On the application of the Arlequin method to the coupling of particle and continuum models

Bauman, Paul T.; Dhia, Hachmi Ben; Elkhodja, Nadia; Oden, J. T.; Prudhomme, Serge

doi:10.1007/s00466-008-0291-1

Cited by 129 publications

(163 citation statements)

References 18 publications

(16 reference statements)

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“…This is the case in the so-called quasicontinuum method where, roughly spoken, the resolution of a FE domain is locally increased to that of the underlying atomic lattice. Other approaches, such as the bridging domain method 33 or the Arlequin method, 34 define an overlap region which does not require a particle lattice any more.…”

Section: Introductionmentioning

confidence: 99%

Nonperiodic stochastic boundary conditions for molecular dynamics simulations of materials embedded into a continuum mechanics domain

Rahimi

Karimi–Varzaneh

Böhm

et al. 2011

The Journal of Chemical Physics

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A scheme is described for performing molecular dynamics simulations on polymers under nonperiodic, stochastic boundary conditions. It has been designed to allow later the embedding of a particle domain treated by molecular dynamics into a continuum environment treated by finite elements. It combines, in the boundary region, harmonically restrained particles to confine the system with dissipative particle dynamics to dissipate energy and to thermostat the simulation. The equilibrium position of the tethered particles, the so-called anchor points, are well suited for transmitting deformations, forces and force derivatives between the particle and continuum domains. In the present work the particle scheme is tested by comparing results for coarse-grained polystyrene melts under nonperiodic and regular periodic boundary conditions. Excellent agreement is found for thermodynamic, structural, and dynamic properties.

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Section: Introductionmentioning

confidence: 99%

Nonperiodic stochastic boundary conditions for molecular dynamics simulations of materials embedded into a continuum mechanics domain

Rahimi

Karimi–Varzaneh

Böhm

et al. 2011

The Journal of Chemical Physics

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“…The Bridging Domain method (BDM) uses the concepts of the Arlequin approach [65][66][67][68] which can intermix energies of several continuum mechanical models and constrain consistent displacements within an overlaping zone (also termed as the bridging domain). Xiao et al applied this strategy for coupling continuum models with molecular dynamics (MD) [49,69].…”

Section: State Of the Art Of Multiscale Methodsmentioning

confidence: 99%

MD/FE Multiscale Modeling of Contact

Ramisetti

Anciaux

Molinari

2014

Fundamentals of Friction and Wear on the Nanoscale

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Limitations of single scale approaches to study the complex physics involved in friction have motivated the development of multiscale models. We review the state-of-the-art multiscale models that have been developed up to date. These have been successfully applied to a variety of physical problems, but that were limited, in most cases, to zero Kelvin studies. We illustrate some of the technical challenges involved with simulating a frictional sliding problem, which by nature generates a large amount of heat. These challenges can be overcome by a proper usage of spatial filters, which we combine to a direct finite-temperature multiscale approach coupling molecular dynamics with finite elements. The basic building block relies on the proper definition of a scale transfer operator using the least square minimization and spatial filtering. Then, the restitution force from the generalized Langevin equation is modified to perform a two-way thermal coupling between the two models. Numerical examples are shown to illustrate the proposed coupling formulation.

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“…A representative example of an energy-based method, defined by blending of atomistic and continuum energy functionals, can be found in [8]. One-dimensional results and analysis for blending harmonic potentials and linear elasticity via the Arlequin method [16] is the subject of [6,34]. The overlapping AtC method presented in [24] can also be considered a blending method, and demonstrates how ghost forces can be eliminated by considering a patch test.…”

Section: An Overview Of Atc Blending Methodsmentioning

confidence: 99%

“…We remind that in this approach the constraints are imposed on the solution spaces, which transforms (6.33) into the following unconstrained minimization problem: find 6 …”

Section: Blending Methods For Coupling Atomistic and Continuum Modelsmentioning

confidence: 99%

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Blending Methods for Coupling Atomistic and Continuum Models

Bochev¹,

Lehoucq²,

Parks³

et al. 2009

Multiscale Methods

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In this paper we review recent developments in blending methods for atomisticto-continuum (AtC) coupling in material statics problems. Such methods tie together atomistic and continuum models by using a bridge domain that connects the two models. There are several reasons why AtC coupling methods (of which blending methods are a subset) are important and have been subject to an increased interest in the recent years. Despite tremendous increases in computational power, fully atomistic simulations on an entire model domain remain computationally infeasible for many applications of interest. As a result, attention has focused on hybrid schemes where in all regions with well-behaved solutions, the atomistic (microscopic) model is replaced by a (macroscopic) continuum model enabling a more efficient computational scheme (see [14,29,9] for general information). The main challenge is the synthesis of the two distinct models in a manner that minimizes, or altogether eliminates, undesirable artifacts such as ghost forces, unphysical solutions let alone supporting mathematical analysis. Notable AtC coupling methods include the quasicontinuum method [39], the bridging scale decomposition [41], and [24] where atomistic and continuum models are overlapped (see the latter two references, and those mentioned above for numerous citations to the literature). The numerical analysis of AtC methods has lagged in comparison to the number of methods proposed; see the recent papers [2,3,17,31,26,27] for analyses of the quasicontinuum method.Blending methods couple atomistic/continuum modes via a dedicated blending, or bridge, region inserted between the atomistic and continuum subdomains. The atomistic and continuum models are tied together by using a suitable "continuity" condition (or balance law) for the atomistic and continuum positions or displacements in this region. A complicating factor is that the atomistic and (classical) continuum elastic models rely on nonlocal and local models of force interaction, respectively. In the (classical) elastic context, the "local force" is that exerted on a body by contact forces occurring on the surface (of the body). In contrast, in the atomistic model, forces are summed from atoms separated by a finite distance. The incompatibility arising from coupling local and nonlocal force models is intrinsic. The goal of our paper is threefold. First, we review how blending approaches attempt to ameliorate the various negative effects by relying on an interface between the two models. Second, we discuss the beginnings of a JFISH: "CHAP06" -2009/6/4 -17:33 -PAGE 166 -#2 166Blending methods for coupling atomistic and continuum models numerical analysis by discussing consistency of the resulting numerical schemes. Third, we suggest how the intrinsic limitation associated with coupling nonlocal and local mechanical theories may be avoided by replacing the classical elastic theory with a nonlocal elastic theory.The use of a bridge domain in blending methods bears a resemblance to conventional overlapping...

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On the application of the Arlequin method to the coupling of particle and continuum models

Cited by 129 publications

References 18 publications

Nonperiodic stochastic boundary conditions for molecular dynamics simulations of materials embedded into a continuum mechanics domain

Nonperiodic stochastic boundary conditions for molecular dynamics simulations of materials embedded into a continuum mechanics domain

MD/FE Multiscale Modeling of Contact

Blending Methods for Coupling Atomistic and Continuum Models

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