An extended finite element/level set method to study surface effects on the mechanical behavior and properties of nanomaterials

International Journal for Numerical Methods in Engineering

Volumn 84, Issue 12, 2010, Pages 1466-1489

  Farsad, Mehdi ^a   Vernerey, Franck J ^a   Park, Harold S ^a  

^a UCB 450   (United States)

Author keywords

Level set; Nano structure; Surface elasticity; Surface stress; XFEM

Indexed keywords

ANALYTICAL SOLUTIONS; ATOMISTIC SIMULATIONS; BI-LAYER; BORN MODEL; EFFECTIVE STIFFNESS; EXTENDED FINITE ELEMENT METHOD; INTERFACE DECOHESION; LEVEL SET; LEVEL SET APPROACH; MECHANICAL BEHAVIOR; MECHANICAL DEFORMATION; MULTISCALES; NANO-MATERIALS; NANO-PLATE; NANO-SCALE SURFACES; NANOPLATES; NEW APPROACHES; NUMERICAL RESULTS; SURFACE AND INTERFACES; SURFACE EFFECT; SURFACE ELASTICITIES; SURFACE ELASTICITY; SURFACE ENERGIES; SURFACE STRESS; SURFACES AND INTERFACES; XFEM;

COMPUTER SIMULATION; ELASTICITY; FINITE ELEMENT METHOD; MECHANICAL ENGINEERING; MECHANICAL PROPERTIES; NANOSTRUCTURED MATERIALS; NANOWIRES; SURFACE CHEMISTRY; SURFACE PROPERTIES;

SURFACE STRUCTURE;

EID: 78649652762     PISSN: 00295981     EISSN: 10970207     Source Type: Journal    
DOI: 10.1002/nme.2946     Document Type: Article

References (40)

