Insights from the quantitative calibration of an elasto-plastic model from a Lennard-Jones atomic glass
The main goal of materials science is to design new materials tailored to meet the demands of specific engineering applications and industries. Regarding the mechanical properties, specifically plastic deformation and failure, multi-scale models are used to establish links between microscale deformation mechanisms and macroscale, experimentally-observable behavior. The macroscale behavior arises from the complex interplay of different physical mechanisms operating at the smaller microscales. Sometimes, which are such mechanisms are not clear. Other times, the mechanisms are clear, but not so much as how the experimental observations originate from them. Between the micro and the macroscale, mesoscale models represent a material’s plastic deformation based on stochastic processes, with great independence of microscale details (see here for an introduction to mesocale models).
By tailoring the properties of such stochastic processes to reproduce experimental observations, we learn about the origins of the macroscale observations. Also, it helps us establish the links between the scales mentioned above. However, this process corresponds only to the forward problem. The biggest challenge lies in the inverse problem, i.e., what is the mesoscale model setup that quantitatively reproduces the observations better? This is an optimization problem that entails finding the optimum stochastic processes and parameter values.
Nonetheless, mesoscale models have remained widely qualitative and have rarely attempted to solve the inverse optimization problem. The reason is that it is very difficult to obtain detailed information about mesoscale processes from macroscale observations or atomistic microscale properties. Moreover, some mesoscale parameters behave as latent variables whose values cannot be directly measured and must be inferred from the observed variables assuming a statistical model.
To perform mesoscale measurements, we sample the local mechanical response at different coarse-graning scales
Moreover, proving that mesoscale models can quantitatively reproduce the observations beyond qualitative similarity is crucial since that justifies and legitimizes the mesoscale approach. To this end, in this work, we apply a newly developed method that extracts mesoscale information from atomistic models. We can use this method to optimize different mesoscale models by minimizing a loss function. We show that we can establish optimal parameter values and microscale physical deformation mechanisms that lead to excellent agreements between the model and the observations. Moreover, our work sheds light on the relevance of different model ingredients. For example, spatial correlations do not significantly improve the model’s ability to reproduce experimental observations. This fact might considerably reduce the complexity of the problem and be leveraged by future models. Also, we find that structural heterogeneity is fundamental. However, the results are not sensitive to the exact origin of such heterogeneity. This work is one of the first in a novel direction, namely designing quantitatively accurate mesoscale models of plastic deformation. This is an area with the potential to impact the multi-scale modeling of the mechanical properties of materials.
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Article Abstract
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. We show that the macroscale 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. In particular, we show that the elasto-plastic model reproduces the Bauschinger effect, namely the plasticity-induced anisotropy in the 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.
D. F. Castellanos, S. Roux & S. Patinet