Machine learning-based multiscale framework for mechanical behavior of nano-crystalline structures

In this paper, a computational atomistic-continuum multiscale framework is developed based on the machine learning (ML) architecture to capture the nonlinear behavior of nano-crystalline structures. The dataset of the ML process is derived from analyzing the atomistic representative volume element (RVE) through the molecular dynamics method under various deformation paths. A comprehensive investigation is performed on the influential parameters of the atomistic RVE that leads to the determination of an appropriate atomistic RVE for reproducing the mechanical characteristics from fine-scale to coarse-scale level. The multilayer perceptron neural network approach (MLP-ANN) is employed in the optimization algorithm of the ML process to train the atomistic dataset. The performance of the ML model is validated by predicting the response of atomistic RVE under various deformation gradients. Finally, the proposed computational algorithm is employed for the simulation of several mechanical benchmark problems, including the uniaxial tensile test, pure shear test, pure torsion test, and nano-indentation problem. Numerical simulations are validated by comparing the results of machine learning-based multiscale analysis with the fully atomistic model and experimental data. It is shown that the proposed ML-based method enhances the multiscale analysis to capture the nonlinear behavior of nanocrystalline structures without computational complexities associated with conventional multiscale methods. The results highlight that the proposed multiscale framework can be utilized as a constitutive model for the largescale analysis with a great accuracy and unique efficiency.