Skip to main content
SpringerLink
Log in

Multiscale Modeling of Surface Effects on the Mechanical Behavior and Properties of Nanowires

  • Chapter
  • First Online:
Trends in Computational Nanomechanics

Part of the book series: Challenges and Advances in Computational Chemistry and Physics ((COCH,volume 9))

  • 1299 Accesses

Abstract

Surface effects have recently been recognized as having the dominant effect on the mechanical behavior and properties of nanowires. Understanding these effects will be critical, in particular for the accurate design and functionalization of future nanowire-based nanoelectromechanical systems, including sensors, resonators and actuators. The purpose of this chapter is therefore to overview a recently developed multiscale continuum model, the surface Cauchy-Born model, which was developed to study nanomaterials where surface effects such as surface stresses are expected to contribute significantly to the mechanical response. The approach is based upon a simple extension to Cauchy-Born theory, in which continuum properties such as stress and stiffness are obtained for a given material and crystal structure directly from an underlying atomistic potential. In particular, by explicitly accounting for differences in energy for both bulk and surface atoms, we develop a variational formulation that leads to a nanomechanical boundary value problem that can be solved using standard nonlinear finite element methods for displacements, stresses and strains while naturally accounting for the effects of atomistic surface stresses. Finite element calculations using the proposed surface Cauchy-Born model demonstrate how surface stresses cause variations in the resonant frequencies of silicon nanowires as compared to those expected from continuum beam theory, and emphasize the importance of nonlinear elasticity in understanding and capturing the resonant frequency variations

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 259.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 329.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 329.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 1.

    Portions of Section 1, 2.1, 2.2 and 3.1 are from [87]. Copyright John Wiley and Sons Limited. Reproduced with permission.

  2. 2.

    Portions of Section (2.4), (6), (7) and (8) are reprinted with permission from [84]. Copyright (2008), American Institute of Physics.

  3. 3.

    Portions of Section 2.3, 3.1 and 5, including Figures 3,6,7,8, are reprinted with permission from [88]. Copyright (2007) by the American Physical Society.

References

  1. C. M. Lieber, Nanoscale science and technology: building a big future from small things, MRS Bulletin 28(7) (2003) 486–491.

    CAS  Google Scholar 

  2. P. Yang, The chemistry and physics of semiconductor nanowires, MRS Bulletin 30(2) (2005) 85–91.

    CAS  Google Scholar 

  3. Y. Xia, P. Yang, Y. Sun, Y. Wu, B. Mayers, B. Gates, Y. Yin, F. Kim, H. Yan, One-dimensional nanostructures: synthesis, characterization, and applications, Advanced Materials 15(5) (2003) 353–389.

    Article  CAS  Google Scholar 

  4. H. G. Craighead, Nanoelectromechanical systems, Science 290 (2000) 1532–1535.

    Article  CAS  Google Scholar 

  5. K. L. Ekinci, M.L. Roukes, Nanoelectromechanical systems, Review of Scientific Instruments 76 (2005) 061101.

    Article  Google Scholar 

  6. A. N. Cleland, M.L. Roukes, Fabrication of high frequency nanometer scale mechanical resonators from bulk Si crystals, Applied Physics Letters 69(18) (1996) 2653–2655.

    Article  CAS  Google Scholar 

  7. X. M. H. Huang, C.A. Zorman, M. Mehregany, M.L. Roukes, Nanodevice motion at microwave frequencies, Nature 42 (2003) 496.

    Article  Google Scholar 

  8. N. V. Lavrik, M.J. Sepaniak, P.G. Datskos, Cantilever transducers as a platform for chemical and biological sensors, Review of Scientific Instruments 75(7) (2004) 2229–2253.

    Article  CAS  Google Scholar 

  9. K. L. Ekinci, Electromechanical transducers at the nanoscale: actuation and sensing of motion in nanoelectromechanical systems (NEMS), Small 1(8–9) (2005) 786–797.

    Article  CAS  Google Scholar 

  10. H. Petrova, J. Perez-Juste, Z.Y. Zhang, J. Zhang, T. Kosel, G.V. Hartland, Crystal structure dependence of the elastic constants of gold nanorods, Journal of Materials Chemistry 16(40) (2006) 3957–3963.

    Article  CAS  Google Scholar 

  11. E. W. Wong, P. E. Sheehan, C. M. Lieber, Nanobeam mechanics: elasticity, strength, and toughness of nanorods and nanotubes, Science 277 (1997) 1971–1975.

