Temperature-related Cauchy-Born rule for multiscale modeling of crystalline solids

Computational Materials Science

Volumn 37, Issue 3, 2006, Pages 374-379

  Xiao, Shaoping ^a   Yang, Weixuan ^b  

^a UNIVERSITY OF IOWA   (United States)

^b IA United States   (United States)

Author keywords

Cauchy Born rule; Crack; Meshfree particle method; Multiscale modeling; Nanoscale continuum approximation; Temperature

Indexed keywords

ATOMS; CRACK PROPAGATION; DEFORMATION; FREE ENERGY; MOLECULAR DYNAMICS; THERMAL EFFECTS; VIBRATION CONTROL;

CAUCHY-BORN RULE; MESHFREE PARTICLE METHOD; MULTISCALE MODELING; NANOSCALE CONTINUUM APPROXIMATION;

CRYSTALLINE MATERIALS;

EID: 33746000391     PISSN: 09270256     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.commatsci.2005.09.007     Document Type: Article

References (27)

1. Rountree C.L., Kalia R.K., Lidorikis E., Nakano A., Van B.L., and Vashishta P. Atomistic aspects of crack propagation in brittle materials: multimillion atom molecular dynamics simulation. Annu. Rev. Mater. Res. 32 (2002) 377-400
2. Abraham F.F., Walkup R., Gao H., Duchaineau M., Rubia T.D., and Seager M. Simulating materials failure by using up to one billion atoms and the world's fastest computer: brittle fracture. Proc. Nat. Acad. Mater. Sci. USA 99 (2002) 5777-5782
3. Miller R.E., and Tadmor E.B. The quasicontinuum method: overview, applications and current directions. J. Comput. Aid. Mater. Des. 9 (2002) 203-239
4. Tadmor E.B., Phillips R., and Ortiz M. Hierarchical modeling in the mechanics of materials. Int. J. Solids Struct. 37 (2003) 379-389
5. Abraham F., Broughton J., Bernstein N., and Kaxiras E. Spanning the continuum to quantum length scales in a dynamic simulation of brittle fracture. Europhys. Lett. 44 (1998) 783-787
6. Belytschko T., and Xiao S.P. Coupling methods for continuum model with molecular model. Int. J. Multi. Comput. Engrg. 1 (2003) 115-126
7. Xiao S.P., and Belytschko T. A bridging domain method for coupling continua with molecular dynamics. Comput. Method. Appl. Mech. Engrg. 193 (2004) 1645-1669
8. Wagner G.J., and Liu W.K. Coupling of atomic and continuum simulations using a bridging scale decomposition. J. Comput. Phys. 190 (2003) 249-274
9. Curtin W.A., and Miller R.E. Atomistic/continuum coupling in computational materials science. Model. Simul. Mater. Sci. Engrg. 11 (2003) R33-R68
10. Muralidharan K., Deymier P.A., and Simmons J.H. A concurrent multiscale finite difference time domain/molecular dynamics method for bridging an elastic continuum to an atomic system. Model. Simul. Mater. Sci. Engrg. 11 (2003) 487-501
11. Milstein F. In: Hopkins H.G., and Sewell M.J. (Eds). Mechanics of Solids (1982), Pergamon, Oxford
12. Ericksen J.L. The Cauchy-Born hypothesis for crystals. In: Gurtin M. (Ed). Phase Transformations and Material Instabilities in Solids (1984), Academic Press, New York 50-66
13. Arroyo M., and Belytschko T. A finite deformation membrane based on inter-atomic potentials for the transverse mechanics of nanotubes. Mech. Mater. 25 (2003) 193-215
14. Arroyo M., and Belytschko T. An atomistic-based finite deformation membrane for single layer crystalline films. J. Mech. Phys. Solids 50 (2002) 1941-1977
15. Belytschko T., Liu W.K., and Moran B. Nonlinear Finite Elements for Continua and Structures (2001), Wiley, New York
16. Shenoy V., Shenoy V., and Phillips R. Finite temperature quasicontinuum methods. Mater. Res. Soc. Symp. Proc. 538 (1999) 465-471
17. Najafabadi R., and Srolovitz D.J. Order-disorder transitions at and segregation to (0 0 1) NI-PT surfaces. Surf. Sci. 286 (1993) 104-115
18. Garbulsky G.D., and Ceder G. Effect of lattice vibrations on the ordering tendencies in substitutional binary alloys. Phys. Rev. B 49 (1994) 6327-6330
19. Diestler D.J. Coarse-grained descriptions of multiple scale processes in solid systems. Phys. Rev. B 66 (2002) Art. No. 184104
20. Diestler D.J., Wu Z.B., and Zeng X.C. An extension of the quasicontinuum treatment of multiscale solid systems to nonzero temperature. J. Chem. Phys. 121 (2004) 9279-9282
21. Rickman J.M., and LeSar R. Free-energy calculation in material research. Annu. Rev. Mater. Res. 32 (2002) 195-217
22. LeSar R., Najafabadi R., and Srolovitz D.J. Finite-temperature defect properties from free-energy minimization. Phys. Rev. Lett. 63 (1989) 624-627
23. Berendsen H.J.C., Postma J.P.M., van Gunsteren W.F., DiNola A., and Haak J.R. Molecular dynamics with coupling to an external bath. J. Chem. Phys. 81 (1984) 3684-3690
24. Zhou M. A new look at the atomic level virial stress: on continuum-molecular system equivalence. Proc. R. Soc. Lond. A 459 (2003) 2347-2392
25. Buehler M.J., Abraham F.F., and Gao H.J. Hyperelasticity governs dynamic fracture at a critical length scale. Nature 426 (2003) 141-146
26. Xiao S.P., and Yang W.X. A nanoscale meshfree particle method with the implementation of quasicontinuum method. Int. J. Comput. Methods 2 3 (2004) 293-313
27. Klein P.A., Foulk J.W., Chen E.P., Wimmer S.A., and Gao H.J. Physics-based modeling of brittle fracture: cohesive formulations and the application of meshfree methods. Theor. Appl. Fract. Mech. 37 (2001) 99-166