Traction Boundary Conditions for Molecular Static Simulations

TL;DR

This paper develops a consistent method for applying traction boundary conditions in atomistic simulations, addressing the complexity of multiple-neighbor interactions and extending the approach to higher dimensions with practical applications.

Contribution

It introduces a novel formulation for traction boundary conditions in atomistic models, including stability analysis and continuum limit derivation, applicable to higher-dimensional problems.

Findings

Boundary conditions formulated for 1D models

Stability analysis of the proposed boundary conditions

Extension to higher-dimensional atomistic problems

Abstract

This paper presents a consistent approach to prescribe traction boundary conditions in atomistic models. Due to the typical multiple-neighbor interactions, finding an appropriate boundary condition that models a desired traction is a non-trivial task. We first present a one-dimensional example, which demonstrates how such boundary conditions can be formulated. We further analyze the stability, and derive its continuum limit. We also show how the boundary conditions can be extended to higher dimensions with an application to a dislocation dipole problem under shear stress.