own [96,100], has focused on RPR->DR [176,180,179,178,177,142,211,171]. Here, we focus instead on the ER->RPR transition -which we show below to have a mixed first-second order character.…”

“…In the case of forward steady shear, we must slightly modify our scaling arguments based on σ 0 , but we arrive at a prediction for σ y which differs quantitatively from the prediction for Γ 0 , but has the same overall trend. Amorphous systems subject to forward-reverse shear cycling have been the focus of an increasing number of experimental, theoretical, and numerical studies over the past several years [124,98,91,90,94,93,92,95,24,66,106,23,170,171,212,70,177,176,178,197,179,142,180,96,100]. In their seminal work [92], Keim and coworkers identified three steady state response regimes for an amorphous material under cyclic shearing: at low amplitudes, the material eventually becomes elastic with no rearrangement of particles or atoms.…”