A continuum-to-atomistic bridging domain method for composite lattices

International Journal for Numerical Methods in Engineering

Volumn 81, Issue 13, 2010, Pages 1635-1658

  Xu, Mei ^a   Gracie, Robert ^b   Belytschko, Ted ^a  

^a Northwestern University   (United States)

^b UNIVERSITY OF WATERLOO   (Canada)

Author keywords

Atomistic continuum coupling; Bridging domain; Composite lattice; Lagrange multipliers; Molecular mechanics; Multiscale

Indexed keywords

BRIDGING DOMAINS; COMPOSITE LATTICE; COMPOSITE LATTICES; MULTISCALE; MULTISCALES;

ATOMS; CONTINUUM MECHANICS; CORRELATION THEORY; DOMAIN DECOMPOSITION METHODS; FUNCTION EVALUATION; MOLECULAR MECHANICS;

LAGRANGE MULTIPLIERS;

EID: 77149180119     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2745     Document Type: Article

References (43)

1. Abraham FF, Broughton JQ, Bernstein N, Kaxiras E. Spanning the length scales in dynamic simulation. Computational Physics 1998; 12(6):538-546.
2. Broughton JQ, Abraham FF, Bernstein N, Kaxiras E. Concurrent coupling of length scales: methodology and application. Physical Review B 1999; 60(4):2391-2403.
3. Khare R, Mielke SL, Schatz GC, Belytschko T. Multiscale coupling schemes spanning the quantum mechanical, atomistic forcefield, and continuum regimes. Computer Methods in Applied Mechanics and Engineering 2008; 197:3190-3202.
4. Smith GS, Tadmor EB, Bernstain N, Kaxiras E. Multiscale simulations of silicon nanoindentation. Acta Materialia 2001; 49(5):4089-4101.
5. Tadmor EB, Ortiz M, Phillips R. Quasicontinuum analysis of defects in solids. Philosophical Magazine A 1996; 73(6):1529-1563.
6. Shilkrot LE, Curtin WA, Miller RE. A coupled atomistic/continuum model of defects in solids. Journal of the Mechanics and Physics of Solids 2002; 50(10):2085-2106.
7. Gracie R, Belytschko T. Concurrently coupled atomistic and XFEM models for dislocations and cracks. International Journal for Numerical Methods in Engineering 2008; 78(3):354-378.
8. Abraham F, Walkup R, Gao H, Duchaineau M, la Rubia TD, Seager M. Simulating materials failure by using up to one billion atoms and the world's fastes computer: work-hardening. Proceedings of the National Academy of Sciences of the United States of America 2002; 99(9):5783-5787.
9. Buehler MJ, Hartmaier A, Gao H, Duchaineau M, Abraham FF. Atomic plasticity: description and analysis of a one-billion atom simulation of ductile materials failure. Computer Methods in Applied Mechanics and Engineering 2004; 193:5257-5282.
10. Baskes MI, Melius CF, Wilson WD. Solubility and diffusivity of hydrogen and helium at dislocations and in the stress field near a crack tip. Journal of Metals 1980; 32(8):14-14.
11. Mullins M, Dokainish MA. Simulation of the (001) plane crack in-iron employing a new boundary scheme. Philosophical Magazine A 1982; 46(5):771-787.
12. Kohlhoff S, Gumbsch P, Fischmeister HF. Crack propagation in bcc crystals studied with a combined finite-element and atomistic model. Philosophical Magazine A 1991; 64(4):851-878.
13. Shenoy VB, Miller R, Tadmor EB, Rodney D, Phillips R, Ortiz M. An adaptive finite element approach to atomistic-scale mechanics-the quasicontinuum method. Journal of the Mechanics and Physics of Solids 1999; 47(5):611-642.
14. Knap J, Ortiz M. An analysis of the quasicontinuum method. Journal of the Mechanics and Physics of Solids 2001; 49(5):1899-1923.
15. Belytschko T, Xiao SP. Coupling methods for continuum model with molecular model. International Journal for Multiscale Computational Engineering 2003; 1(1):115-126.
16. Xiao SP, Belytschko T. A bridging domain method for coupling continua with molecular dynamics. Computer Methods in Applied Mechanics and Engineering 2004; 193:1645-1669.
17. Ben Dhia H. Multiscale mechanical problems: the Arlequin method. Comptes Rendus de l'Acadmie des sciences, Paris 1998; 326(12):899-904.
18. Ben Dhia H, Rateau G. The Arlequin method as a flexible engineering design tool. International Journal for Numerical Methods in Engineering 2005; 62(11):1442-1462.
19. Guidault P-A, Belytschko T. Bridging domain methods for coupled atomistic-continuum models with L2 or H1 couplings. International Journal for Numerical Methods in Engineering 2007; 77(11):1566-1592.
