A closed-form energy expression ensuring consistency in the atomistic-continuum coupling: A one-dimensional atomic chain study

Abstract

It is well known that coupling atomistic and continuum domains introduces inconsistencies near the interface. These inconsistencies manifest as nonphysical forces, known as “ghost forces,” which can lead to significant errors in the solution. In this paper, we propose a novel approach to achieve a consistent atomistic-continuum interface for the quasicontinuum method, applicable to two-body potentials with unlimited range of interaction. To this end, artificial nodes and elements are introduced located at specified positions, and appropriate constraints are applied. We show that in this way, not only ghost forces are eliminated but also the energy remains compatible through the interface. The method is applied to model surface effect and void defect in static problems, as well as to simulate wave propagation. The results demonstrate that the approach substantially improves accuracy in both static and dynamic problems.