Buckling Of Nanowires Research Articles

Surface Effects and Small-Scale Impacts on the Bending and Buckling of Nanowires Using Various Nonlocal HSDTs

Surface Effects and Small-Scale Impacts on the Bending and Buckling of Nanowires Using Various Nonlocal HSDTs

Influence of surface effects on the bending and buckling of nanowires

The static bending and longitudinal stability of nanowires under liquid or gas pressure are considered. Two surface effects are taken into account. The first is due to the difference in elastic properties in the thin surface layer and in the bulk of the material. Effective tensile and flexural stiffness can be more or less than conventional stiffness, depending on the material. The second effect is due to the interaction of excess pressure on the circular side surface of the wire and the difference of the areas of the convex and concave sides of the surface that appears during bending. This effect is manifested the stronger, the greater the ratio of pressure to the modulus of elasticity of the material and the length of the wire to its diameter. These effects are determined by dimensionless parameters. It has been established that a loss of wire stability may occur under the influence of the second effect. A possible method for determining the dimensionless parameter, which determines the differences of elastic properties in a thin layer near the surface and the base material, is proposed.

Influence of Surface Effects on Bending and Buckling of Nanowires

Influence of Surface Effects on Bending and Buckling of Nanowires

Thermo-Elastic Column Buckling of Tapered Nanowires with Axially Varying Material Properties: A Critical Study on the Roles of Shear and Surface Energy

At the nanoscale, shear and surface energy play important roles in mechanical behavior of nanostructures, and therefore, such effects should be appropriately considered in the corresponding structural modeling. Herein, surface energy-based Euler–Bernoulli, Timoshenko, and higher-order beam theories are implemented to study buckling of thermally affected tapered nanowires with axial variation of materials. The governing equations associated with thermo-elastic buckling of nanowires are derived for an arbitrary variation of material properties of both bulk and surface layer across the length of nanostructure. In the lack of analytical solution, reproducing kernel particle method is adopted and the critical buckling load is evaluated. The effects of temperature gradient, slenderness ratio, power-law index of the material and geometry of the nanowire, radius, as well as transverse and rotational stiffness of the surrounding elastic medium on the buckling behavior of the nanowire are investigated. The importance of consideration of both surface energy and shear deformation effects on the obtained results is also highlighted. This work could be taken into account as a preliminary research in examining buckling of more complex nanosystems such as vertically aligned nanowires with arbitrary material’s distribution and cross section.

Surface Effects on the Buckling of Nanowires Based on Modified Core-Shell Model

In this work, surface effects including surface elasticity and residual surface stress on the buckling of nanowires are theoretically investigated. Based on modified core-shell (MC-S) model, the effective elasticity incorporating surface elasticity effect of the nanowire is derived, and by using the generalized Young-Laplace equation the residual surface stress is accounted for. The ratio of critical load with and without surface effects are obtained for a nanowire loaded in uniaxial compression. Taking silver (Ag) nanowires as an example, the analyzed results demonstrate that the influence of surface effects on the critical load of buckling becomes more and more significant as the nanowire diameter decreases. Moreover, it is shown that the influence of residual surface stress on the critical load is more prominent than that of surface elasticity.

On the importance of surface elastic contributions to the flexural rigidity of nanowires

We present a theoretical model to calculate the flexural rigidity of nanowires from three-dimensional elasticity theory that incorporates the effects of surface stress and surface elasticity. The unique features of the model are that it incorporates, through the second moment, the heterogeneous nature of elasticity across the nanowire cross section, and that it accounts for transverse surface-stress-induced relaxation strains. The model is validated by comparison to benchmark atomistic calculations, existing one-dimensional surface elasticity theories based on the Young–Laplace equation, and also three-dimensional surface elasticity theories that assume homogeneous elastic properties across the nanowire cross section via three examples: surface-stress-induced axial relaxation, resonant properties of unstrained, strained and top-down nanowires, and buckling of nanowires. It is clearly demonstrated that the one-dimensional Young–Laplace models lead to errors of varying degrees for all of the boundary value problems considered because they do not account for transverse surface stress effects, and it is also shown that the Young–Laplace model results from a specific approximation of the proposed formulation. The three-dimensional surface elasticity model of Dingreville et al. (2005) is found to be more accurate than the Young–Laplace model, though both lose accuracy for ultrasmall (<5nm diameter) nanowires where the heterogeneous nature of the cross section elasticity becomes important. Overall, the present work demonstrates that continuum mechanics can be utilized to study the elastic and mechanical behavior and properties of ultrasmall nanowires if surface elastic contributions to the heterogeneous flexural rigidity are accounted for.

Timoshenko Beam Model for Buckling of Nanowires with High-Order Surface Stresses Effects

High-order surface effects can have a significant effect in the mechanical behavior of micro- and nano-sized materials and structures. In the literature the mathematical framework of surface/interface stresses are generally described by generalized Young-Laplace equations based on membrane theory. A refined model of surface stress, counting into surface stresses as well as surface moments, collectively referred to as high-order surface stress, was recently derived by the authors. This framework allows us to simulate the interface between two neighboring media which may have varying in-plane stress through the thickness of the thin membrane. To illustrate surface stress effects, we consider the critical force of axial buckling of nanowires by accounting various degrees of surface stresses. Using the refined Timoshenko beam theory, we incorporate the high-order surface effect in the simulation of axial buckling of nanowires. The results are compared with the solutions based on conventional surface stress model as well as existing experimental data. This study might be helpful to characterize the mechanical properties of nanowires in a wide range of applications.