History dependent plasticity of glass: A mapping between atomistic and elasto-plastic models

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 modelled 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 quasistatic 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 structural properties' evolution rate depends on the magnitude of local plastic deformation events, introducing an effective local 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, systems quenched from high-temperature liquids show a slow strain-hardening with statistically homogeneous plastic deformation. In these initially soft glasses, numerous plastic rearrangements are required to converge toward the stationary flow state. The elasto-plastic model successfully reproduces the stress-strain curves in the transient regime for the whole range of parent temperatures by including this local memory mechanism. The limitations of the model are finally discussed, together with possible improvements.