History Dependent Plasticity of Glass: A Mapping between Atomistic and Elasto-Plastic Models

Abstract

Mesoscale elasto-plastic models, with statistically distributed structural properties and elastic coupling between discrete blocks, have been shown to quantitatively reproduce the main phenomenology observed in the stationary flow state of glasses as modeled at the atomic scale[1]. In the present study, an extension of such approaches is proposed to describe the transient mechanical response of glasses from different off-equilibrium states in the athermal quasi-static limit. Equilibrated liquids are simulated using two-dimensional molecular dynamics, quenched instantaneously to zero temperature, and then sheared. The mechanical observables measured in atomistic and elasto-plastic models are compared at the same length scales to calibrate a state-dependent constitutive law. A physical mechanism is proposed where the rate of evolution of structural properties depends on the magnitude of local plastic deformation events, introducing an effective memory of previous states in the system. This mechanism naturally leads to a brittle-ductile transition in the mechanical response of glasses, which depends exclusively on the quenched structure. Specifically, initially stable glasses exhibit strain-softening and localization, where the memory of the initial states is lost abruptly after the first plastic rearrangements. On the other hand, initially soft glasses, quenched from high-temperature liquids, show a slow strain-hardening, and numerous plastic rearrangements are required to converge toward the stationary flow state. By including this memory mechanism, the elasto-plastic model successfully reproduces the stress-strain curves in the transient regime for the whole range of parent temperatures. The limitations of the model are finally discussed together with possible improvements.

Keywords: plasticity, amorphous solid, atomistic simulation, elasto-plastic model, multiscale modeling