A machine-learning aided multiscale homogenization model for crystal plasticity: application for face-centered cubic single crystals

摘要

Quantitative prediction on mesoscale crystal plasticity via first principle-based methods or first principle-based multiscale methods is still unreachable, even though several approaches have arisen throughout decades for developing atomic-informed models for modeling crystalline materials from first principles. Several major difficulties have prevented to first principle-based realistic prediction of mechanical material properties. For instance, the solution of numerical models is highly affected by the loading rate and the size of the model. In this work, we aim to develop a procedure that efficiently eliminates the loading rate and the mesh size effects. This is achieved by first using machine learning (ML)-aided constitutive relations extrapolated from the first-principle-based modeling for the finite element solver, and then assessing the stress-strain relation at the mesoscale based on the homogenized strain field but utilizing the same atomistic or lattice information. As it may compromise the consistency at the finite element level, yet the calculations are based on the same atomistic potential, but performed independently. This can be interpreted as using the FE as an auxiliary tool for calculating the deformations field and achieving homogenization, while the stresses are computed from the atomic-based potential. It is shown herein that the proposed ML-based multiscale method significantly enhances the accuracy of the homogenization results comparing with other multiscale methods reported in the literature.