Free Access
Issue
ESAIM: M2AN
Volume 47, Number 1, January-February 2013
Page(s) 109 - 123
DOI https://doi.org/10.1051/m2an/2012021
Published online 31 July 2012
  1. X. Blanc, C. Le Bris, and P.-L. Lions, From molecular models to continuum mechanics. Arch. Ration. Mech. Anal. 164 (2002) 341–381. [CrossRef] [MathSciNet]
  2. X. Blanc, C. Le Bris, and F. Legoll, Analysis of a prototypical multiscale method coupling atomistic and continuum mechanics. ESAIM : M2AN 39 (2005) 797–826. [CrossRef] [EDP Sciences]
  3. A. Braides and M. Cicalese, Surface energies in nonconvex discrete systems. Math. Models Methods Appl. Sci. 17 (2007) 985–1037. [CrossRef]
  4. A. Braides, A.J. Lew and M. Ortiz, Effective cohesive behavior of layers of interatomic planes. Arch. Ration. Mech. Anal. 180 (2006) 151–182. [CrossRef] [MathSciNet]
  5. R.C. Cammarata, Surface and interface stress effects in thin films. Prog. Surf. Sci. 46 (1994) 1–38. [CrossRef]
  6. S. Cuenot, C. Frétigny, S. Demoustier-Champagne and B. Nysten, Surface tension effect on the mechanical properties of nanomaterials measured by atomic force microscopy. Phys. Rev. B 69 (2004) 165410. [CrossRef]
  7. J. Diao, K. Gall and M.L. Dunn, Surface-stress-induced phase transformation in metal nanowires. Nat. Mater. 2 (2003) 656–660. [CrossRef] [PubMed]
  8. M. Dobson and M. Luskin, An analysis of the effect of ghost force oscillation on quasicontinuum error. ESAIM : M2AN 43 (2009) 591–604. [CrossRef] [EDP Sciences]
  9. M. Dobson, M. Luskin and C. Ortner, Accuracy of quasicontinuum approximations near instabilities. J. Mech. Phys. Solids 58 (2010) 1741–1757. [CrossRef] [MathSciNet]
  10. W. E and P. Ming, Cauchy–Born rule and the stability of crystalline solids : static problems. Arch. Ration. Mech. Anal. 183 (2007) 241–297. [CrossRef] [MathSciNet]
  11. M. Farsad, F.J. Vernerey and H.S. Park, An extended finite element/level set method to study surface effects on the mechanical behavior and properties of nanomaterials. Int. J. Numer. Methods Eng. 84 (2010) 1466–1489. [CrossRef]
  12. G. Friesecke and F. Theil, Validity and failure of the Cauchy–Born hypothesis in a two-dimensional mass-spring lattice. J. Nonlinear Sci. 12 (2002) 445–478. [CrossRef] [EDP Sciences] [MathSciNet]
  13. W. Gao, S.W. Yu and G.Y. Huang, Finite element characterization of the size-dependent mechanical behaviour in nanosystems. Nanotechnol. 17 (2006) 1118–1122. [CrossRef]
  14. M.E. Gurtin and A. Murdoch, A continuum theory of elastic material surfaces. Arch. Ration. Mech. Anal. 57 (1975) 291–323. [CrossRef] [MathSciNet]
  15. J. He and C.M. Lilley, The finite element absolute nodal coordinate formulation incorporated with surface stress effect to model elastic bending nanowires in large deformation. Comput. Mech. 44 (2009) 395–403. [CrossRef]
  16. A. Javili and P. Steinmann, A finite element framework for continua with boundary energies. part I : the two-dimensional case. Comput. Methods Appl. Mech. Eng. 198 (2009) 2198–2208. [CrossRef]
  17. H. Liang, M. Upmanyu and H. Huang, Size-dependent elasticity of nanowires : nonlinear effects. Phys. Rev. B 71 (2005) R241–403. [CrossRef]
  18. W. Liang, M. Zhou and F. Ke, Shape memory effect in Cu nanowires. Nano Lett. 5 (2005) 2039–2043. [CrossRef] [PubMed]
  19. C. Ortner and F. Theil, Nonlinear elasticity from atomistic mechanics. E-prints arXiv:1202.3858v3 (2012).
  20. H.S. Park, Surface stress effects on the resonant properties of silicon nanowires. J. Appl. Phys. 103 (2008) 123504. [CrossRef]