20. Fish J, Nuggehally MA, Shephard MS, Picu CR, Badia S, Parks ML, Gunzburger M. Concurrent AtC coupling based on a blend of the continuum stress and the atomistic force. Computer Methods in Applied Mechanics and Engineering 2007; 196:4548-4560.
21. Badia S, Bochev P, Fish J, Gunzburger M, Lehoucq R, Nuggehally M, Parks ML. A force-based blending model for atomistic-to-continuum coupling. International Journal for Multiscale Computational Engineering 2007; 5(5):387-406.
22. Wagner GJ, Liu WK. Coupling of atomistic and continuum simulations using a bridging scale decomposition. Journal of Computational Physics 2003; 190(1):249-274.
23. Prudhomme S, Ben Dhia H, Bauman PT, Elkhodja N, Oden JT. Computational analysis of modeling error for the coupling of particle and continuum models by the Arlequin method. Computer Methods in Applied Mechanics and Engineering 2008; 197:3399-3409.
24. Xiao S, Yang W. A temperature-related homogenization technique and its implementation in the meshfree particle method for nanoscale simulations. International Journal for Numerical Methods in Engineering 2007; 69(10):2099-2125.
25. Karpov EG, Park HS, Liu WK. A phonon heat bath approach for the atomistic and multiscale simulation of solids. International Journal for Numerical Methods in Engineering 2007; 70(3):351-378.
26. Chirputkar SU, Qian D, Source C. Coupled atomistic/continuum simulation based on extended space-time finite element method. Computer Modeling in Engineering and Sciences 2008; 24:185-202.
27. To AC, Li S. Perfectly matched multiscale simulations. Physical Review B 2005; 72(3):035414.
28. Engquist WEB, Li X, Ren W, Eijnden EV. Heterogeneous multiscale methods: a review. Communications in Computational Physics 2007; 2(3):367-450.
29. Curtin WA, Miller RE. Atomistic/continuum coupling in computational materials science. Modelling and Simulation in Materials Science and Engineering 2003; 11(3):R33-R68.
30. Miller RE, Tadmor EB. Hybrid continuum mechanics and atomistic methods for simulating materials. MRS Bulletin 2007; 32:920-926.
31. Miller RE, Tadmor EB, Rajgarhia RK, Spearot DE, Saxena A, Massih AR, Jernkvist LO. A unified framework and performance benchmark of fourteen multiscale atomistic/continuum coupling methods. Modelling and Simulation in Materials Science and Engineering 2009; 17:053001.
32. Weiner JH. Statistical Mechanics of Elasticity. Dover Publications Inc.: New York, 2002.
33. Tadmor EB, Smith GS, Bernstein N, Kaxiras E. Mixed finite element and atomistic formulation for complex crystals. Physical Review B 1999; 59(1):235-245.
34. Klein PA. A virtual internal bond approach to modeling crack nucleation and growth. Ph.D. Dissertation, Stanford University, 1999.
35. Arroyo M, Belytschko T. An atomistic-based finite deformation membrane for single layer crystalline films. Journal of the Mechanics and Physics of Solids 2002; 50(9):1941-1977.
36. Martin JW. Many-body forces in solids and the Brugger elastic constants. II. Inner elastic constants. Journal of Physics C: Solid State Physics 1975; 8:2858-2868.
37. Zhou J, Huang R. Internal lattice relaxation of single-layer graphene under in-plain deformation. Journal of the Mechanics and Physics of Solids 2008; 56:1609-1623.
38. Bauman PT, Ben Dhia H, Elkhodja N, Oden JT, Prudhomme S. On the application of the Arlequin method to the coupling of particle and continuum models. Computational Mechanics 2008; 42(5):511-530.
39. Zhang S, Mielke SL, Khare R, Troya D, Ruoff RS, Schatz GC, Belytschko T. Mechanics of defects in carbon nanotubes: Atomistic and multiscale simulations. Physical Review B 2005; 71:115403.
40. Brenner DW, Shenderova OA, Harrison JA, Stuart SJ, Ni B, Sinnott SB. A second-generation reactive empirical bond order (REBO) potential energy expression for hydrocarbons. Journal of Physics: Condensed Matter 2002; 14(4):783-802.
41. Arroyo M, Belytschko T. Finite element methods for the non-linear mechanics of crystalline sheets and nanotubes. International Journal for Numerical Methods in Engineering 2004; 59(3):419-456.
42. Park H, Klein P, Wagner G. A surface Cauchy-Born model for nanoscale materials. International Journal for Numerical Methods in Engineering 2006; 68:1072-1095.
43. Klein PA, Zimmerman JA. Coupled atomistic-continuum simulations using arbitrary overlapping domains. Journal of Computational Physics 2006; 213:86-116.