Finite Element Modeling of two-dimensional Nanoscale Structures with Surface Effects

Authors: Weifeng Wang, Xianwei Zeng, Jianping Ding

Abstract:

Nanomaterials have attracted considerable attention during the last two decades, due to their unusual electrical, mechanical and other physical properties as compared with their bulky counterparts. The mechanical properties of nanostructured materials show strong size dependency, which has been explained within the framework of continuum mechanics by including the effects of surface stress. The size-dependent deformations of two-dimensional nanosized structures with surface effects are investigated in the paper by the finite element method. Truss element is used to evaluate the contribution of surface stress to the total potential energy and the Gurtin and Murdoch surface stress model is implemented with ANSYS through its user programmable features. The proposed approach is used to investigate size-dependent stress concentration around a nanosized circular hole and the size-dependent effective moduli of nanoporous materials. Numerical results are compared with available analytical results to validate the proposed modeling approach.

Keywords: Nanomaterials, finite element method, sizedependency, surface stress

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1055040

References:

[1] G. Y. Jing, H. L. Duan, X. M. Su, Z. S. Zhang, J. Xu, Y. D. Li, J. X. Wang and D. P. Yu, "Surface effects on elastic properties of silver nanowires: contact atomic-force microscopy," Physical Review B, vol.73, pp. 235409(1)-235409(6), 2006.
[2] M. E. Gurtin, and A. I. Murdoch, "A continuum theory of elastic material surfaces," Arch. Ration. Mech. Anal., vol. 57, pp. 291-323, 1975.
[3] M. E. Gurtin, and A. I. Murdoch, "Surface stress in solids," Int. J. Solids and Struct., vol.14, pp. 431-440, 1978.
[4] R. E. Miller, and V. Shenoy, "Size-dependent elastic properties of nanosized structural elements," Nanotechnology, vol. 11, pp. 139-147, 2002.
[5] P. Sharma, S. Ganti, and N. Bhate, "Effect of surfaces on the size-dependent elastic state of nano-imhomogeneities," Applied Physics Letters, vol. 82, pp.535-537, 2003.
[6] P. Sharma P, and S. Ganti, "Size-dependent Eshelby's tensor for embedded nano-inclusions incorporating surface/interface energies," J. Applied Mechanics, vol. 71, pp. 663-671, 2004.
[7] F. Yang, "Size-dependent effective modulus of elastic composite materials: spherical nanocavities at dilute concentrations," J. Applied Physics, vol. 95, pp. 3516-3520, 2004.
[8] G. F. Wang, and T. J. Wang, "Deformation around a nanosized elliptical hole with surface effect," Applied Physics Letters, vol. 89: pp. 161901-161903, 2006.
[9] L. Tian L, and R. K. N. D. Rajapakse, "Analytical solution for size-dependent elastic field of a nanoscale circular inhomogeneity," J. Applied Mechanics, vol. 74, pp. 568-574, 2007.
[10] L. Tian L, and R. K. N. D. Rajapakse, "Elastic field of an isotropic matrix with a nanoscale elliptical imhomogeneity," Int. J. Solids Struct., vol. 44, pp. 7988-8005, 2007.
[11] H. L. Duan, J. Wang, Z. P. Huang, and B. L. Karihaloo, "Size-dependent effective elastic constants of solids containing nano-imhomogeneities with interface stress," J. Mech. Phys. Solids, vol. 53, pp. 1574-1596, 2005.
[12] H. L. Duan, J. Wang, B. L. Karihaloo, and Z. P. Huang, "Nanoporous materials can be made stiffer than non-porous counterparts by surface modification," Acta Mater., vol. 54, pp. 2983-2990, 2006.
[13] T. Chen, G. J. Dvorak, and C. C. Yu, "Solids containing spherical nano-inclusions with interface stresses: effective properties and thermal-mechanical connections," Int. J. Solids Struct., vol. 44, pp. 941-955, 2007.
[14] W. Gao, S. W. Yu, and G. Y. Huang, " Finite element characterization of the size-dependent mechanical behavior in nanosystems," Nanotechnology, vol. 17, pp. 1118-1122, 2006,
[15] L. Tian, and R. K. N. D. Rajapakse, " Finite element modeling of nanoscale inhomogeneities in an elastic matrix," Computational Materials Science, vol. 41, pp. 44-53, 2007.
[16] ANYSY INC, Documentation for ANSYS, Release 10.0, 2006.