    Article  CAS  Google Scholar 

  12. B. Wu, A. Heidelberg, J. J. Boland, Mechanical properties of ultrahigh-strength gold nanowires, Nature Materials 4 (2005) 525–529.

    Article  CAS  Google Scholar 

  13. A. Heidelberg, L. T. Ngo, B. Wu, M. A. Phillips, S. Sharma, T. I. Kamins, J. E. Sader, J. J. Boland, A generalized description of the elastic properties of nanowires, Nano Letters 6(6) (2006) 1101–1106.

    Article  CAS  Google Scholar 

  14. S. Cuenot, C. Frétigny, S. Demoustier-Champagne, B. Nysten, Surface tension effect on the mechanical properties of nanomaterials measured by atomic force microscopy, Physical Review B 69 (2004) 165410.

    Article  Google Scholar 

  15. G. Y. Jing, H. L. Duan, X. M. Sun, Z. S. Zhang, J. Xu, Y. D. Li, J. X. Wang, D. P. Yu, Surface effects on elastic properties of silver nanowires: contact atomic-force microscopy, Physical Review B 73 (2006) 235409.

    Article  Google Scholar 

  16. S. Hoffmann, I. Utke, B. Moser, J. Michler, S. H. Christiansen, V. Schmidt, S. Senz, P. Werner, U. Gosele, C. Ballif, Measurement of the bending strength of vapor-liquid-solid grown silicon nanowires, Nano Letters 6(4) (2006) 622–625.

    Article  CAS  Google Scholar 

  17. Y. Chen, B. L. Dorgan, D. N. McIlroy, D. E. Aston, On the importance of boundary conditions on nanomechanical bending behavior and elastic modulus determination of silver nanowires, Journal of Applied Physics 100 (2006) 104301.

    Article  Google Scholar 

  18. T. Namazu, Y. Isono, T. Tanaka, Evaluation of size effect on mechanical properties of single crystal silicon by nanoscale bending test using AFM, Journal of Microelectromechanical Systems 9(4) (2000) 450–459.

    Article  Google Scholar 

  19. S. Sundararajan, B. Bhushan, T. Namazu, Y. Isono, Mechanical property measurements of nanoscale structures using an atomic force microscope, Ultramicroscopy 91 (2002) 111–118.

    Article  CAS  Google Scholar 

  20. A. S. Paulo, J. Bokor, R. T. Howe, R. He, P. Yang, D. Gao, C. Carraro, R. Maboudian, Mechanical elasticity of single and double clamped silicon nanobeams fabricated by the vapor-liquid-solid method, Applied Physics Letters 87 (2005) 053111.

    Article  Google Scholar 

  21. M. Tabib-Azar, M. Nassirou, R. Wang, S. Sharma, T. I. Kamins, M. S. Islam, R.S. Williams, Mechanical properties of self-welded silicon nanobridges, Applied Physics Letters 87 (2005) 113102.

    Article  Google Scholar 

  22. S. S. Verbridge, J. M. Parpia, R. B. Reichenbach, L. M. Bellan, H. G. Craighead, High quality factor resonance at room temperature with nanostrings under high tensile stress, Journal of Applied Physics 99 (2006) 124304.

    Article  Google Scholar 

  23. A. Husain, J. Hone, H. W. C. Postma, X. M. H. Huang, T. Drake, M. Barbic, A. Scherer, M. L. Roukes, Nanowire-based very-high-frequency electromechanical oscillator, Applied Physics Letters 83(6) (2003) 1240–1242.

    Article  CAS  Google Scholar 

  24. C.Y. Nam, P. Jaroenapibal, D. Tham, D. E. Luzzi, S. Evoy, J. E. Fischer, Diameter-dependent electromechanical properties of GaN nanowires, Nano Letters 6(2) (2006) 153–158.

    Article  CAS  Google Scholar 

  25. D. A. Dikin, X. Chen, W. Ding, G. Wagner, R. S. Ruoff, Resonance vibration of amorphous \({\textrm{SiO}}_{2}\) nanowires driven by mechanical or electrical field excitation, Journal of Applied Physics 93(1) (2003) 226–230.

    Article  CAS  Google Scholar 

  26. J. Yang, T. Ono, M. Esashi, Investigating surface stress: surface loss in ultrathin single-crystal silicon cantilevers, Journal of Vacuum Science and Technology B 19(2) (2001) 551–556.

    Article  CAS  Google Scholar 

  27. B. H. Houston, D. M. Photiadis, M. H. Marcus, J. A. Bucaro, X. Liu, J. F. Vignola, Thermoelastic loss in microscale oscillators, Applied Physics Letters 80(7) (1976) 1300–1302.

