S.S. Nanthakumar, N. Valizadeh, H.S. Park and T. Rabczuk

*Computational Mechanics* 2015; 56:97-112

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K. Jayawardana, C. Mordacq, C. Ortner and H.S. Park

*ESAIM: Mathematical Modelling and Numerical Analysis* 2013; 47:109-123.

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H.S. Park

*Computational Materials Science* 2012; 51:396-401.

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G. Yun and H.S. Park

*Finite Elements in Analysis and Design* 2012; 49:3-12.

(Invited paper: Special Issue on Analysis and Design of MEMS/NEMS).

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F. Song, G.L. Huang, H.S. Park and X.N. Liu

*International Journal of Solids and Structures* 2011; 48:2154-2163.

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M. Farsad, F.J. Vernerey and H.S. Park

*International Journal for Numerical Methods in Engineering* 2010; 84:1466-1489.

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H.S. Park

*International Journal for Numerical Methods in Engineering* 2010; 83:1237-1254.

(Invited paper: Special Issue on Atomistic and Multiscale Analysis).

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G. Yun and H.S. Park

*Physical Review B* 2009; 79:195421.

Second, we find that the deformation induced by surface stresses also has a significant impact on the nanowire Young's modulus that is extracted from the bending simulations, where a strong boundary condition dependence is also found. By comparing all results to those that would be obtained using various linear surface elastic theories, we demonstrate that a nonlinear, finite deformation formulation that captures changes in both bulk and surface elastic properties resulting from surface stress induced deformation is critical to reproducing the experimentally observed boundary condition dependence in the bending-derived Young's modulus of metal nanowires. Furthermore, we demonstrate that linear surface elastic theories based solely on the surface energy erroneously predict an increase in Young's modulus with decreasing nanowire size regardless of boundary condition. In contrast, while the linear surface elastic theories based upon the Gurtin and Murdoch formalism can theoretically predict elastic softening with decreasing size, we demonstrate that, regardless of boundary condition, the stiffening due to the surface stress dominates the softening due to the surface stiffness for the range of nanowire geometries considered in the present work. Finally, we determine that the nanowire Young's modulus is essentially identical when calculated via either bending or resonance for both boundary conditions, indicating that surface effects have a similar impact on the elastic properties of nanowires for both loading conditions.

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H.S. Park

*Nanotechnology* 2009; 20:115701.

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H.S. Park and P.A. Klein

*Journal of the Mechanics and Physics of Solids* 2008;56:3144-3166.

The second major goal of this work is to quantify, for the first time, how both the residual (strain-independent) and surface elastic (strain-dependent) parts of the surface stress impact the resonant frequencies of metal nanowires within the framework of nonlinear, finite deformation kinematics. We find that if finite deformation kinematics are considered, the strain-independent surface stress substantially alters the resonant frequencies of the nanowires; however, we also find that the strain-dependent surface stress has a significant effect, one that can be comparable to or even larger than the effect of the strain-independent surface stress depending on the boundary condition, in shifting the resonant frequencies of the nanowires as compared to the bulk material.

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H.S. Park

*Journal of Applied Physics* 2008;104:013516.

(Also selected for publication in the *Virtual Journal of Nanoscale Science and Technology*, July 21, 2008).

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H.S. Park

*Journal of Applied Physics* 2008; 103:123504.

(Also selected for publication in the *Virtual Journal of Nanoscale Science and Technology*, June 30, 2008.)

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G. Yun and H.S. Park

*Computer Methods in Applied Mechanics and Engineering* 2008; 197:3337-3350

(Invited paper: Special Issue on Computational Methods of Nanostructures).

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G. Yun and H.S. Park

*Computer Methods in Applied Mechanics and Engineering* 2008; 197:3324-3336

(Invited paper: Special Issue on Computational Methods of Nanostructures).

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H.S. Park and P.A. Klein

*Computer Methods in Applied Mechanics and Engineering* 2008; 197:3249-3260

(Invited paper: Special Issue on Computational Methods of Nanostructures).

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H.S. Park and P.A. Klein

*Physical Review B* 2007; 75:085408

(Also selected for publication in the *Virtual Journal of Nanoscale Science and Technology*, Feb. 19, 2007.)

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H.S. Park, P.A. Klein and G.J. Wagner

*International Journal for Numerical Methods in Engineering* 2006; 68:1072-1095.

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