Xiaohu Yao

Nonlocal beam model for axial buckling of carbon nanotubes with surface effect

Small-size effect and surface effect are two of the most specific intrinsic properties of nanostructures, both of which are of great significance to the related applications. In this letter, the nonlocal Euler-Bernoulli beam model, together with surface elasticity and surface tension are implemented to investigate the buckling behavior of axially compressed carbon nanotubes. Explicit expression of solutions to the critical buckling loads corresponding to typical boundary conditions is presented. Through contrast to molecular dynamics results, it is vitally important to note that both small-size effect and surface effect have a profound consequence and should be taken into account thoroughly.

Dynamic Stability of a Thin Film Bonded to a Compliant Substrate Subjected to a Step Load with Damping

Abstract The flexible electronic structure is based on the buckling of a thin film on a compliant substrate. This paper studies the dynamic stability of this structure subjected to a uniaxial step load with damping. The equation of motion is derived by Hamilton’s principle and Euler-Lagrange equation. Through the qualitative analysis of the phase portraits of the dynamic equation, as well as the quantitative analysis of the responses according to Budiansky-Roth criterion, the critical dynamic load is determined. It is the same as that in static buckling. Affected by damping, at the stage of pre-buckling, the amplitude of the film vibrates and attenuates, where the maximum response is the initial amplitude. The structural damping can be derived by the logarithm of the ratio between two adjacent peaks of the vibration. At the stage of post-buckling, the amplitude of the film vibrates and tends to a stable response, which is the amplitude in static buckling. The upper and lower bounds of the post-buckling response are asymmetric and solved by modified Krylov-Bogoliubov method.

THE BUCKLING OF THE STRETCHABLE ELECTRONIC STRUCTURE

The structure of stiff thin film on a compliant substrate has important applications in international advanced stretchable electronics. Based on the Von Karman plate theory, we model a stiff thin film on a compliant substrate to deduce the buckling governing equations through energy method. The relations between characteristic parameters of buckling, material properties and geometric parameters are obtained. Then the numerical simulation are achieved by ABAQUS, and compared with the theoretical solutions. It is shown that, the equilibrium wavelength and critical strain are dependent on the plane strain elasticity modulus of the film and the substrate and the film thickness