    Article  Google Scholar 

  28. S. Evoy, A. Olkhovets, L. Sekaric, J. M. Parpia, H. G. Craighead, D. W. Carr, Temperature-dependent internal friction in silicon nanoelectromechanical systems, Applied Physics Letters 77(15) (2000) 2397–2399.

    Article  CAS  Google Scholar 

  29. X. Li, T. Ono, Y. Wang, M. Esashi, Ultrathin single-crystalline-silicon cantilever resonators: fabrication technology and significant specimen size effect on Young's modulus, Applied Physics Letters 83(15) (2003) 3081–3083.

    Article  CAS  Google Scholar 

  30. X. L. Feng, R. He, P. Yang, M. L. Roukes, Very high frequency silicon nanowire electromechanical resonators, Nano Letters 7(7) (2007) 1953–1959.

    Article  CAS  Google Scholar 

  31. X. Han, K. Zheng, Y .F. Zhang, X. Zhang, Z. Zhang, Z. L. Wang, Low-temperature in situ large-strain plasticity of silicon nanowires, Advanced Materials 19 (2007) 2112–2118.

    Article  CAS  Google Scholar 

  32. T. Kizuka, Y. Takatani, K. Asaka, R. Yoshizaki, Measurements of the atomistic mechanics of single crystalline silicon wires of nanometer width, Physical Review B 72 (2005) 035333.

    Article  Google Scholar 

  33. R. C. Cammarata, Surface and interface stress effects in thin films, Progress in Surface Science 46(1) (1994) 1–38.

    Article  CAS  Google Scholar 

  34. J. Diao, K. Gall, M. L. Dunn, Surface-stress-induced phase transformation in metal nanowires, Nature Materials 2(10) (2003) 656–660.

    Article  CAS  Google Scholar 

  35. H. S. Park, K. Gall, J. A. Zimmerman, Shape memory and pseudoelasticity in metal nanowires, Physical Review Letters 95 (2005) 255504.

    Article  Google Scholar 

  36. W. Liang, M. Zhou, F. Ke, Shape memory effect in Cu nanowires, Nano Letters 5(10) (2005) 2039–2043.

    Article  CAS  Google Scholar 

  37. H. S. Park, Stress-induced martensitic phase transformation in intermetallic nickel aluminum nanowires, Nano Letters 6(5) (2006) 958–962.

    Article  CAS  Google Scholar 

  38. Y. Kondo, K. Takayanagi, Gold nanobridge stabilized by surface structure, Physical Review Letters 79(18) (1997) 3455–3458.

    Article  CAS  Google Scholar 

  39. Y. Kondo, Q. Ru, K. Takayanagi, Thickness induced structural phase transition of gold nanofilm, Physical Review Letters 82(4) (1999) 751–754.

    Article  CAS  Google Scholar 

  40. L. G. Zhou, H. Huang, Are surfaces elastically softer or stiffer? Applied Physics Letters 84(11) (2004) 1940–1942.

    Article  CAS  Google Scholar 

  41. V. B. Shenoy, Atomistic calculations of elastic properties of metallic FCC crystal surfaces, Physical Review B 71 (2005) 094104.

    Article  Google Scholar 

  42. H. Liang, M. Upmanyu, H. Huang, Size-dependent elasticity of nanowires: nonlinear effects, Physical Review B 71 (2005) 241403(R).

    Article  Google Scholar 

  43. H. S. Park, K. Gall, J. A. Zimmerman, Deformation of FCC nanowires by twinning and slip, Journal of the Mechanics and Physics of Solids 54(9) (2006) 1862–1881.

    Article  CAS  Google Scholar 

  44. P. Lu, H. P. Lee, C. Lu, S. J. O'Shea, Surface stress effects on the resonance properties of cantilever sensors, Physical Review B 72 (2005) 085405.

    Article  Google Scholar 

  45. P. Lu, F. Shen, S. J. O'Shea, K. H. Lee, T. Y. Ng, Analysis of surface effects on mechanical properties of microcantilevers, Materials Physics and Mechanics 4 (2001) 51–55.

    CAS  Google Scholar 

  46. M. E. Gurtin, X. Markenscoff, R. N. Thurston, Effects of surface stress on the natural frequency of thin crystals, Applied Physics Letters 29(9) (1976) 529–530.

