Spherical nano-inhomogeneity with the Steigmann–Ogden interface model under general uniform far-field stress loading

Free and forced vibrations of nanowires on elastic substrates

To investigate the surface effects on thermomechanical vibration and buckling of embedded circular curved nanosize beams, nonlocal elasticity model is used in combination with surface properties including surface elasticity, surface tension, and surface density for modeling the nanoscale effect. The governing equations are determined via the energy method. Analytically Navier method is utilized to solve the governing equations for simply supported nanobeam at both ends. Solving these equations enables us to estimate the natural frequency and critical buckling load for circular curved nanobeam including Winkler and Pasternak elastic foundations and under the effect of a uniform temperature change. The results determined are verified by comparing the results with available ones in literature. The effects of various parameters such as nonlocal parameter, surface properties, Winkler and Pasternak elastic foundations, temperature, and opening angle of circular curved nanobeam on the natural frequency and critical buckling load are successfully studied. The results reveal that the natural frequency and critical buckling load of circular curved nanobeam are significantly influenced by these effects.

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Investigating Surface Effects on Thermomechanical Behavior of Embedded Circular Curved Nanosize Beams

https://iopscience.iop.org/article/10.1088/2053-1591/aaa9a6/pdf

Closed-form nonlinear frequency of flexoelectric nanobeams with surface and nonlocal effects under closed circuit electric field

It is widely recognized that the extension limit of polymer chains has a significant effect on the snap-through instability of dielectric elastomers (DEs). The snap-through instability performance of DEs has been extensively studied by two limited-stretch models, i.e., the eight-chain model and Gent model. However, the real polymer networks usually have many entanglements due to the impenetrability of the network chains as well as a finite extensibility resulting from the full stretching of the polymer chains. The effects of entanglements on the snap-through instability of DEs cannot be captured by the previous two limited-stretch models. In this paper, the nonaffine model proposed by Davidson and Goulbourne is adopted to characterize the influence of entanglements and extension limit of the polymer chains. It is demonstrated that the nonaffine model is almost identical to the eight-chain model and is close to the Gent model if we ignore the effects of chain entanglements and adopt the affine assumption. The suitability of the nonaffine model to characterize the mechanical behavior of elastomers is validated by fitting the experimental results reported in the open literature. After that, the snap-through stability performance of an ideal DE membrane under equal-biaxial prestretches is studied with the nonaffine model. It is revealed that besides the prestretch and chain extension limit, the chain entanglements can markedly influence the snap-through instability and the path to failure of DEs. These results provide a more comprehensive understanding on the snap-through instability of a DE and may be helpful to guide the design of DE devices.

http://iopscience.iop.org/article/10.1088/2053-1591/aac6fe/pdf

Snap-through instability analysis of dielectric elastomers with consideration of chain entanglements

This article studies the axial buckling of a nanowire (NW) lying on Winkler–Pasternak substrate medium with the Timoshenko beam theory. The surface effect of the NW is accounted for with the Steigmann–Ogden model. An explicit solution of the critical buckling force and its associated buckling mode are obtained analytically. The influences of the surface stress effect, the geometry of the NW, and the elastic foundation moduli on the buckling behavior are fully discussed.

/pdf/buckling-analysis-of-a-nanowire-lying-on-winkler-pasternak-42ysjbymzq.pdf

Jun Luo

Papers

Buckling Analysis of a Nanowire Lying on Winkler–Pasternak Elastic Foundation.