A finite temperature continuum theory based on interatomic potential in crystalline solids

Computational Mechanics

Volumn 42, Issue 4, 2008, Pages 531-541

  To, Albert C ^a   Liu, Wing Kam ^a   Kopacz, Adrian ^a  

^a Northwestern University   (United States)

Author keywords

Cauchy Born rule; Crystalline solids; Finite temperature continuum; Interatomic potential; Quasicontinuum

Indexed keywords

CONTINUUM MECHANICS; CRYSTALLINE MATERIALS; FREE ENERGY; QUANTUM ELECTRONICS; QUANTUM THEORY; STATISTICAL MECHANICS; THERMAL EXPANSION;

CAUCHY-BORN RULE; CRYSTALLINE SOLIDS; FINITE TEMPERATURES; INTERATOMIC POTENTIAL; QUASICONTINUUM;

TEMPERATURE;

EID: 47249126848     PISSN: 01787675     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00466-007-0239-x     Document Type: Article

References (46)

1. Liu WK, Jun S, Qian D (2006) Computational nanomechanics of materials. In: Rieth M, Schommers W(eds) Handbook of theoretical and computational nanotechnology, vol X. American Scientific, Stevension Ranch, CA
2. Liu WK, Karpov EG, Park HS (2005) Nano-mechanics and materials: theory, multiscale methods and applications. Wiley, New York
3. Liu WK, Karpov EG, Zhang S, Park HS (2004) An introduction to computational nanomechanics and materials. Comput Method Appl Mech Eng 193: 1529-1578
4. Kohlhoff S, Gumbsch P, Fischmeister HF (1991) Crack propagation in bcc crystals studied with a combined finite element and atomistic model. Philos Mag A 64: 851-878
5. Abraham FF, Broughton JQ, Bernstein N, Kaxiras E (1998) Spanning the length scales in dynamic simulation. Comput Phys 12: 538-546
6. Tadmor EB, Ortiz M, Phillips R (1996) Quasicontinuum analysis of defects in solids. Philos Mag A 73: 1529-1563
7. Engquist WEB, Huang Z (2003) Heterogeneous multiscale method: A general methodology for multiscale modelling. Phys Rev B 67(092101): 1-14
8. Shilkrot LE, Curtin WA, Miller RE (2002) A coupled atomistic/continuum model of defects in solids. J Mech Phys Solid 50: 2085-2106
9. Wagner GJ, Liu WK (2003) Coupling of atomistic and continuum simulations using a bridging scale decomposition. J Comput Phys 190: 249-274
10. Fish J, Wen J (2004) Discrete-to-continuum bridging based on multigrid principles. Comput Method Appl Mech Eng 193: 1693-1711
11. Xiao SP, Belytschko T (2004) A bridging domain method for coupling continua with molecular dynamics. Comput Method Appl Mech Eng 193: 1645-1669
12. To AC, Li S (2005) Perfectly matched multiscale simulations. Phys Rev B 72: 035414
13. Oden JT, Prudhomme S, Romkes A, Bauman P (2005) Multi-scale modeling of physical phenomena: adaptive control of models. Technical report, Institute of Computational Engineering and Sciences, University of Texas, Austin
14. Lu G, Kaxiras E (2005) Overview of multiscale simulations of materials. In: Rieth M, Schommers W(eds) Handbook of theoretical and computational nanotechnology, vol X. American Scientific, Stevension Ranch, pp 1-33
15. Arroyo M, Belytschko T (2002) An atomistic-based finite deformation membrane for single layer crystalline films. J Mech Phys Solid 50: 1941-1977
16. Zhang P, Huang Y, Geubelle PH, Hwang KC (2002) On the continuum modeling of carbon nanotubes. Acta Mech Sin 18: 528-536
17. Cai W, de Koning M, Bulatov VV, Yip S (2000) Minimizing boundary reflections in coupled domain simulations. Phys Rev Lett 85: 3213-3216
