Finite Element Modeling of two-dimensional Nanoscale Structures with Surface Effects
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.
[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.
[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.
@article{"International Journal of Architectural, Civil and Construction Sciences:50493", author = "Weifeng Wang and Xianwei Zeng and Jianping Ding", title = "Finite Element Modeling of two-dimensional Nanoscale Structures with Surface Effects", 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", volume = "4", number = "12", pages = "375-6", }