Coupled atomistic-continuum simulations using arbitrary overlapping domains

Journal of Computational Physics

Volumn 213, Issue 1, 2006, Pages 86-116

  Klein, P A ^a   Zimmerman, J A ^a  

^a SANDIA NATIONAL LABORATORIES   (United States)

Author keywords

Atomistic simulation; Continuum mechanics; Coupling; Finite elements

Indexed keywords

FINITE ELEMENT METHOD; POTENTIAL ENERGY;

ATOMISTIC SIMULATIONS; ATOMISTICS; CAUCHY-BORN RULE; COMPUTATIONAL DOMAINS; CONTINUUM SIMULATIONS; DISCRETIZATIONS; FINITE ELEMENT; QUASI-STATIC AND DYNAMIC ANALYSIS; REGION-OF-INTEREST; REGIONS OF INTEREST;

CONTINUUM MECHANICS;

EID: 31744436105     PISSN: 00219991     EISSN: 10902716     Source Type: Journal    
DOI: 10.1016/j.jcp.2005.08.014     Document Type: Article

References (39)

1. Materials research by means of multiscale computer simulation, Bulletin, Materials Research Society, March, 2001.
2. J. Fish Z. Yuan Multiscale enrichment based on partition of unity International Journal of Numerical Methods in Engineering 62 10 2005 1341-1359
3. S. Kohlhoff S. Schmauder A new method for coupled elastic-atomistic modelling V. Vitek D.J. Srolovitz Atomistic Simulation of Materials: Beyond Pair Potentials 1989 Plenum Press New York 411-418
4. S. Kohlhoff P. Gumbsch H.F. Fischmeister Crack propagation in BCC crystals studied with a combined finite-element and atomistic model Philosophical Magazine A 64 1991 851-878
5. E.B. Tadmor M. Ortiz R. Phillips Quasicontinuum analysis of defects in solids Philosophical Magazine A 73 6 1996 1529-1563
6. R.E. Rudd J.Q. Broughton Coarse-grained molecular dynamics and the atomic limit of finite elements Physical Review B 58 1998 R5893-R5896
7. J.Q. Broughton F.F. Abraham N. Bernstein E. Kaxiras Concurrent coupling of length scales: Methodology and application Physical Review B 60 1999 2391-2403
8. G.J. Wagner W.K. Liu Coupling of atomistic and continuum simulations using a bridging scale decomposition Journal of Computational Physics 190 2003 249-274
9. L.E. Malvern Introduction to the Mechanics of a Continuous Medium 1969 Wiley New York
10. K. Huang On the atomic theory of elasticity Proceedings of the Royal Society of London A 203 1950 178-194
11. M. Born K. Huang Dynamical Theories of Crystal Lattices 1956 Clarendon Press Oxford
12. R.E. Rudd Coarse-grained molecular dynamics: Dissipation due to internal modes Thin Films: Stresses and Mechanical Properties IX Materials Research Society Symposium Proceedings vol. 695 2002 Materials Research Society 499-504
13. H.S. Park E.G. Karpov W.K. Liu P.A. Klein The bridging scale for two-dimensional atomistic/continuum coupling Philosophical Magazine 85 1 2005 79-113
14. H.S. Park E.G. Karpov P.A. Klein W.K. Liu Three-dimensional bridging scale analysis of dynamic fracture Journal of Computational Physics 207 2 2005 588-609
15. S.P. Xiao T. Belytschko A bridging domain method for coupling continua with molecular dynamics Computer Methods in Applied Mechanics and Engineering 193 2004 1645-1669
16. W.A. Curtin R.A. Miller Atomistic/continuum coupling in computational materials science Modelling and Simulation in Materials Science and Engineering 11 2003 R33-R68
17. V.B. Shenoy R. Miller E.B. Tadmor D. Rodney R. Phillips M. Ortiz An adaptive finite element approach to atomic-scale mechanics - the quasicontinuum method Journal of the Mechanics and Physics of Solids 47 1999 611-642
18. J. Knap M. Ortiz An analysis of the quasicontinuum method Journal of the Mechanics and Physics of Solids 49 2001 1899-1923
19. I. Stakgold The Cauchy relations in a molecular theory of elasticity Quarterly of Applied Mechanics 8 1950 169-186
20. E.B. Tadmor G.S. Smith N. Bernstein E. Kaxiras Mixed finite element and atomistic formulation for complex crystals Physical Review B 59 1 1999 235-245
21. P. Zhang Y. Huang P.H. Geubelle P.A. Klein K.C. Hwang The elastic modulus of single-wall carbon nanotubes: A continuum analysis incorporating interatomic potentials International Journal of Solids and Structures 39 2002 3893-3906
22. T.J.R. Hughes The Finite Element Method: Linear Static and Dynamic Finite Element Analysis 1987 Prentice-Hall Englewood Cliffs, NJ
23. J.R. Shewchuk, An introduction to the conjugate gradient method without the agonizing pain (1994). Available from: .
24. W.K. Liu Y. Chen S. Jun J.S. Chen T. Belytschko C. Pan R.A. Uras C.T. Chang Overview and applications of the reproducing kernel particle methods Archives of Computational Methods in Engineering: State of the Art Reviews 3 1996 3-80
25. W.K. Liu Y. Chen Reproducing kernel particle methods International Journal for Numerical Methods in Fluids 20 1995 1081-1106
26. H. Gao P. Klein Numerical simulation of crack growth in an isotropic solid with randomized internal cohesive bonds Journal of the Mechanics and Physics of Solids 46 2 1998 187-218
27. P. Klein H. Gao Crack nucleation and growth as strain localization in a virtual-bond continuum Engineering Fracture Mechanics 61 1998 21-48
28. H. Engl M. Hanke A. Neubauer Regularization of Inverse Problems 1996 Kluwer Academic Publishers Dordrecht
29. Tahoe, Sandia National Laboratories, 2004. Available from: .
30. E. Hinton T. Rock O.C. Zienkiewicz A note on mass lumping and related processes in the finite element method Earthquake Engineering and Structural Dynamics 4 1976 245-249
31. J.E. Lennard-Jones The determination of molecular fields I. From the variation of the viscosity of a gas with temperature Proceedings of the Royal Society of London A 106 1924 441
32. J.E. Lennard-Jones The determination of molecular fields II. From the equation of state of a gas Proceedings of the Royal Society of London A 106 1924 463
33. J.M. Haile Molecular Dynamics Simulation Elementary Methods 1992 Wiley New York
34. R. Miller E.B. Tadmor R. Phillips M. Ortiz Quasicontinuum simulation of fracture at the atomic scale Modelling and Simulation in Materials Science and Engineering 6 1998 607-638
35. E.B. Tadmor R. Miller R. Phillips M. Ortiz Nanoindentation and incipient plasticity Journal of Materials Research 14 6 1999 2233-2250
36. G.S. Smith E.B. Tadmor N. Bernstein E. Kaxiras Multiscale simulations of silicon nanoindentation Acta Materialia 49 2001 4089-4101
37. J. Knap M. Ortiz Effect of indenter-radius size on Au(0 0 1) nanoindentation Physical Review Letters 90 22 2003 226102
38. S.M. Foiles M.I. Baskes M.S. Daw Embedded-atom-method functions for the fcc metals cu, ag, au, ni, pd, pt, and their alloys Physical Review B 33 1986 7983-7991
39. F.H. Stillinger T.A. Weber Computer simulation of local order in condensed phases of silicon Physical Review B 31 1985 5262-5271