iMechanica - suo group research - Comments

Thanks for the materials

changyongcao — Fri, 22 Jan 2010 06:00:09 -0500

Hi, Prof.Suo,

Thank you for sharing your good lectures to community.

It is interesting and nice.

Hello Zhigang, Thank you

Jung W. Hong — Fri, 22 Jan 2010 00:06:43 -0500

Hello Zhigang,

Thank you for the interesting information and nice presentation materials.

Dielectric elastomers look really promising. Compared with Piezoelectric materials, still there are some tradeoffs regarding the maximum generated force although elastomer can make much larger deformation. However, elastomers are under development by many manufacturers. So maybe the material will be very versatile for the engineering use in the near future!

I already found the answer.

Mario Juha — Thu, 10 Dec 2009 15:16:16 -0500

I already found the answer. Thanks I was measuring lambda respect to the free-swelling state and not from the dry network state. Now I have same results. But if you could send the info, I would appreciate it.

Thanks,

Mario

Material model implementation

Mario Juha — Thu, 10 Dec 2009 10:34:08 -0500

Dear Dr. Hong.

I have implemented your material model in a non-linear finite element program that I wrote. I am using a Continuum Mechanics Total Lagrangian formulation to deal with nonlinearities, and my measure for stress and strain are Second Piola-Kirchhoff stress tensor and Green-Lagrange strain tensor, respectively. In order to test the program, I would like to reproduce your results. I have followed what you nicely explained in the paper, but I feel I need an extra help.

If it is appropiate, could you give me extra information about the finite element model?, that is, what exactly boundary conditions you used and how many substeps?.

To use your model and doing the following:

1) Specify the initial chemical potential and then calculate lambda_0 using Eq.(19). This value of lambda_0 is what I am going to use in Eq.(23)

2) Increment linearly the current chemical potential using the following relation:

current_mu = mu_0 + delta * ( current_mu - mu_0 ), where delta is the increment corresponding to the load step.

current_mu is what I am going to use in Eq.(23)

3) Solve nonlinear equations using Newton-Raphson.

Thanks in advance,

Mario

Thanks for the descriptive notes

Hari — Mon, 09 Nov 2009 14:36:43 -0500

Dr. Suo,

Thanks very much for your notes. I personally prefer to start with class/lecture notes before reading papers on a new topic.

Hari

Re: Future work

Wei Hong — Wed, 30 Sep 2009 09:46:33 -0400

Dear Mario,

Sure you can! Please let me know if you need more information than those on the paper.

Wei

Future work...

Mario Juha — Tue, 29 Sep 2009 16:47:13 -0400

Dear Dr. Hong.

I am really interested in this work. I have been studied it for weeks and I would like to extend your results. In section 8.3, last paragraph, you said something about instabilities that you can not solve currently with ABAQUS. I would like to know if I can collaborate with you and or your students.

thank you,

Mario

Re: Molecular incompressibility

Wei Hong — Tue, 01 Sep 2009 16:35:06 -0400

Dear Mario,

It is actually similar to the constraint you are familiar with, the only difference being the volume of solvent. When solvent migrate into a polymer network, the network expands. Here we assume the total volume to be a constant.

Your understanding of C(X) is correct.

Wei

Molecular incompressibility and the free-energy function

Mario Juha — Tue, 01 Sep 2009 15:26:00 -0400

Dear Dr. Hong. I have been busy studying your papers and I have more questions than answer (to me that is good). In: W.Hong, X. Zhao, J. Zhou, Z. Suo. A theory of coupled diffusion and large deformation in polymeric gels. Journal of the mechanics and physics 56, 1779 - 1793 (2008), section 3, you specify the molecular incompressibility as:

1 + vC = det(F)

I am familiar with the incompressibility constraint of det(F) = 1, but not with the above equation. Could you give more insight about it? Probably it is an standard constraint in gel theory, but I am not familiar with it.

Other question that I have is related with C(X), distribution of solvent molecules in the gel. Do I need to understand this notation as C(X) = C(phi^-1(x))? , where phi(x)^-1 is the inverse of the motion, lower x is the spatial coordinate and capital X is the reference coordinate. In general terms, what I have understood is that C is an inhomogeneous field, is it correct?

cordially,

Mario J. Juha

www.eng.usf.edu/~mjuha/

Re: Questions about your paper

Wei Hong — Thu, 27 Aug 2009 20:50:12 -0400

Dear Mario,

Thank you for your interest in our work.

I don't quite understand your first question though. I = F_iK F_iK is an invariant of the deformation gradient F. It is not the first invariant of F. In fact, it is the first invariant of the right Cauchy-Green deformation tensor. You can find reference on these quantities on almost any textbook on finite-deformation continuum mechanics, or even on wikipedia.