    Article  CAS  Google Scholar 

  47. J. E. Sader, Surface stress induced deflections of cantilever plates with applications to the atomic force microscope: rectangular plates, Journal of Applied Physics 89(5) (2001) 2911–2921.

    Article  CAS  Google Scholar 

  48. G. Y. Huang, W. Gao, S. W. Yu, Model for the adsorption-induced change in resonance frequency of a cantilever, Applied Physics Letters 89 (2006) 043506.

    Article  Google Scholar 

  49. D. W. Dareing, T. Thundat, Simulation of adsorption-induced stress of a microcantilever sensor, Journal of Applied Physics 97 (2005) 043526.

    Article  Google Scholar 

  50. A. W. McFarland, M. A. Poggi, M. J. Doyle, L. A. Bottomley, J. S. Colton, Influence of surface stress on the resonance behavior of microcantilevers, Applied Physics Letters 87 (2005) 053505.

    Article  Google Scholar 

  51. M. E. Gurtin, A. Murdoch, A continuum theory of elastic material surfaces, Archives of Rational Mechanics and Analysis 57 (1975) 291–323.

    Google Scholar 

  52. R. E. Miller, V. B. Shenoy, Size-dependent elastic properties of nanosized structural elements, Nanotechnology 11 (2000) 139–147.

    Article  CAS  Google Scholar 

  53. D. E. Segall, S. Ismail-Beigi, T. A. Arias, Elasticity of nanometer-sized objects, Physical Review B 65 (2002) 214109.

    Article  Google Scholar 

  54. L. H. He, C. W. Lim, B. S. Wu, A continuum model for size-dependent deformation of elastic films of nano-scale thickness, International Journal of Solids and Structures 41 (2004) 847–857.

    Article  Google Scholar 

  55. P. Sharma, S. Ganti, N. Bhate, Effect of surfaces on the size-dependent elastic state of nano-inhomogeneities, Applied Physics Letters 82(4) (2003) 535–537.

    Article  CAS  Google Scholar 

  56. C. T. Sun, H. Zhang, Size-dependent elastic moduli of platelike nanomaterials, Journal of Applied Physics 92(2) (2003) 1212–1218.

    Article  Google Scholar 

  57. R. Dingreville, J. Qu, M. Cherkaoui, 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 53 (2005) 1827–1854.

    Article  CAS  Google Scholar 

  58. G. Wei, Y. Shouwen, H. Ganyun, Finite element characterization of the size-dependent mechanical behaviour in nanosystems, Nanotechnology 17 (2006) 1118–1122.

    Article  Google Scholar 

  59. J. Wang, H. L. Duan, Z. P. Huang, B. L. Karihaloo, A scaling law for properties of nano-structured materials, Proceedings of the Royal Society A 462 (2006) 1355–1363.

    Article  Google Scholar 

  60. Z. Tang, H. Zhao, G. Li, N. R. Aluru, Finite-temperature quasicontinuum method for multiscale analysis of silicon nanostructures, Physical Review B 74 (2006) 064110.

    Article  Google Scholar 

  61. E. Tadmor, M. Ortiz, R. Phillips, Quasicontinuum analysis of defects in solids, Philosophical Magazine A 73 (1996) 1529–1563.

    Article  Google Scholar 

  62. L.E. Shilkrot, R. E. Miller, W. A. Curtin, Multiscale plasticity modeling: coupled atomistics and discrete dislocation mechanics, Journal of the Mechanics and Physics of Solids 52 (2004) 755–787.

    Article  Google Scholar 

  63. J. Fish, W. Chen, Discrete-to-continuum bridging based on multigrid principles, Computer Methods in Applied Mechanics and Engineering 193 (2004) 1693–1711.

    Article  Google Scholar 

  64. P. A. Klein, J. A. Zimmerman, Coupled atomistic-continuum simulation using arbitrary overlapping domains, Journal of Computational Physics 213 (2006) 86–116.

    Article  Google Scholar 

  65. F. F. Abraham, J. Broughton, N. Bernstein, E. Kaxiras, Spanning the continuum to quantum length scales in a dynamic simulation of brittle fracture, Europhysics Letters 44 (1998) 783–787.

    Article  CAS  Google Scholar 

  66. R. E. Rudd, J. Q. Broughton, Coarse-grained molecular dynamics and the atomic limit of finite elements, Physical Review B 58 (1998) 5893–5896.

    Article  Google Scholar 

  67. E. Weinan, Z. Y. Huang, A dynamic atomistic-continuum method for the simulation of crystalline materials, Journal of Computational Physics 182 (2002) 234–261.

