On the importance of boundary conditions on nanomechanical bending behavior and elastic modulus determination of silver nanowires

Journal of Applied Mechanics

2014

Recent investigations into surface-energy density of nanomaterials lead to a ripe chance to propose, within the framework of continuum mechanics, a new theory for nanomaterials based on surface-energy density. In contrast to the previous theories, the linearly elastic constitutive relationship that is usually adopted to describe the surface layer of nanomaterials is not invoked and the surface elastic constants are no longer needed in the new theory. Instead, a surface-induced traction to characterize the surface effect in nanomaterials is derived, which depends only on the Eulerian surface-energy density. By considering sample-size effects, residual surface strain, and external loading, an explicit expression for the Lagrangian surface-energy density is achieved and the relationship between the Eulerian surface-energy density and the Lagrangian surface-energy density yields a conclusion that only two material constants-the bulk surface-energy density and the surface-relaxation parameter-are needed in the new elastic theory. The new theory is further used to characterize the elastic properties of several fcc metallic nanofilms under biaxial tension, and the theoretical results agree very well with existing numerical results. Due to the nonlinear surface effect, nanomaterials may exhibit a nonlinearly elastic property though the inside of nanomaterials or the corresponding bulk one is linearly elastic. Moreover, it is found that externally applied loading should be responsible for the softening of the elastic modulus of a nanofilm. In contrast to the surface elastic constants required by existing theories, the bulk surface-energy density and the surface-relaxation parameter are much easy to obtain, which makes the new theory more convenient for practical applications.

Section: Introductionmentioning

confidence: 79%

Elastic Theory of Nanomaterials Based on Surface-Energy Density

Journal of Applied Mechanics

2014

“…It is found that the effective Young's modulus of a fixed-fixed nanowire shows an oppositely sizedependent behavior to that of a cantilever one. [3][4][5][6][7][8] It increases with a decreasing characteristic size for fixed-fixed nanowires, while decreases for cantilever ones. Such a behavior cannot be predicted by the classical beam theory, a proper one considering surface effect should be developed.…”

Section: Introductionmentioning

confidence: 99%

“…[43][44][45] All the theoretical predictions agree well with the experimental and numerical results. [3][4][5]7,[46][47][48][49] In the present paper, the resonant vibration of both fixed-fixed nanowires and cantilevered ones is investigated with the new developed elastic theory for nanomaterials and theoretical predictions are further compared with the existing numerical results. Geometrical factors governing the size dependent characteristics of resonant frequency are also discussed, which could provide a theoretical guidance for the design of nanowire resonators and sensors in NEMs.…”

Section: Introductionmentioning

confidence: 99%

Surface effect on resonant properties of nanowires predicted by an elastic theory for nanomaterials

Journal of Applied Physics

2015

Articles you may be interested inA recently developed continuum theory considering surface effect in nanomaterials is adopted to investigate the resonant properties of nanowires with different boundary conditions in the present paper. The main feature of the adopted theory is that the surface effect in nanomaterials is characterized by the surface energy density of the corresponding bulk materials and the surface relaxation parameter in nanoscale. Based on a fixed-fixed beam model and a cantilever one, the governing equation of resonant frequency for corresponding nanowires is obtained. Numerical calculation of the fundamental resonant frequency is carried out, the result of which is well consistent with the existing numerical ones. Comparing to the result predicted by the conventionally structural dynamics, the resonant frequency of a fixed-fixed nanowire is improved, while that of a cantilever nanowire is weakened due to the surface effect. Both a decreasing characteristic size (height or diameter) and an increasing aspect ratio could further enhance the varying trend of resonant properties for both kinds of nanowires. The present result should be helpful for the design of nano-devices and nanostructures related to nanowires. V C 2015 AIP Publishing LLC.

“…In contrast to bulk materials, the elastic property of nanowires exhibits a distinct size-dependent behavior due to a large surface-to-volume ratio [4,5]. Both static and dynamic bending tests have been widely adopted in order to investigate the special mechanical feature of nanowires [6][7][8][9][10][11], in which it was found that the elastic modulus of a fixed-fixed nanowire increases, while that of a cantilevered one decreases with a decreasing characteristic length scale of nanowires. However, such a size (surface) effect cannot be predicted within the framework of the classical elasticity theory.…”

Section: Introductionmentioning

confidence: 99%

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

2016

Acta Mech

The axial buckling behavior of nanowires is investigated with a new continuum theory, in which the surface effect of nanomaterials is characterized by the surface energy density. Only the surface energy density of bulk materials and the surface relaxation parameter are involved, instead of the surface elastic constants in the classical surface elasticity theory. Two kinds of nanowires with different boundary conditions are discussed. It is demonstrated that the new continuum theory can predict the buckling behavior of nanowires very well. Similar to the prediction of the classical elasticity theory, the critical compressive load of axial buckling of nanowires predicted by the new continuum theory increases with an increasing characteristic length, such as the diameter or height of nanowires. With the same aspect ratio, a nanowire with a rectangular cross section possesses a larger critical buckling load than that with a circular one. However, the surface effect could enhance the critical buckling load not only for a fixed-fixed nanowire but also for a cantilevered one in contrast to the classical elastic model. All the results predicted by the new continuum theory agree well with predictions by the surface elasticity models. The present research not only verifies the validation of the new continuum theory, but also gives a much more convenient characterization of buckling behaviors of nanowires. This should be helpful for the design of nanodevices based on nanomaterials, for example, nanobeams in NEMS or high-precision instruments.