Accurate Evaluations of Strain and Stress in Atomistic Simulations of Crystalline Solids

TL;DR

This paper evaluates and improves the accuracy of atomistic simulation formulas for stress and strain in crystalline solids by proposing new kernel functions and validation methods.

Contribution

It introduces criteria and a procedure for selecting kernel functions that enhance the sampling accuracy of continuum quantities from atomistic data.

Findings

Proposed new criteria for kernel function selection.

Developed a procedure to construct improved kernel functions.

Validated the approach with numerical tests on various systems.

Abstract

In this paper, we study the accuracy of Irving-Kirkwood type of formulas for the approximation of continuum quantities from atomistic simulations. Such formulas are derived by expressing the displacement, deformation gradient and stress in terms of certain kernel functions. We propose two criteria for choosing the kernel functions to significantly improve the sampling accuracy. We present a simple procedure to construct kernel functions that meet these criteria. Further, numerical tests on homogeneous and non-homogeneous systems provide validations for our analysis.