屈曲

Q. Lu and R. Huang, Excess energy and deformation along free edges of graphene nanoribbons. Posted online atarXiv:0910.0912, October 2009.

Hi everyone,

Does anyone have the work experience on stepped column kind of structure?

I would like to know, how to determine the crippling load for stepped column kind of structures? If anyone have the materials pertaining to the subject, please do share (if interested).

Thanks and Regards

M Gopalakrishnan.

We have studied the scaling of controlled nonlinear buckling processes in materials with dimensions in the molecular range (i.e., ～1 nm) through experimental and theoretical studies of buckling in individual single-wall carbon nanotubes on substrates of poly(dimethylsiloxane). The results show not only the ability to create and manipulate patterns of buckling at these molecular scales, but also, that analytical continuum mechanics theory can explain, quantitatively, all measurable aspects of this system.

Qiang Lu and Rui Huang

Department of Aerospace Engineering and Engineering mechanics, University of Texas, Austin,
TX 78712, USA

In MEMS fields, a need arises in engineering practice to predict accurately the nonlinear response of slender post-buckling beams, especially the nonlinear transverse stiffness. The bistability of the post-buckling beams is excellent in reducing power consumption of micro-devices or micro-systems. However, the major difficulty in analyzing the post-buckling and snap-through response is the intractability of the geometric nonlinear control equations of large deflection beams.

I. Arias and M. Arroyo, Size-Dependent Nonlinear Elastic Scaling of Multiwalled Carbon Nanotubes,Phys. Rev. Lett.100, 085503 (2008).

许多研究薄膜/基底结构and its failure mechanism were reported in recent years. The direct experimental results of thin film/substrate structure by scanning electron microscopy (SEM) presents an intriguing problem:there exists a buckling failure mechanism at the lateral edge of metal film under pure bending. The qualitative theoretical analysis has been done on such buckling failure of thin film/substrate structure.

B. Li, M. K. Kang, K. Lu, R. Huang, P. S. Ho, R. A. Allen, and M. W. Cresswell, Nano Letters 8, 92 -98 (2008).(Web Release Date: 07-Dec-2007; DOI:10.1021/nl072144i)

H. Mei, J.Y. Chung, H.-H. Yu, C.M. Stafford, and R. Huang,Buckling modes of elastic thin films on elastic substrates. Applied Physics Letters 90, 151902 (2007).

Two modes of thin film buckling are commonly observed, one with interface delamination (e.g., telephone cord blisters) and the other with no delamination (i.e., wrinkling). Which one would occur for your film?

Appl Phys Lett, 90, 201910, 2007

(J Appl Phys, 100, 114327, 2006)

R. Huang, Applied Physics Letters 87, 151911 (2005).

Rui Huang and Se Hyuk Im, Physical Review E 74, 026214 (2006).

软基板上的强调薄膜可以猛击op complex wrinkle patterns. The onset of wrinkling and initial growth is well described by a linear perturbation analysis, and the equilibrium wrinkles can be analyzed using an energy approach. In between, the wrinkle pattern undergoes a coarsening process with a peculiar dynamics. By using a proper scaling and two-dimensional numerical simulations, this paper develops a quantitative understanding of the wrinkling dynamics from initial growth through coarsening till equilibrium. It is found that, during the initial growth, a stress-dependent wavelength is selected and the wrinkle amplitude grows exponentially over time. During coarsening, both the wrinkle wavelength and amplitude increases, following a simple scaling law under uniaxial compression. Slightly different dynamics is observed under equi-biaxial stresses, which starts with a faster coarsening rate before asymptotically approaching the same scaling under uniaxial stresses. At equilibrium, a parallel stripe pattern is obtained under uniaxial stresses and a labyrinth pattern under equi-biaxial stresses. Both have the same wavelength, independent of the initial stress. On the other hand, the wrinkle amplitude depends on the initial stress state, which is higher under an equi-biaxial stress than that under a uniaxial stress of the same magnitude.

A recent discussion here aboutthe effect of surface stress on vibrations of microcantileverhas gained some interest from our members. A few years ago,Zhigangand I looked atsurface effect on buckling of a thin elastic film on a viscous layer (Huang and Suo, Thin Solid Films 429, 273-281, 2003). Although the physical phenomena (buckling vs vibrations) are different, the conclusion is quite consistent withWei Hong and Pradeep's commentstoward the end of the discussion. That is, surface stress only contributes as a residual stress and thus does not affect the buckling wavelength (frequency in space in analogy to frequency in time for vibrations).

A possible explanation of the variety of fingerprints comes from the consideration of the mechanics of tissue growth. Formation of fingerprints can be a result of the surface buckling of the growing skin. Remarkably, the surface bifurcation enjoys infinite multiplicity. The latter can be a reason for the variety of fingerprints. Tissue morphogenesis with the surface buckling mechanism and the growth theory underlying this mechanism are presented in the attached notes.