    Article  Google Scholar 

  68. G. J. Wagner, W. K. Liu, Coupling of atomistic and continuum simulations using a bridging scale decomposition, Journal of Computational Physics 190 (2003) 249–274.

    Article  Google Scholar 

  69. H. S. Park, E. G. Karpov, W. K. Liu, P. A. Klein, The bridging scale for two-dimensional atomistic/continuum coupling, Philosophical Magazine 85 (1) (2005) 79–113.

    Article  CAS  Google Scholar 

  70. H. S. Park, E. G. Karpov, W. K. Liu, A temperature equation for coupled atomistic/continuum simulations, Computer Methods in Applied Mechanics and Engineering 193 (2004) 1713–1732.

    Article  Google Scholar 

  71. S.P. Xiao, T. Belytschko, A bridging domain method for coupling continua with molecular dynamics, Computer Methods in Applied Mechanics and Engineering 193 (2004) 1645–1669.

    Article  Google Scholar 

  72. W. K. Liu, E. G. Karpov, H. S. Park, Nano Mechanics and Materials: Theory, Multiscale Methods and Applications, John Wiley and Sons, New York, 2006.

    Google Scholar 

  73. X. Li, E. Weinan, Multiscale modeling of the dynamics of solids at finite temperature, Journal of the Mechanics and Physics of Solids 53 (2005) 1650–1685.

    Article  Google Scholar 

  74. W. K. Liu, E. G. Karpov, S. Zhang, H. S. Park, An introduction to computational nano mechanics and materials, Computer Methods in Applied Mechanics and Engineering 193 (2004) 1529–1578.

    Article  Google Scholar 

  75. P.A. Klein, A virtual internal bond approach to modeling crack nucleation and growth, Ph.D. Thesis (1999) Stanford University.

    Google Scholar 

  76. M. Arroyo, T. Belytschko, An atomistic-based finite deformation membrane for single layer crystalline films, Journal of the Mechanics and Physics of Solids 50 (2002) 1941–1977.

    Article  CAS  Google Scholar 

  77. P. Zhang, Y. Huang, P. H. Geubelle, P. A. Klein, K. C. Hwang, The elastic modulus of single-wall carbon nanotubes: a continuum analysis incorporating interatomic potentials, International Journal of Solids and Structures 39 (2002) 3893–3906.

    Article  Google Scholar 

  78. E. B. Tadmor, G. S. Smith, N. Bernstein, E. Kaxiras, Mixed finite element and atomistic formulation for complex crystals, Physical Review B 59(1) (1999) 235–245.

    Article  CAS  Google Scholar 

  79. H. . Park, P. A. Klein, A surface cauchy-born model for silicon nanostructures, Computer Methods in Applied Mechanics and Engineering 197 (2008) 3249–3260.

    Article  Google Scholar 

  80. M. S. Daw, M. I. Baskes, Embedded-atom method: derivation and application to impurities, surfaces, and other defects in metals, Physical Review B 29(12) (1984) 6443–6453.

    Article  CAS  Google Scholar 

  81. T. Belytschko, W. K. Liu, B. Moran, Nonlinear Finite Elements for Continua and Structures, John Wiley and Sons, New York, 2002.

    Google Scholar 

  82. S. M. Foiles, M. I. Baskes, M. S. Daw, Embedded-atom-method functions for the FCC metals Cu, Ag, Au, Ni, Pd, Pt, and their alloys, Physical Review B 33(12) (1986) 7893–7991.

    Article  Google Scholar 

  83. Y. Zhao, B. I. Yakobson, What is the ground-state structure of the thinnest Si nanowires? Physical Review Letters 91(3) (2003) 035501.

    Article  Google Scholar 

  84. H.S. Park, Surface stress effects on the resonant properties of silicon nanowires, Journal of Applied Physics 103 (2008) 123504.

    Article  Google Scholar 

  85. J. Tersoff, Modeling solid-state chemistry: interatomic potentials for multicomponent systems, Physical Review B 39(8) (1989) 5566–5568.

    Article  Google Scholar 

  86. H. Balamane, T. Halicioglu, W. A. Tiller, Comparative study of silicon empirical interatomic potentials, Physical Review B 46(4) (1992) 2250–2279.

    Article  CAS  Google Scholar 

  87. H. S. Park, P. A. Klein, G. J. Wagner, A surface cauchy-born model for nanoscale materials, International Journal for Numerical Methods in Engineering 68 (2006) 1072–1095.

