A Spectral Multiscale Method for Wave Propagation Analysis: Atomistic-Continuum Coupled Simulation

TL;DR

This paper introduces a spectral multiscale method that effectively couples atomistic and continuum models for high-frequency wave propagation, reducing non-physical reflections and accurately simulating complex crystalline dynamics.

Contribution

A novel spectral domain decomposition approach that eliminates interfacial wave reflection in atomistic-continuum coupling for wave analysis.

Findings

Accurately matches molecular dynamics results in 1D and 2D lattice simulations.

Effectively reduces non-physical wave reflections at scale interfaces.

Demonstrates robustness in simulating complex crystalline behaviors.

Abstract

In this paper, we present a new multiscale method which is capable of coupling atomistic and continuum domains for high frequency wave propagation analysis. The problem of non-physical wave reflection, which occurs due to the change in system description across the interface between two scales, can be satisfactorily overcome by the proposed method. We propose an efficient spectral domain decomposition of the total fine scale displacement along with a potent macroscale equation in the Laplace domain to eliminate the spurious interfacial reflection. We use Laplace transform based spectral finite element method to model the macroscale, which provides the optimum approximations for required dynamic responses of the outer atoms of the simulated microscale region very accurately. This new method shows excellent agreement between the proposed multiscale model and the full molecular dynamics (MD) results. Numerical experiments of wave propagation in a 1D harmonic lattice, a 1D lattice with Lennard-Jones potential, a 2D square Bravais lattice, and a 2D triangular lattice with microcrack demonstrate the accuracy and the robustness of the method. In addition, under certain conditions, this method can simulate complex dynamics of crystalline solids involving different spatial and/or temporal scales with sufficient accuracy and efficiency.