18. Knap J, Ortiz M (2001) An analysis of the quasicontinuum method. J Phys Mech Solid 49: 1899-1923
19. Born M, Huang K (1954) Dynamic theory of crystal lattices. Clarendon Press, Oxford
20. Qian D, Wagner GJ, Liu WK (2004) A multiscale projection method for the analysis of carbon nanotubes. Comput Method Appl Mech Eng 193: 1603-1632
21. Li X, Weinan E (2005) Multiscale modeling of the dynamics of solids at finite temperature. J Mech Phys Solid 53: 1650-1685
22. Senturia SD (2000) Microsystem design. Kluwer, New York
23. Frenkel D, Smit B (2002) Understanding molecular simulation: from algorithms to applications, 2nd edn. Academic Press, San Diego
24. Karpov EG, Park HS, Liu WK (2007) A phonon heat bath approach for the atomistic and multiscale simulation of solids. Int J Numer Method Eng 70: 351-378
25. Shenoy V, Shenoy V, Phillips R (1999) Finite temperature quasicontinuum methods. In: Materials research society symposium proceedings. Materials Research Society
26. Dupuy LM, Tadmor EB, Miller RE, Phillips R (2005) Finite-temperature quasicontinuum: molecular dynamics without all the atoms. Phys Rev Lett 95: 060202
27. Jiang H, Huang Y, Hwang KC (2005) A finite-temperature continuum theory based on interatomic potentials. J Eng Mater Tech 127: 408-416
28. Tang Z, Zhao H, Li G, Aluru NR (2006) Finite-temperature quasicontinuum method for multiscale analysis of silicon nanostructures. Phys Rev B 74: 064110
29. Zhao H, Tang Z, Li G, Aluru NR (2006) Quasiharmonic models for the calculation of thermodynamic properties of crystalline silicon under strain. J Appl Phys 99: 064314
30. Chandler D (1987) Introduction to modern statistical mechanics. Oxford University press, Oxford
31. Wallace DC (1970) Thermodynamics of crystals. Wiley, New York
32. Qian D, Gondhalekar RH (2004) A virtual atom cluster approach to the mechanics of nanostructures. Int J Multiscale Comput Eng 2: 277-289
33. Lincoln RC, Koliwad KM, Ghate PB (1967) Morse-potential evaluation of second- and third-order elastic constants of some cubic metals. Phys Rev 157: 463-466
34. Born M (1940) On the stability of crystal lattices. Proc Camb Philol Soc 36: 160-172
35. Overton WC Jr., Gaffney J (1955) Temperature variation of the elastic constants of cubic elements. I. copper. Phys Rev 98: 969-977
36. Ziman JM (1972) Principles of the theory of solids. Cambridge University Press, Cambridge
37. Marder M (2004) Condensed matter physics. Wiley, New York
38. Moruzzi VL, Janak JF, Schwarz K (1988) Calculated thermal properties of metals. Phys Rev B 37: 790-799
39. Barrera GD, Bruno JAO, Barron THK, Allan NL (2005) Negative thermal expansion. J Phys Condens Matter 17: R217-R252
40. Gray DE (ed) (1963) American institute of physics handbook, 2nd edn. McGraw-Hill, New York
41. 2O. J Appl Crystallogr 36: 1461-1463
42. Kos JF, Lamache GL, Savary L (1968) The anomalous thermal expansion of gold below 15 k. Phys Lett 28: 219-220
43. Gupta OP, Kharoo HL (1981) Analysis of the Gruneisen parameters of some fcc metals by an improved elastic force model. J Chem Phys 74: 3577-3583
44. Nix FC, MacNair D (1941) The thermal expansion of pure metals: copper, gold, aluminum, nickel, and iron. Phys Rev 60: 597-605
45. Sutton PM (1953) The variation of the elastic constants of crystalline aluminum with temperature between 63 K and 773 K. Phys Rev 91: 816-821
46. Neighbours JR, Alers GA (1958) Elastic constants of silver and gold. Phys Rev 111: 707-712