Studies of validity of the Cauchy-Born rule by direct comparison of continuum and atomistic modelling

Modelling and Simulation in Materials Science and Engineering

Volumn 15, Issue 1, 2007, Pages

  Steinmann, P ^a   Elizondo, A ^a   Sunyk, R ^a  

^a France   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

COMPUTER SIMULATION; KINEMATICS; MOLECULAR DYNAMICS; PHASE TRANSITIONS; PLASTIC DEFORMATION; CONTINUUM MECHANICS;

ACOUSTIC TENSOR; ATOMIC SYSTEM; CAUCHY-BORN RULE; MATERIAL BEHAVIOR;

CONTINUUM MECHANICS; MOLECULAR DYNAMICS;

ATOMIC SYSTEM; ATOMISTIC MODELING; CAUCHY-BORN RULE; DIRECT MOLECULAR DYNAMICS; KINEMATIC ASSUMPTIONS; MATERIAL BEHAVIOUR; NON-AFFINE DEFORMATION; STANDARD METHOD;

EID: 34247179139     PISSN: 09650393     EISSN: 1361651X     Source Type: Journal    
DOI: 10.1088/0965-0393/15/1/S21     Document Type: Conference Paper

References (23)

1. Curtin W A and Miller R E 2003 Atomistic/continuum coupling in computational materials science Modelling Simul. Mater. Sci. Eng. 11 33-68
2. Abraham F F, Walkup R, Gao H, Duchaineau M, Diaz de la Rubia T and Seager M 2002 Simulating materials failure by using up to one billion atoms and the world's fastes computer: Brittle fracture PNAS 99 5777-82
3. Adelman S A and Doll J D 1976 Generalized langevin equation approach for atom/solid-surface scattering: general formulation for classical scatterin of harmonic solids J. Chem. Phys. 64 2375-88
4. Allen M P and Tildsley P J 1987 Computer Simulation of Liquids (Oxford: Oxford University Press)
5. Cai W, de Koenig V V, Bulatov M and Yip S 2000 Minimizing boundary reflections in coupled-domain simulations Phys. Rev. Lett. 85 3213-16
6. Ericksen J L 1984 Phase transformations and material instabilities in solids Academic Press 23 1-28
7. Friesecke G and Theil F 2002 Validity and failure of the Cauchy-Born hypthesis in a two-dimensional mass-spring lattice J. Nonlinear Sci. 12 445-78
8. Haile J M 1991 Molecular Dynamics Simulation: Elementary Method (New York: Wiley)
9. Holian B L and Ravelo R 1995 Fracture simulation using large-scale molecular dynamics Phys. Rev. B 51 275-88
10. Holmes N and Belytschko T 1976 Postprocessing of finite element transient response calculations by digital filters Comput. Structures 6 211-16
11. Lambrecht M 2002 Theorie und numerik von materialinstabilitäten elastoplastischer festkörper auf der grundlage inkrementeller variationsformulierungen PhD Thesis
12. Milstein F 1982 Mechanics of Solids (Oxford: Pergamon Press)
13. Nishimura K and Miyazaki N 2004 Molecular dynamics simulation of crack growth under cyclic loading Comput. Mater. Sci.
14. Ortiz M and Phillis R 1999 Nanomechanics of defects in solids Adv. Appl. Mech. 36 1-71
15. Qu S, Curtin W A and Miller R E 2005 A finite-temperature dynamic coupled atomistic/discrete dislocation method Model. Simul. Mater. Sci. Eng. 13 1101-18
16. Rapaport D 1995 The Art of Molecular Dynamics Simulation (Cambridge: Cambridge University Press)
17. Shenoy V B, Miller R, Tadmor E B, Rodney D, Phillips R and Ortiz M 1997 An adaptive finite element approach to atomic-scale mechanics-the quasicontinuum method ArXiv Condensed Matter e-prints
18. Sunyk R 2004 On aspects of mixed continuum-atomistic material modelling PhD Thesis
19. Sunyk R and Steinmann P 2001 Localization analysis of mixed continuum-atomistic models J. Phys. IV France 11 251-8
20. Sunyk R and Steinmann P 2003 On higher gradients in continuum-atomistic modelling Int. J. Solids Structures 40 6877-96
21. Tadmor E B 1996 The quasicontinuum method PhD Thesis
22. Wang J, Yip S, Phillpot S and Wolf D 1993 Crystal instabilities at finite strain Phys. Rev. Lett. 71 4182-5
23. Zanzotto G 1996 The Cauchy-Born hypotesis, nonlinear elasticity and mechanical twinning in crystals Acta Cryst. A52 839-49