Insights from the quantitative calibration of an elasto-plastic model from a Lennard-Jones atomic glass

Abstract

Quantitative multi-scale modeling of mechanical properties of disordered materials is still an open challenge. Bridging scales requires an intense dialogue between physics and mechanics to keep track of the complexity of the mechanisms at play, especially when passing from a discrete atomistic description to a continuous one. Here, we compare the macroscopic and the local plastic behavior of a model amorphous solid based on two radically different numerical descriptions. On the one hand, we simulate glass samples by atomistic simulations. On the other, we implement a mesoscale elasto-plastic model based on a solid-mechanics description. The latter is extended to consider the anisotropy of the yield surface via statistically distributed local and discrete weak planes on which shear transformations can be activated. To make the comparison as quantitative as possible, we consider the simple case of a quasistatically driven two-dimensional system in the stationary flow state and compare mechanical observables measured on both models over the same length scales. To this end, we first calibrate the macroscale behavior of the elasto-plastic model based on molecular static simulations. We show that the macroscale mechanical response, including its fluctuations, can be quantitatively recovered for a range of elasto-plastic mesoscale parameters. Using a newly developed method that makes it possible to probe the local yield stresses in atomistic simulations, we calibrate the local mechanical response of the elasto-plastic model at different coarse-graining scales. In this case, the calibration shows a qualitative agreement only for an optimized subset of mesoscale parameters and for sufficiently coarse probing length scales. This calibration allows us to establish a length scale for the mesoscopic elements that corresponds to an upper bound of the shear transformation size, a key physical parameter in elasto-plastic models. We find that certain properties naturally emerge from the elasto-plastic model, such as accurate correlations between external stress fluctuations or between local yield stresses and local stress drops. In particular, we show that the elasto-plastic model reproduces the Bauschinger effect, namely the plasticity-induced anisotropy in the macroscale stress–strain response. We discuss the successes and failures of our approach, the impact of different model ingredients and propose future research directions for quantitative multi-scale models of amorphous plasticity.

Keywords

• Glass
• Plasticity
• Mesoscale
• Atomistic
• Yield threshold
• Bauschinger effect