Prediction of nonlocal elasticity parameters using high-throughput molecular dynamics simulations and machine learning

Higher-order elasticity theories are able to model the mechanics at nanoscale. However, these theories have length-scale parameters that need to be evaluated either through experiments or molecular dynamics (MD) simulations. In the current literature, these length-scale parameters are assumed to be constant for a chosen material. However, this is not true, as shown in this paper through a set of high-throughput MD simulations on a variety of boundary value problems (BVP). For carbon and boron nitride nanotubes, the length-scale parameter in the modified strain gradient theory is found to vary with the absolute dimensions, type of the BVP, and the deformation level. This complex dependence makes prediction of the length-scale parameter 10 challenging. To address this issue, a supervised machine learning (ML) based framework is developed here. In this new framework, MD, continuum formulation, and ML are used in tandem to predict the length-scale parameter for a given material, dimension, and boundary condition. It is a three-step process. First, a number of MD simulations are performed for varying chirality, length, and boundary conditions. Then, the values of 10 are found using these MD output in the continuum formulation. Finally, an ML-based regression model is used to capture the variability of 10 and subsequently predict its value for any chirality, length, and boundary condition. Here three regression models - Gaussian process regression, support vector machine, and neural network - are used to make the predictions.This predictive tool eliminates need for expensive MD simulations for further continuum scale analysis. In a broader context, this novel three-step framework opens an accurate yet inexpensive door for applying non-classical continuum theories to nanoscale mechanics problems. The accuracy is imposed by the MD simulations, while the computational cost reduction is achieved by machine learning.