Fast and accurate quasi-atom method for simultaneous atomistic and continuum simulation of solids

TL;DR

This paper introduces a hybrid simulation method combining atomistic and continuum models using quasi-atoms optimized via machine learning, achieving high accuracy and significantly improved computational efficiency for solid simulations.

Contribution

The paper presents a novel quasi-atom based hybrid simulation approach that integrates machine learning optimization, enabling fast and accurate atomistic-continuum modeling of solids.

Findings

The method accurately reproduces atomic simulation results.

It significantly reduces computational time compared to full-atomic simulations.

The approach outperforms existing hybrid methods in speed and ease of implementation.

Abstract

We report a novel hybrid method of simultaneous atomistic simulation of solids in critical regions (contacts surfaces, cracks areas, etc.), along with continuum modeling of other parts. The continuum is treated in terms of quasi-atoms of different size, comprising composite medium. The parameters of interaction potential between the quasi-atoms are optimized to match elastic properties of the composite medium to those of the atomic one. The optimization method coincides conceptually with the online Machine Learning (ML) methods, making it computationally very efficient. Such an approach allows a straightforward application of standard software packages for molecular dynamics (MD), supplemented by the ML-based optimizer. The new method is applied to model systems with a simple, pairwise Lennard-Jones potential, as well with multi-body Tersoff potential, describing covalent bonds. Using LAMMPS software we simulate collision of particles of different size. Comparing simulation results, obtained by the novel method, with full-atomic simulations, we demonstrate its accuracy, validity and overwhelming superiority in computational speed. Furthermore, we compare our method with other hybrid methods, specifically, with the closest one -- AtC (Atomic to Continuum) method. We demonstrate a significant superiority of our approach in computational speed and implementation convenience. Finally, we discuss a possible extension of the method for modeling other phenomena.