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Research Papers

Elastic Energy of Surfaces and Residually Stressed Solids: An Energy Approach for the Mechanics of Nanostructures

[+] Author and Article Information
Xiang Gao

LTCS and Department of Mechanics
and Engineering Science,
College of Engineering,
Peking University,
Beijing 100871, China

Daining Fang

LTCS and Department of Mechanics
and Engineering Science,
College of Engineering,
Peking University,
Beijing 100871, China
e-mail: fangdn@pku.edu.cn

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received October 13, 2014; final manuscript received November 11, 2014; accepted manuscript posted November 17, 2014; published online December 3, 2014. Editor: Yonggang Huang.

J. Appl. Mech 82(1), 011010 (Jan 01, 2015) (9 pages) Paper No: JAM-14-1483; doi: 10.1115/1.4029091 History: Received October 13, 2014; Revised November 11, 2014; Accepted November 17, 2014; Online December 03, 2014

The surface energy plays a significant role in solids and structures at the small scales, and an explicit expression for surface energy is prerequisite for studying the nanostructures via energy methods. In this study, a general formula for surface energy at finite deformation is constructed, which has simple forms and clearly physical meanings. Next, the strain energy formulas both for isotropic and anisotropic surfaces under small deformation are derived. It is demonstrated that the surface elastic energy is also dependent on the nonlinear Green strain due to the impact of residual surface stress. Then, the strain energy formula for residually stressed elastic solids is given. These results are instrumental to the energy approach for nanomechanics. Finally, the proposed results are applied to investigate the elastic stability and natural frequency of nanowires. A deep analysis of these two examples reveals two length scales characterizing the significance of surface energy. One is the critical length of nanostructures for self-buckling; the other reflects the competition between residual surface stress and surface elasticity, indicating that the surface effect does not always strengthen the stiffness of nanostructures. These results are conducive to shed light on the importance of the residual surface stress and the initial stress in the bulk solids.

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References

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Figures

Grahic Jump Location
Fig. 1

The critical buckling load of the nanowires

Grahic Jump Location
Fig. 2

The postbuckling modulus of nanowires near the critical point

Grahic Jump Location
Fig. 3

The effect of initial geometrical imperfection on the buckling of nanowires

Grahic Jump Location
Fig. 4

The reduction of the load capacity near the critical point

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