Ghost forces and spurious effects in atomic-to-continuum coupling methods by the arlequin approach

The main objective of this work is to identify spurious effects and propose a corrective method when coupling a particle model involving long-range interaction potentials with a first gradient homogenized model using the Arlequin framework. The most significant spurious effects are generally created by the so-called ghost forces that arise in coupling methods based on the minimization of a global energy functional. They depend as well on the coupling formulation itself, on the notion of representative volume element, and on the discretization of the continuum model. The proposed corrective technique is based on post-processing of the approximate solution by introducing dead forces that can be systematically evaluated and consistently inserted within the Arlequin formulation. Efficiency of the corrective procedure is demonstrated on 1D and 2D examples.