    Article  Google Scholar 

  88. H. S. Park, P. A. Klein, Surface cauchy-born analysis of surface stress effects on metallic nanowires, Physical Review B 75 (2007) 085408.

    Article  Google Scholar 

  89. T. J. R. Hughes, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis, Prentice-Hall, Englewood Cliffs, NJ, 1987.

    Google Scholar 

  90. J. Diao, K. Gall, M. L. Dunn, Yield asymmetry in metal nanowires, Nano Letters 4(10) (2004) 1863–1867.

    Article  CAS  Google Scholar 

  91. K. Gall, J. Diao, M. L. Dunn, The strength of gold nanowires, Nano Letters 4(12) (2004) 2431–2436.

    Article  CAS  Google Scholar 

  92. J. Diao, K. Gall, M. L. Dunn, Atomistic simulation of the structure and elastic properties of gold nanowires, Journal of the Mechanics and Physics of Solids 52 (2004) 1935–1962.

    Article  CAS  Google Scholar 

  93. Trilinos, http://software.sandia.gov/trilinos/index.html.

  94. Tahoe, http://tahoe.ca.sandia.gov.

  95. J. Diao, K. Gall, M. L. Dunn, Surface stress driven reorientation of gold nanowires, Physical Review B 70 (2004) 075413.

    Article  Google Scholar 

  96. Warp, http://www.cs.sandia.gov/ \(\sim\)sjplimp/lammps.html.

  97. B. Lee, R. E. Rudd, First-principles calculation of mechanical properties of \(Si \langle100\rangle\) nanowires and comparison to nanomechanical theory, Physical Review B 75 (2007) 195328.

    Article  Google Scholar 

  98. W. Weaver, S. P. Timoshenko, D. H. Young, Vibration Problems in Engineering, John Wiley and Sons, New York, 1990.

    Google Scholar 

  99. D.W. Carr, S. Evoy, L. Sekaric, H. G. Craighead, J. M. Parpia, Measurement of mechanical resonance and losses in nanometer scale silicon wires, Applied Physics Letters 75(7) (1999) 920–922.

    Article  CAS  Google Scholar 

  100. J. Q. Broughton, C. A. Meli, P. Vashishta, R. K. Kalia, Direct atomistic simulation of quartz crystal oscillators: bulk properties and nanoscale devices, Physical Review B 56(2) (1997) 611–618.

    Article  CAS  Google Scholar 

  101. F. H. Streitz, R. C. Cammarata, K. Sieradzki, Surface-stress effects on elastic properties. I. Thin metal films, Physical Review B 49(15) (1994) 10699–10706.

    Article  CAS  Google Scholar 

  102. G. Yun, H. S. Park, A finite element formulation for nanoscale resonant mass sensing using the surface cauchy-born model, Computer Methods in Applied Mechanics and Engineering 197 (2008) 3324–3336.

    Article  Google Scholar 

  103. G. Yun, H. S. Park, A multiscale, finite deformation formulation for surface stress effects on the coupled thermomechanical behavior of nanomaterials, Computer Methods in Applied Mechanics and Engineering 197 (2008) 3337–3350.

    Article  Google Scholar 

  104. H. S. Park, Strain sensing through the resonant properties of deformed metal nanowires, Journal of Applied Physics 104 (2008) 013516.

    Article  Google Scholar 

  105. H. S. Park, P. A. Klein, 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 56 (2008) 3144–3166.

    Article  CAS  Google Scholar 

Download references

Acknowledgments

HSP acknowledges NSF grant number CMMI-0750395 in support of this research.

Author information

Authors and Affiliations

  1. University of Colorado at Boulder, Boulder, CO, USA

    Harold S. Park

  2. Franklin Templeton Investments, San Mateo, CA, USA

    Patrick A. Klein

Authors
  1. Harold S. Park
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Patrick A. Klein
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Harold S. Park .

Editor information

Editors and Affiliations

  1. Dept. Mechanical Engineering, University of Minnesota, Church St. SE., 111, Minneapolis, 55455, U.S.A.

    Traian Dumitrica

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer Science+Business Media B.V.

About this chapter

Cite this chapter

Park, H.S., Klein, P.A. (2010). Multiscale Modeling of Surface Effects on the Mechanical Behavior and Properties of Nanowires. In: Dumitrica, T. (eds) Trends in Computational Nanomechanics. Challenges and Advances in Computational Chemistry and Physics, vol 9. Springer, Dordrecht. https://doi.org/10.1007/978-1-4020-9785-0_8

Download citation

Publish with us

Policies and ethics

Search

Navigation