1. Sharma P, Ganti S, Bhate N. Effect of surfaces on the size-dependent elastic state of nano-inhomogeneities. Applied Physics Letters 2003; 82(4):535-537.
2. Diao J, Gall K, Dunn ML. Surface stress driven reorientation of gold nanowires. Physical Review B 2004; 70. 075413.
3. Chen T et al. Size-dependent elastic properties of unidirectional nano-composites with interface stresses. Acta Mechanica 2007; 188:39-54.
4. Cammarata RC. Surface and interface stress effects in thin films. Progress in Surface Science 1994; 46(1):1-38.
5. Shenoy VB. Atomistic calculations of elastic properties of metallic FCC crystal surfaces. Physical Review B 2005; 71: 094104.
6. Mi C, Jun S, Kouris DA, Kim SY. Atomistic calculations of interface elastic properties in noncoherent metallic bilayers. Physical Review B 2008; 77: 075425.
7. Park HS, Klein PA. Surface Cauchy-Born analysis of surface stress effects on metallic nanowires. Physical Review B 2007; 75: 085408.
8. Park HS, Cai W, Espinosa HD, Huang H. Mechanics of crystalline nanowires. MRS Bulletin 2009; 34(3):178-183.
9. Gurtin ME, Murdoch A. A continuum theory of elastic material surfaces. Archives of Rational Mechanics and Analysis 1975; 57:291-323.
10. Yang P. The chemistry and physics of semiconductor nanowires. MRS Bulletin 2005; 30(2):85-91.
11. Streitz FH, Cammarata RC, Sieradzki K. Surface-stress effects on elastic properties. I. Thin metal films. Physical Review B 1994; 49(15):10699-10706.
12. Miller RE, Shenoy VB. Size-dependent elastic properties of nanosized structural elements. Nanotechnology 2000; 11:139-147.
13. He LH, Lim CW, Wu BS. A continuum model for size-dependent deformation of elastic films of nano-scale thickness. International Journal of Solids and Structures 2004; 41:847-857.
14. Sun CT, Zhang H. Size-dependent elastic moduli of platelike nanomaterials. Journal of Applied Physics 2003; 92(2):1212-1218.
15. Dingreville R, Qu J, Cherkaoui M. Surface free energy and its effect on the elastic behavior of nano-sized particles, wires and films. Journal of the Mechanics and Physics of Solids 2005; 53:1827-1854.
16. Wei G, Shouwen Y, Ganyun H. Finite element characterization of the size-dependent mechanical behaviour in nanosystems. Nanotechnology 2006; 17:1118-1122.
17. She H, Wang B. A geometrically nonlinear finite element model of nanomaterials with consideration of surface effects. Finite Elements in Analysis and Design 2009; 45:463-467.
18. He J, Lilley CM. The finite element absolute nodal coordinate formulation incorporated with surface stress effect to model elastic bending nanowires in large deformation. Computational Mechanics 2009; 44(3):395-403.
19. Yvonnet J, Quang HL, He QC. An XFEM/level set approach to modelling surface/interface effects and to computing the size-dependent effective properties of nanocomposites. Computational Mechanics 2008; 42:119-131.
20. Park HS, Klein PA, Wagner GJ. A surface Cauchy-Born model for nanoscale materials. International Journal for Numerical Methods in Engineering 2006; 68:1072-1095.
21. Park HS, Klein PA. A surface Cauchy-Born model for silicon nanostructures. Computer Methods in Applied Mechanics and Engineering 2008; 197:3249-3260.
22. Park HS, Klein PA. Surface stress effects on the resonant properties of metal nanowires: the importance of finite deformation kinematics and the impact of the residual surface stress. Journal of the Mechanics and Physics of Solids 2008; 56:3144-3166.
23. Park HS. Surface stress effects on the resonant properties of silicon nanowires. Journal of Applied Physics 2008; 103:123504.
24. Park HS. Quantifying the size-dependent effect of the residual surface stress on the resonant frequencies of silicon nanowires if finite deformation kinematics are considered. Nanotechnology 2009; 20:115701.
25. Yun G, Park HS. Surface stress effects on the bending properties of fcc metal nanowires. Physical Review B 2009; 79:195421.
26. Gurtin ME. A general theory of curved deformable interfaces in solids at equilibrium. Philosophical Magazine A 1998; 78(5):1093-1109.
27. Belytschko T, Liu WK, Moran B. Nonlinear Finite Elements for Continua and Structures. Wiley: New York, 2006.
28. Dolbow J, Moes N, Belytschko T. An extended finite element method for modeling crack growth with frictional contact. Computer Methods in Applied Mechanics and Engineering 2001; 190(51-52):6825-6846.
29. Hettich T, Hund A, Ramm E. Modeling of failure in composites by x-fem and level sets within a multiscale framework. Computer Methods in Applied Mechanics and Engineering 2008; 197:414-424.
30. Belytschko T, Parimi C, Moes N, Sukumar N, Usui S. Structured extended finite element methods for solids defined by implicit surfaces. International Journal for Numerical Methods in Engineering 2003; 56(4):609-635.
31. Belytschko T, Gracie R. On xfem applications to dislocations and interfaces. International Journal of Plasticity 2007; 23(10-11):1721-1738.
32. Moes N, Cloirec M, Cartraud P, Remacle JF. A computational approach to handle complex microstructure geometries. Computer Methods in Applied Mechanics and Engineering 2003; 192:3163-3177.
33. Mohammadi S. Extended Finite Element Method. Blackwell: Oxford, 2008.
34. Dolbow J, Belytschko T. Finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering 1999; 46(1):131-150.
35. Jing GY, Duan HL, Sun XM, Zhang ZS, Xu J, Li YD, Wang JX, Yu DP. Surface effects on elastic properties of silver nanowires: contact atomic-force microscopy. Physical Review B 2006; 73:235409.
36. Cuenot S, Frétigny C, Demoustier-Champagne S, Nysten B. Surface tension effect on the mechanical properties of nanomaterials measured by atomic force microscopy. Physical Review B 2004; 69:165-410.
37. Hibbeler R. Structural Analysis. Pearson, 2006.
38. Vernerey FJ et al. The 3-d computational modeling of shear-dominated ductile failure in steel. Journal of the Minerals, Metals and Materials Society 2006; 58(12):45-51.
39. Vernerey FJ, Liu W, Moran B. Multi-scale micromorphic theory for hierarchical materials. Journal of the Mechanics and Physics of Solids 2007; 57(12):2603-2651.
40. Vernerey FJ et al. A micromorphic model for the multiple scale failure of heterogeneous materials. Journal of the Mechanics and Physics of Solids 2007; 56(4):1320-1347.