Ghost forces and spurious effects in atomic‐to‐continuum coupling methods by the Arlequin approach

Abstract

SUMMARYThe 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.

A new adaptive modeling strategy based on optimal control for atomic-to-continuum coupling simulations

“…The methodology is necessarily convergent since, in the worst case scenario, the whole domain would be converted to the particle model. The proposed coupling method has already been extensively studied in earlier works [3,16,9,13,4,14]. Let X = X c [ X d denote the domain covered by the lattice with boundary @X.…”

“…The definition of a d ij using an average formulation enables one to weigh the particle energy in a consistent manner that corresponds to defining an energy density at the particle scale. In other words, the partition of unity used to split the two energies is performed in an average sense (see [14] for details). The strain energy E of the original lattice system is then approximated by the global strain energy:…”

Coupling of nonlocal and local continuum models by the Arlequin approach

“…The displacement u d is imposed on the part u of @ and the surface tractions T 1 is imposed on the complementary part T of @ . We refer here to an Arlequin technique [15,20] to couple both models together. The key idea is to implement a partition of the energy over the gluing area between the two models using complementary weight functions, which fall into the category of a partition of unity in terms of energy.…”

A multiscale coupling approach between discrete element method and finite difference method for dynamic analysis

“…All the coupling approaches used in the examples described belong to the class of non-overlapping methods, that is, coupling is performed through a common interface and therefore will result in spurious reflections of high-frequency waves at the discrete/continuum interface [23]. This phenomenon has already been addressed by Adelman and Doll [24], Doll and Dion [25], and Celep and Bažant [26] and analyzed in detail in [27].…”