iMechanica - surface pattern - Comments

Re: orthogonal pattern

Rui Huang — Wed, 30 Jul 2008 23:14:00 -0400

Dear Jizhou,

Thanks for your comment. Yes, the orthogonal pattern is similar to the herringbone pattern. There are two main differences: (1) a herringbone pattern does not have to be orthogonal, namely, the jog angle can be oblique or anything, such as the pattern we show in Fig. 9 (second and third in the last row); (2) an orthogonal pattern need not to be a perfect herringbone either. The overall pattern consists of stripes in two orthogonal directions, which does not necessarily have the long-range order as the herringbone pattern. Locally they may resemble an orthogonal herringbone, but with abundant defects here and there, as you can see from the last pattern in Fig. 8.

I beleive that our results of the equilirbium wavelength and energy agree closely with each other, although we made some different assumptions in the shear stress and displacements. One tricky issue is that the observed wrinkle patterns may not solely depend on the energetics. For example, the loading history and initial defects may affect the formation of the wrinkle patterns. Furthermore, a global energy minimum state (with all possible wrinkle patterns, ordered and disordered) is almost impossible to reach, both theoretically and practically. It may be an interesting topic to study the defect dynamics in the wrinkle patterns for both isotropic and anisotropic elastic films.

Best regards,

orthogonal pattern

Jizhou Song — Wed, 30 Jul 2008 19:08:48 -0400

Dear Prof. Huang,

It is a very good work! I think the orthogonal pattern you mentioned in the paper is very similar to the herringbone pattern. Am I right? What is the main difference between them? As you know, I have studied the anisotropic effect on the herringbone mode. Our results showed (1) the anisotropy has little effect on the equilibrium wavelength of the herringbone mode for Si/PDMS system (2) when [100] and [010] are the wavevectors, the system has the lower energy than the case when [110] and [-110] are the wavevectors, which agrees with your conclusion.

Jizhou Song

energetically similar states

Hanqing Jiang — Sun, 27 Jul 2008 12:58:03 -0400

Dear Rui: I agree that there exist many energetically similar states. Song et al. also showed that the energies of the checkerboard
and herringbone modes are very close at very small strains, which suggests that small imperfection may trigger different buckling patterns.

crystal anisotropy effect

Rui Huang — Sun, 27 Jul 2008 10:33:00 -0400

Dear Hanqing,

Thanks for your comments. Indeed the effect of crystal anisotropy on the equilibrium wavelength shown in this paper is no more than a few per cent. This has to be a result of the relatively weak anisotropy of the SiGe crystal. The effect on the evolution and final wrinkle pattern for two-dimensional films is not surprising either. To elucidate the effect, we deliberately used a relatively small stress in Figs. 8 and 9. As you see from Fig. 10, the effect is much reduced by the stress isotropy at higher stress levels. I believe most of the experiments by Rogers' group were for very high stress or strain levels, in which case material nonlinearity of the substrate plays a role too as you and your colleagues have shown. A couple of other experiments (Peterson, 2006; and Yu et al., 2005) did show clearly the orientation of the wrinkles at both the early stage and the final pattern. It shall also be noted that the wrinkle pattern may depend on the loading history for both isotropic and anisotropic films, because there seem to exist many energetically equivalent (or similar) states. For example, the energies of the ordered zigzag pattern and the disordered labyrinth pattern in isotropic films were found to be very close (see Z. Huang, Hong, and Suo, Phys. Rev. E 70, 030601R, 2004).

excellent work

Hanqing Jiang — Sun, 27 Jul 2008 02:34:17 -0400

Dear Rui: This is an excellent work for the general area of wrinkling of thin films on compliant substrates. It is interesting to see that (1) the crystal anisotropy does not strongly affects the equilibrium wavelength of one-dimensional strips, but (2) determines the evolution of patterns for two-dimensional films. Rogers' experiments for buckled single crystal silicon ribbons on PDMS substrates verifies the first statement. I am just curious how to experimentally verify the second statement. It will be extremely challenging to well control the pre-strain with about 0.001% accuracy.

I agree with you, but try to contact prof. Barber he is nice

Mike Ciavarella — Sun, 08 Jun 2008 11:59:13 -0400

I agree with you the paper by Barber and Ting is extremely sophisticated.

But maybe they can give you all the mathematica routines you need.

You obviously find his email in the link.

Regards

Mike

michele ciavarella
www.micheleciavarella.it

extended Stroh formalism

Rui Huang — Sat, 07 Jun 2008 18:01:58 -0400

Michele,

Thanks. I did take a look at Barbar and Ting's paper. However, I must admit that I do not have a good understanding of the Stroh formalism and found it difficult to follow in some cases. For the problem we had in this study, the method of Fourier transform seems to be straightforward. It may has some similarity with the Stroh formalism, but it is not a simple extension.

Regards,

excellent contribution Rui

Mike Ciavarella — Sat, 07 Jun 2008 15:40:05 -0400

Rui have you seen also the recent work on JMPS by Barber and Ting? Maybe you can extend that to films. Ask Jim.

Three-dimensional anisotropic elasticity - an extended Stroh formalism

Tom Ting and I have recently
developed a method of extending Stroh's anisotropic formalism to
problems in three dimensions. The unproofed paper can be accessed at http://www-personal.umich.edu/~jbarber/Stroh.pdf .

.Regards, Mike

michele ciavarella
www.micheleciavarella.it

thanks

Rui Huang — Mon, 29 Jan 2007 11:02:56 -0500

Yanfei:

Thanks for pointing out these two papers. I do have copies of these papers. They are indeed relevant. We probably should have cited them in addition to Lu and Suo's PRB paper. Compared to self-assembled monolayers (may be considered as a film of zero thickness), the patterns of epitaxial islands can be quite different (an effect of surface curvature as well as wetting, I think). Nevertheless, the principle of bifurcation illustrated in this paper is similar to the previous works on monolayers and surface reaction, with a root in the classical half-space problems in elasticity.

interesting wrok

Yanfei Gao — Mon, 29 Jan 2007 10:11:45 -0500

You may find out that the following two references are useful to you:

doi:10.1063/1.371999 by Yu and Suo

doi:10.1016/S1359-6454(02)00056-3 by Gao, Lu and Suo