Buckling behavior of nanowires predicted by a new surface energy density model

Yao, Yin; Chen, Shaohua

doi:10.1007/s00707-016-1597-2

Cited by 21 publications

(10 citation statements)

References 52 publications

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“…Both the surface energy density of bulk materials and the surface relaxation parameter are easy to determine with clearly physical meanings. Such a new theory has been used to analyze the static bending, resonant vibration, and buckling of Euler-Bernoulli nanobeams, the results of which agree well with existing experimental measurements [33][34][35].…”

Section: Introductionsupporting

confidence: 71%

“…The lateral surface of a circular nanobeam, which may consist of different crystal facets [6,40], is assumed as a perfectly and isotropically cylindrical surface in the theoretical analysis [18,21,26]. Thus, the Lagrangian surface energy density of such a nanobeam can be expressed as [33][34][35],…”

Section: The Potential Energy Function Of a Bending Timoshenko Nanobeammentioning

confidence: 99%

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Size effect in the bending of a Timoshenko nanobeam

et al. 2017

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The size effect should be considered due to the large ratio of surface area to volume when the characteristic length of a beam lies in the nanoscale. The size effect in the bending of a Timoshenko nanobeam is investigated in this paper based on a recently developed elastic theory for nanomaterials, in which only the bulk surface energy density and the surface relaxation parameter are involved as independent parameters to characterize the surface property of nanomaterials. In contrast to the Euler nanobeams and the classical Timoshenko beam, not only the size effect but also the shear deformation effect in Timoshenko nanobeams is included. Closed-form solutions of the deflection and the effective elastic modulus for both a fixed-fixed Timoshenko nanobeam and a cantilevered one are achieved. Comparing to the classical solution of Timoshenko beams, the size effect is obviously significant in Timoshenko nanobeams. The shear deformation effect in nanobeams cannot be neglected in contrast to the solution of Euler-Bernoulli nanobeams when the aspect ratio of a nanobeam is relatively small. Furthermore, the size effect exhibits different influences on the bending behavior of nanobeams with different boundary conditions. A nanobeam with a fixed-fixed boundary would be stiffened, while a cantilevered one is softened by the size effect, compared to the classical solution. All the findings are consistent with the existing experimental measurement. The results in this paper should be very useful for the precision design of nanobeam-based devices.

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Section: Introductionsupporting

confidence: 71%

Section: The Potential Energy Function Of a Bending Timoshenko Nanobeammentioning

confidence: 99%

Size effect in the bending of a Timoshenko nanobeam

et al. 2017

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“…Both parameters are easily found from Material Handbooks or simple MD simulations. Typical problems have been well analyzed based on such a novel theory and the predicted results agree well with the existing experimental data and numerical calculations [38][39][40][41] .…”

Section: Introductionsupporting

confidence: 66%

“…Consequently, we have the relaxation parameter 1 = 2 = and the lattice length a 01 = a 02 = a 0 . The Lagrangian surface energy density of the nanobeam can then be written as [38][39][40]…”

Section: Kinetic Equations Of a Timoshenko Nanobeammentioning

confidence: 99%

Surface effect on the resonant frequency of Timoshenko nanobeams

Jia

Yao

Yang

et al. 2017

International Journal of Mechanical Sciences

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The dynamic behavior of a Timoshenko nanobeam would be significantly different from a macro-one due to the large ratio of surface area to volume of nanomaterials. Furthermore, the shear deformation effect would be obvious for a Timoshenko nanobeam in contrast to an Eulerian one. In this paper, a recently developed elastic theory is adopted in order to predict the resonant frequency of a Timoshenko nanobeam, in which not only the surface effect but also the shear deformation effect and the rotary inertia one are considered. In contrast to the existing surface effect theories, surface effect of nanomaterials is characterized by the surface energy density in the adopted theory. The resonant frequency of both a fixed-fixed nanobeam and a cantilevered one is analyzed. It is found that the dynamic behavior of nanobeams deviates significantly from the one predicted by both the classical Timoshenko beam theory and the Euler-Bernoulli one due to the surface effect. Furthermore, the shear deformation effect and the rotary inertia effect cannot be neglected in nanobeams with a relative small aspect ratio, which cannot be precisely characterized by the Euler-Bernoulli beam theory. In addition, the influencing mechanism of surface effect on the dynamic behavior of nanobeams would depend on the boundary conditions. The resonant frequency of a fixed-fixed Timoshenko nanobeam would be improved, while that of a cantilevered one would be weakened by the surface effect in contrast to the corresponding classical solutions. The results in this paper should be useful for precise design of nano-devices and helpful for reasonable assessment of test results of nano-instruments.

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“…Only two kinds of material parameter are involved in the new theory to characterize the surface effect, i.e., the bulk surface energy density (the surface energy density of the corresponding bulk material) and the surface relaxation parameter, both of which have clearly physical meanings and are easy to find in material handbooks or simple molecular dynamics simulations. To this end, the Chen-Yao model has been introduced to investigate the size-dependent mechanical behaviors of some typical nanostructures, such as nanowires [17][18][19], nanoparticles [20], and nanobeams [21]. In particular, with regard to the Hertzian contact problem considering the surface effect, the normal pressure at the contact area would no longer obey the classically elliptical expressions, owing to modification of the boundary conditions by surface-induced tractions [22].…”

Section: Introductionmentioning

confidence: 99%

Surface effect on deformation around an elliptical hole by surface energy density theory

Wang

2019

Mathematics and Mechanics of Solids

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The finite plane deformation of nanomaterial surrounding an elliptical hole subjected to remote loading is systematically investigated using a recently developed continuum theory. A complex variable formulation is utilized to obtain a closed-form solution for the hoop stress along the edge of the hole. The results show that when the size of the hole reduces to the same order as the ratio of the surface energy density to the applied remote stress, the influence of the surface energy density plays an even more significant role, and the shape of the hole coupled with surface energy density has a significant effect on the elastic state around the hole. Surprisingly, in the absence of any external loading, the hoop stress induced solely by surface effects is identical to that for a hole with surface energy in a linearly elastic solid derived by the Gurtin–Murdoch surface elasticity model. The results in this paper should be useful for the precise design of nanodevices and helpful for the reasonable assessment of test results of nano-instruments.

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Buckling behavior of nanowires predicted by a new surface energy density model

Cited by 21 publications

References 52 publications

Size effect in the bending of a Timoshenko nanobeam

Size effect in the bending of a Timoshenko nanobeam

Surface effect on the resonant frequency of Timoshenko nanobeams

Surface effect on deformation around an elliptical hole by surface energy density theory

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