Reformulation of microscopic balance equations for multiscale materials modeling

Area of Science:

• Multiscale modeling
• Materials science
• Computational physics

Background:

• Atomistic simulations are crucial for understanding materials at the nanoscale.
• Bridging the gap between atomistic and continuum models remains a challenge.
• Existing methods struggle to accurately represent complex lattice dynamics.

Purpose of the Study:

• To present a novel formalism for atomistic systems with general lattice structures.
• To develop a concurrent two-level representation of balance laws.
• To enable accurate multiscale simulations of crystalline materials.

Main Methods:

• Analytically linking atomic variables to continuously distributed local properties.
• Decomposing fluxes in multiatomic lattices into lattice distortions and atomic rearrangements.
• Formulating balance laws suitable for both fine-scale atomistic and coarse-scale continuum analysis.

Main Results:

• A new formalism for atomistic systems with general lattice structures.
• A concurrent two-level representation of balance laws.
• A continuum field representation of classical N-body dynamics capable of reproducing phonon dispersion relations.

Conclusions:

• The new formulation facilitates direct atomistic analysis and continuum analysis.
• It enables coupled atomistic and continuum simulations within a unified framework.
• This work provides a pathway for accurate multiscale simulations of crystalline materials.