You are right that on the final published paper, the lambda_0^3 is missing in eq (23). The version here on imechanica was correct. Thank you for pointing this out, I appologize for our carelessness on proofreading the final print.

Wei

Questions about your paper

Mario Juha — Thu, 27 Aug 2009 18:01:00 -0400

Dear Dr. Hong.

I am trying to find an idea for my proposal presentation for my Ph.D and I have found interest in yor work about gels. So, I read two papers that you wrote about it.

I have two simple questions related with the paper: W. Hong, Z. Liu, and Z. Suo, Inhomonegeous swelling of a gel in equilibrium with a solvent and mechanical load. International Journal of Solids and Structures 46, 3282-3289 (2009).

1) Why do you relate I = F_ik F_ik with the first invariant of the deformation gradient (eq.(17)) ? Could you give me some reference? Now I am reading the Gerahard Holzapfel's book about continuum mechanics, and I have not found any reference to it.

2) Is there a lambda_0^3 term missing in the second log, in eq.(23) ? I have done the mathematic and I just found a discrepancy in the numerator of the second log.

I am a Ansys user and I want to reproduce your excellents results, but using Ansys.

Thank you,

Mario J. Juha

Civil and environmetal Engineering Department

University of South Florida

http://www.eng.usf.edu/~mjuha/

crease on a gel

Wei Hong — Sat, 11 Jul 2009 18:29:08 -0400

Yes, Zhigang you are right. It has been too long and I could not remember.

The instantaneous response we had in the paper does not need any calculation, it is a direct extension from the elastomer result.

We also did some simulation with our program for the equilibrium state. Now I don't remember whether it is close to that of an instantaneous response.

I could slightly recall that I told you the equilibrium critical condition is higher than that of the instantaneous one. But if it could form instantaneously, the crease will form (if there is no energy barrier), and may disappear as time evolves.

Re: formation of creases

Zhigang Suo — Sat, 11 Jul 2009 17:00:00 -0400

Rui: Thank you for remarkably perceptive questions. Indeed, we struggled with these issues ourselves. The format of the paper is too short to expand these discussions.

Wei: Concerning your response 3), I'd like to add three sub-points:

(3a) The model does agree with several sets of experimental data within factor 2. The model may be incorrect for many reasons, but no model can ever be really correct, just as no painting can be real enough to be the real thing.

(3b) That said, however, some models are better than others. Regarding our long conversations about equilibrium vs. instantaneous models before you left Harvard last year, I now have second thoughts. If we are looking at creases formed duing the swelling of a gel, then the fact that gel swells seems to mean that time is enough for the surface layer to equilibrate with the external solvant. So perhaps equilibrium theory should be more appropriate.

(3c) I recall that you and Xuanhe had some FEM calculations using the equilibrium theory, and told me that results were not too different from the instataneous theory. We should reexamine these calculations, given that the instantaneous theory only predicts a single critical value, but experiments reported a range. Perhas the thermodynamic properties of the gel (e.g., the Flory parameter and Nv) will allow a range of critical values, sufficiant to explain the experimental observations.

Crease length and gel crease

Wei Hong — Sat, 11 Jul 2009 15:08:47 -0400

Dear Rui,

Thank you for your interest in our work, and sorry that it took so long.

1) The length is also free to change from a to c. I only constrained the horizontal displacement, with the vertical direction left free.

2) Very good observation. We did actually tried further. However, if you rethink about it, the (equilibrium) state corresponding to a negative energy does not exist. -- It is simply imposible to have a short contact length as prescribed beyond the critical strain. -- The material will fold back into itself if you allow penatration, or it will make a longer contact on top of A/A'. Since our Fig.3 describes the energy of a state in equilibrium with a prescribed (arbitrary but constant) crease length, the curve physically stops at the critical point. We can not get the exact critical point simply because of numerical reason.

3) Another very insightful point. What you pointed out is a equilibrium state, or long term response of a gel. What we described in the paper is a case in the other limit - the instantaneous response. What I have in mind is that the formation of a crease, especially for the formation of a very tiny one, can be very fast (the time scales with the size^2 under the model described in my previous paper). If we only look at the initiation of an infinitesimal crease, we should look at the instantaneous response of a gel - when time is short, the mobile molecules do not have time to relax or migrate, the gel is just like a piece of rubber. Ofcourse, in reality whenever a crease form, it has a finite size due to various reasons, and takes a finite time period. The real situition is somewhere between the two limiting cases and will need a proper dynamic model. It will be great if you can share your paper with us some time.

Wei

I see

Hua Li — Sat, 11 Jul 2009 03:51:57 -0400

Hi Wei,

ok, I get your point now.

The reseon I have this question on "solvent" is youe Equations (6.1) & (6.4), which include the term "Wion".

Hua