  21. H.S. Park, Quantifying the size-dependent effect of the residual surface stress on the resonant frequencies of silicon nanowires if finite deformation kinematics are considered. Nanotechnol. 20 (2009) 115701. [CrossRef]
  22. H.S. Park and P.A. Klein, Surface Cauchy–Born analysis of surface stress effects on metallic nanowires. Phys. Rev. B 75 (2007) 085408. [CrossRef]
  23. H.S. Park and P.A. Klein, A surface Cauchy–Born model for silicon nanostructures. Comput. Methods Appl. Mech. Eng. 197 (2008) 3249–3260. [CrossRef]
  24. H.S. Park and 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. J. Mech. Phys. Solids 56 (2008) 3144–3166. [CrossRef]
  25. H.S. Park, K. Gall and J.A. Zimmerman, Shape memory and pseudoelasticity in metal nanowires. Phys. Rev. Lett. 95 (2005) 255504. [CrossRef] [PubMed]
  26. H.S. Park, P.A. Klein and G.J. Wagner, A surface Cauchy–Born model for nanoscale materials. Int. J. Numer. Methods Eng. 68 (2006) 1072–1095. [CrossRef]
  27. H.S. Park, W. Cai, H.D. Espinosa and H. Huang, Mechanics of crystalline nanowires. MRS Bull. 34 (2009) 178–183. [CrossRef]
  28. H.S. Park, M. Devel and Z. Wang, A new multiscale formulation for the electromechanical behavior of nanomaterials. Comput. Methods Appl. Mech. Eng. 200 (2011) 2447–2457. [CrossRef]
  29. H.-G. Roos, M. Stynes and L. Tobiska, Robust numerical methods for singularly perturbed differential equations, Convection-diffusion-reaction and flow problems, 2nd edition. Springer Series in Comput. Math. 24 (2008).
  30. P. Rosakis, Continuum surface energy from a lattice model. E-prints arXiv:1201.0712 (2012).
  31. L. Scardia, A. Schlömerkemper and C. Zanini, Boundary layer energies for nonconvex discrete systems. Math. Mod. Methods Appl. Sci. 21 (2011) 777–817. [CrossRef]
  32. B. Schmidt. On the passage from atomic to continuum theory for thin films. Arch. Ration. Mech. Anal. 190 (2008) 1–55. [CrossRef] [MathSciNet]
  33. J.-H. Seo, Y. Yoo, N.-Y. Park, S.-W. Yoon, H. Lee, S. Han, S.-W. Lee, T.-Y. Seong, S.-C. Lee, K.-B. Lee, P.-R. Cha, H.S. Park, B. Kim and J.-P. Ahn, Superplastic deformation of defect-free au nanowires by coherent twin propagation. Nano Lett. 11 (2011) 3499–3502. [CrossRef] [PubMed]
  34. A.V. Shapeev, Consistent energy-based atomistic/continuum coupling for two-body potentials in one and two dimensions. Multiscale Model. Simul. 9 (2011) 905–932. [CrossRef] [MathSciNet]
  35. C.Q. Sun, B.K. Tay, X.T. Zeng, S. Li, T.P. Chen, J. Zhou, H.L. Bai and E.Y. Jiang, Bond-order-bond-length-bond-strength (bond-OLS) correlation mechanism for the shape-and-size dependence of a nanosolid. J. Phys. : Condens. Matter 14 (2002) 7781–7795. [CrossRef]
  36. F. Theil, A proof of crystallization in two dimensions. Commun. Math. Phys. 262 (2006) 209–236. [CrossRef] [MathSciNet]
  37. F. Theil, Surface energies in a two-dimensional mass-spring model for crystals. ESAIM : M2AN 45 (2011) 873–899. [CrossRef] [EDP Sciences]
  38. G. Yun and H.S. Park, A multiscale, finite deformation formulation for surface stress effects on the coupled thermomechanical behavior of nanomaterials. Comput. Methods Appl. Mech. Eng. 197 (2008) 3337–3350. [CrossRef]
  39. G. Yun and H.S. Park, Surface stress effects on the bending properties of fcc metal nanowires. Phys. Rev. B 79 (2009) 195421. [CrossRef]
  40. J. Yvonnet, H. Le Quang and Q.-C. He, An XFEM/level set approach to modelling surface/interface effects and to computing the size-dependent effective properties of nanocomposites. Comput. Mech. 42 (2008) 119–131. [CrossRef] [MathSciNet]

Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.

Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.

Initial download of the metrics may take a while.

Recommended for you