Consistent Energy-based Atomistic/Continuum Coupling for Two-body Potentials in Three Dimensions

TL;DR

This paper introduces a novel, consistent energy-based coupling method for atomistic and continuum models in three dimensions, addressing interface errors and validating stability through numerical tests.

Contribution

It develops a new coupling approach that combines a modified Cauchy-Born continuum model with the exact atomistic model in 3D, ensuring convergence and stability.

Findings

Successful coupling of atomistic and continuum models in 3D

Validated convergence and stability through numerical tests

Enhanced accuracy at the atomistic/continuum interface

Abstract

Very few works exist to date on development of a consistent energy-based coupling of atomistic and continuum models of materials in more than one dimension. The difficulty in constructing such a coupling consists in defining a coupled energy whose minimizers are free from uncontrollable errors on the atomistic/continuum interface. In this paper a consistent coupling in three dimensions is proposed. The main achievement of this work is to identify and efficiently treat a modified Cauchy-Born continuum model which can be coupled to the exact atomistic model. The convergence and stability of the method is confirmed with numerical tests.