A comparison of staggered solution schemes for coupled particle-continuum systems modeled with the Arlequin method

Computational Mechanics

Volumn 49, Issue 5, 2012, Pages 565-579

  Pfaller, S ^a   Possart, G ^a   Steinmann, P ^a   Rahimi, M ^b   Muller Plathe F ^b   Bohm M C ^b  

^a UNIVERSITY OF ERLANGEN NUREMBERG   (Germany)

^b DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

Atomistic continuum coupling; Bridging domain method; Domain decomposition; Lagrange multipliers; Multiscale modeling

Indexed keywords

DOMAIN DECOMPOSITION METHODS; ITERATIVE METHODS; LAGRANGE MULTIPLIERS; PROGRAM PROCESSORS;

ANHARMONIC INTERACTION; BRIDGING DOMAIN METHODS; CONVERGENCE BEHAVIORS; COUPLING CONSTRAINTS; DIFFERENT RESOLUTIONS; MULTI-SCALE MODELING; ONE-DIMENSIONAL SYSTEMS; STANDARD FINITE ELEMENT;

LENNARD-JONES POTENTIAL;

EID: 84862124198     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-011-0657-7     Document Type: Article

References (20)

1. Aubertin P, Rethore J, de Borst R (2009) Energy conservation of atomistic/continuum coupling. Int J Numer Methods Eng 78:1365-1386
2. Bauman PT, Ben Dhia H, Elkhodja N, Oden JT, Prudhomme S (2008) On the application of the Arlequin method to the coupling of particle and continuum models. Comput Mech 42:511-530
3. Bauman PT, Oden JT, Prudhomme S (2009) Adaptive multiscale modeling of polymeric materials with Arlequin coupling and Goals algorithms. Comput Methods Appl Mech Eng 198:799-818
4. Belytschko T, Xiao SP (2003) Coupling methods for continuum model with molecular model. Int J Multiscale Comput Eng 1:115-126
5. Ben Dhia H (1998) Problèmes méchaniques multi-échelles: la méthode Arlequin. Comptes Rendus de l'Académie des Science, Series II b 326:899-904 (Pubitemid 29369493)
6. Ben Dhia H, Rateau G (2001) Analyse mathématique de la méthode Arlequin mixte. Comptes Rendus de l'Académie des Science, Series I 332:649-654 (Pubitemid 33623930)
7. Ben Dhia H, Rateau G (2005) The Arlequin method as a flexible engineering design tool. Int J Numer Methods Eng 62:1442-1462 (Pubitemid 40413094)
8. Ben Dhia H, Elkhodja N, Roux FX (2008) Multimodeling of multi-alterated structures in the Arlequin framework. Solution with a domain-decomposition solver. Eur J Comput Mech 17:969-980
9. Chamoin L, Oden JT, Prudhomme S (2008) A stochastic coupling method for atomic-to-continuum Monte-Carlo simulations. Com-put Methods Appl Mech Eng 197:3530-3546
10. Delgado-Buscalioni R, Kremer K, Praprotnik M (2008) Concurrent triple-scale simulation of molecular liquids. J Chem Phys 128:114110
11. Farhat C, Roux FX (1991) A method of Finite Element tearing and interconnecting and its parallel solution algorithm. Int J Numer Methods Eng 32:1205-1227 (Pubitemid 21718586)
12. 1 couplings for an overlapping domain decomposition method using Lagrange multipliers. Int J Numer Methods Eng 70:322-350 (Pubitemid 46584372)
13. Khare R, Mielke SL, Paci JT, Zhang S, Ballarini R, Schatz GC, Belytschko T (2007) Coupled quantum mechanical/molecular mechanical modeling of the fracture of defective carbon nanotubes and graphene sheets. Phys Rev B 75:075412
14. Khare R, Mielke SL, Schatz GC, Belytschko T (2008) Multiscale coupling schemes spanning the quantum mechanical, atomistic forcefield, and continuum regimes. Comput Methods Appl Mech Eng 197:3190-3202
15. Rahimi M, Karimi-Varzaneh HA, Böhm MC, Müller-Plathe F, Pfaller S, Possart G, Steinmann P (2011) Nonperiodic stochastic boundary conditions for molecular dynamics simulations of materials embedded into a continuum mechanics domain. J Chem Phys 134:154108
16. Schmidt M (2006) Minimization toolbox "minFunc", available as Matlab code at http://www.cs.ubc.ca/~schmidtm
17. Tadmor EB, Ortiz M, Phillips R (1996) Quasicontinuum analysis of defects in solid. Philos Mag A 73(6):1529-1563
18. Xiao SP, Belytschko T (2004) A bridging domain method for coupling continua with molecular dynamics. Comput Methods Appl Mech Eng 193:1645-1669 (Pubitemid 38462116)
19. Xu M, Belytschko T (2008) Conservation properties of the bridging domain method for coupled molecular/continuum dynamics. Int J Numer Methods Eng 76:278-294
20. Zhang S, Khare R, Lu Q, Belytschko T (2007) A bridging domain and strain computation method for coupled atomistic-continuum modelling of solids. Int J Numer Methods Eng 70:913-933 (Pubitemid 46823032)