Automated analysis of continuum fields from atomistic simulations using statistical machine learning

TL;DR

This paper introduces a machine learning-based methodology to analyze continuum fields from atomistic simulations, revealing distribution patterns of strain and microrotation that inform higher-scale material models.

Contribution

It develops a statistical data mining approach to automate the analysis of continuum variables in atomistic simulations, identifying distribution types and deformation mechanisms.

Findings

Elastic strain follows a unimodal log-normal distribution.

Total strain and microrotation exhibit multimodal distributions.

Gaussian mixture models effectively identify distribution peaks.

Abstract

Atomistic simulations of the molecular dynamics/statics kind are regularly used to study small scale plasticity. Contemporary simulations are performed with tens to hundreds of millions of atoms, with snapshots of these configurations written out at regular intervals for further analysis. Continuum scale constitutive models for material behavior can benefit from information on the atomic scale, in particular in terms of the deformation mechanisms, the accommodation of the total strain and partitioning of stress and strain fields in individual grains. In this work we develop a methodology using statistical data mining and machine learning algorithms to automate the analysis of continuum field variables in atomistic simulations. We focus on three important field variables: total strain, elastic strain and microrotation. Our results show that the elastic strain in individual grains exhibits a unimodal log-normal distribution, whilst the total strain and microrotation fields evidence a multimodal distribution. The peaks in the distribution of total strain are identified with a Gaussian mixture model and methods to circumvent overfitting problems are presented. Subsequently, we evaluate the identified peaks in terms of deformation mechanisms in a grain, which e.g., helps to quantify the strain for which individual deformation mechanisms are responsible. The overall statistics of the distributions over all grains are an important input for higher scale models, which ultimately also helps to be able to quantitatively discuss the implications for information transfer to phenomenological models.