iMechanica - wrinkling - 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.

How to cite a journal article in your post?

Zhigang Suo — Sat, 30 Sep 2006 14:26:33 -0400

Rui:

Since this question arises so often among the users, I have summarized our discussion as an entry in FAQ,

How to cite a journal article in your post? (and how to access a paper cited in someone else’s post?)

Please feel free to edit.

Rui,Yes, you are right. This

Konstantin Volokh — Wed, 27 Sep 2006 13:47:26 -0400

Rui,Yes, you are right. This may be a problem. May not... The wrinkles' amplitudes are important as compared to, say, the film thickness. Of course, pure bifurcation analysis should not be strongly affected by this simplification because the bifurcation modes are not fully defined numerically. If you want to see a 'real' distribution of wrinkles, however, nonlinear kinematics of the substrate can matter...

Kosta

continuous rotation of particles?

Rui Huang — Wed, 27 Sep 2006 12:40:27 -0400

Kosta:

Good point! I start to see what could be a flaw in the analysis. We included the contribution of rotation (second order term) in the stretch of the plate, but did not do the same for the surface of the underlayer! If this is what you meant, I need to think more about it. For a quick defense, I may point out that the in-plane deformation of the substrate surface plays a secondary role in the whole problem. In other words, the compatibility of the lateral deflection more or less controls the dynamics, as we did in the scaling analysis (in-plane deformation ignored completely). On the other hand, the in-plane kinematics may be important for long term evolution and even the equilibrium state.

Thank you for the insightful comments!

Thank you Rui! My question

Konstantin Volokh — Wed, 27 Sep 2006 11:32:55 -0400

Thank you Rui!

My question was not clearly formulated. Of course, you meet the continuity condition. I meant something else. If the boundary particle on the film side undergoes, say, large rotation then its adjacent twin on the layer side should also undergo large rotation. The latter, however is ruled out by the linear kinematics...

Kosta

compatibility or continuity is the key

Rui Huang — Wed, 27 Sep 2006 10:46:19 -0400

Dear Kosta:

Thanks for your comment on our work. You are right that the kinematics must be compatible across the boundary (interface) between the film and the viscoelastic layer. In fact, this is the key to form the coupled equations. Both the displacement and traction must be continuous across the interface, but they are related in different ways for the film and the substrate. We use a simple model of linear viscoelasticity to relate the surface displacement of the substrate to the surface tractions (normal and shear), with the help of a thin layer approximation. For the film, we use the nonlinear von Karman plate equation, which is only geometrically nonlinear for moderately large deflections while the material deformation remains in the regime of linear elasticity. The two sets of equations are then coupled together through the continuity condition at the interface.

The following two papers contain more details about derivation of the equations.

[1] S.H. Im and R. Huang, Evolution of wrinkles in elastic-viscoelastic bilayer thin films. J. Applied Mechanics 72, 955-961 (2005).

[2] R. Huang, Kinetic wrinkling of an elastic film on a viscoelastic substrate. J. Mech. Phys. Solids 53, 63-89 (2005).

By the way, I also enjoyed reading your works on fingerprints, which share some similar mechanics with synthetic wrinkles in thin films.

Kinematics

Konstantin Volokh — Wed, 27 Sep 2006 03:49:44 -0400

Hi Sehyuk,

Very interesting paper! I have a question regarding kinematics. You consider nonlinear strain-displacement relationship for the film and the linear one for the viscoelastic layer (if I am not missing something). Is that compatible? I mean that the particles on the boundary between the film and the layer should deform similarly on both sides of the boundary.

Regards,

Kosta

Fix the link to ACS journals

Rui Huang — Tue, 26 Sep 2006 13:46:06 -0400

Indeed, ACS journals (Macromolecules in particular) are not open access (I was too hopeful). I have fixed the link above using DOI. Again, you will need subscription to access the full article, but ACS provides a nice image from the paper in addition to the abstract. Please give it a try and let me know how this works. Thanks.

ACS journals may not be open access

Zhigang Suo — Tue, 26 Sep 2006 07:42:18 -0400

The status of open access of any journal can be found on this web site. The site has labeled the journal Macromolecules gray: authors cannot even post preprints. So please just give a full citation of the paper in your post, with no hyperlink. Let us know if you have more up-to-date information on this journal.

By publishing in such a journal, the authors must have made a decision to give up their rights to post preprint. iMechanica should always honor the decisions of the original authors, as well as any copyright. Since we are not lawyers, we welcome knowledgeable people to educate us.

The new version of your post has gone far beyond

Zhigang Suo — Tue, 26 Sep 2006 07:18:05 -0400

Rui: The new version of your post has gone way beyond the joint paper of Huang and Suo (2003). Your post is no longer an atomic post: it is a very nice molecular post. The tag "suo group research" no longer belongs. You may want to remove it. Best wishes, Zhigang

experience to share

Rui Huang — Mon, 25 Sep 2006 17:01:16 -0400

After I submitted the previous comment, I played a little with the links to journal articles and would like to share with you some experience (seems to be good, to be confirmed by you). For three of my articles in question, I have three different stories to tell. I hope this covers the situation with a large group of journals.

First, for Thin Solid Films, an Elsevier journal, each paper is given a Digital Object Identifier (DOI) number with a link. According to ScienceDirect, a DOI is guaranteed never to change, so you can use it to link permanently to electronic documents. I believe that access to the full paper would still require subscription (you may check with the link above), but the link should work for everyone from anywhere.

Second, for Macromolecules, a ACS journal, I found an URL to the pdf file from the journal web page that does not require subscription. It seems to me this journal (as well as other ACS journals, perhaps) is open access.

The third article that concerned me was posted by my student, which is published in Physical Review B, a AIP journal. It also has a DOI number, but no link is provided from the journal. Instead, an URL is given for the abstract page. Again, the URL should work for everyone from everywhere. If you or your institution has subscription to AIP journals, it automatically allows access to the full paper.

All the three articles are now linked as described above. This seems to solve the copyright problem. Please let me know if you cannot access any one of them. Thanks.