iMechanica - gel - Comments

Dear Wei, Thanks for

marc — Thu, 29 May 2008 22:17:55 -0400

Dear Wei,

Thanks for your explanation for the free-energy function. As you said,we must do some experiments on soft materials which have no corresponding free energy funtion. the acquirement of the free-energy function for a new soft material may be very difficult, and the experimental test is very importrant. For a new soft material without free-energy function,experimental tests may be the only way to describe its mechanical behavior!

THANKS

Lianhua

Limitation of the current work

Wei Hong — Wed, 28 May 2008 16:01:38 -0400

Dear Lianhua,

Thank you for your interest in our work!

As you mentioned, the current implementation does have its limitations: it is only suitable for the final equilibrium state of diffusion. Although the chemical potential is not required to be constant in the simulation, it is a predefined field. In other words, we can not solve for the chemical potential, it must be given. Therefore a steady-state calculation of a complex domain might not be possible either.

No theory could ever predict a general free-energy function, although some theoretical abstraction might give insights to some specific material behavior, Florry-Huggins, for example. The right way to investigate the mechanical behavior of a material would always be experimental. Instead of doing one experiment on one material, one should do a series of experiment on a same material, using different loading conditions, different sample shape/sizes. Instead of starting from nowhere, I think it is always better to start from a theoretical model, and see the deviation. If there is no deviation, good, we extract the material parameter; if, most likely, there is deviation, we either modify the theory to say why, or just use the test result numerically, if a result is important. Also instead of testing the static/equilibrium behavior together with the kinetic properties, I suggest to do separate tests for a same material. These are just my general thoughts. Let's keep on the discussion if you have further interest.

Thanks,

Wei

good job.

Lianhua Ma — Wed, 28 May 2008 07:12:27 -0400

Dear Wei Hong,Your investigation on mechanics of gel is very good job.

you had implemented the theory in the finite element package, ABAQUS. the simulation of large deformation of similar hyperelastic material requires the satisfaction of quasi-static mechanical behavior. so , the FEM simulation in your paper did not reflect the diffusion process of solvent in gel. In other words, you assumed that the chemical potential is constant in one simulation, In fact, the chemical potential is variable in different position of gel. the theory in your paper may be only suitable for final equilibrium state of diffusion.

another question: the key of your paper is the free energy funtion W . For other soft materials, If we have no corresponding free energy funtion put forward by predecessor, How can we investigate the mechanical behavior of soft materials? can you give me any advice? thanks for your paper! Hope to keep in touch with you.

THANKS

L.H. MA

Re: additional questions

Wei Hong — Tue, 27 May 2008 10:58:10 -0400

We don't need to specify the thermal expansion coefficient. We use the "T" just as a general field parameter, not as temperature, so it has nothing to do with thermal expansion.

Due to the definition of the chemical potential, it is always negative. It can be negative infinity to 0. (-0.05 is just an arbitrary number we picked.) As we start from -0.05 and end in 0, so it is still swelling instead of contracting. Just don't read it as temperature.

Please feel free to let me know if you have further concerns.

Wei

additional questions

Minkyoo Kang — Fri, 23 May 2008 18:31:18 -0400

Thank you for your prompt response.

I have additional questions. In defining the temperature in the predifined fields, we usually need to define thermal expansion coefficient in the property module, otherwise we don't see any deformation. I wonder in your simulation whether you also need to specify thermal expansion coefficient, and if that's the case, how does the thermal expansion coefficient relate with the chemical potential?

Your chemical potentials are in the range of -0.05 to 0. Does this means we have to use the same values for the temperture input in the predefiend field which actually means contraction not swelling in the point of temperature?

I'm bothering you with many questions and I really appreciate your help.

Thanks,

Min Kyoo

setting chemical potential

Wei Hong — Fri, 23 May 2008 14:42:40 -0400

Dear Min Kyoo,

Thank you for your interest in our work.

Yes, you should specify the initial chemical potential according to the given initial free swelling ratio (3rd material parameter)

The chemical potential is specified using pre defined fields (temperture) in abaqus input.

Let me know if you have further questions.

Wei

Question about the chemical potential

Minkyoo Kang — Thu, 22 May 2008 19:16:58 -0400

Dear Wei Hong,

Thank you for sharing your source code.

I'm trying to use it for a swelling deformation problem. I have a question about the chemical potential. Since the initial free swelling is an input parameter, shoud we specify the initial chemical potential accoroding to the free swelling equation? If so, since the chemical potential is mimicked by a temperature-like variable in ABAQUS as stated in your paper, How do we specify the increment of the chemical potential or temperature?

Thanks,

Min Kyoo Kang

About the chemical potentials

Wei Hong — Wed, 14 May 2008 08:33:32 -0400

Dear Hua,

Thank you very much for the good words. We will definitely keep in touch.

The chemical potential is defined as the work needed (or increase in the free energy) when adding one extra atom (or particle).

By this definition, there could be chemical potential of the solvent molecules in the vapor and that in the gel: mu_vap = dW_vap/dC=kT(p/p0), mu_gel = dW(F, C)/dC=.... In general, the two are not equal, and the chemical potential can be a field variable. However, we are looking at equilibrium state here, so they must be equal and homogeneous, mu_vap=mu_gel. We didn't put on the subscripts on the two mu's, but they mean different things and they are equal only in equilibrium.

Hope this resolves your concern. Thanks again for your interest!

a concern

Hua Li — Tue, 13 May 2008 21:45:53 -0400

Hi, Zhigang, thank you very much for your info. Also Hello, Wei, Great congratulation to you for your new position in Iowa State University. Hope to keep in close touch in future.

This paper is of great interest to me, especially on the simulation of 2-D complex gel with commercial software ABAQUS. May I have a concern to be clarified, that is, how to understand that the chemical potential of the solvent molecules, mu=kT(p/p0) and is also defined as Eq.(2), say mu=dW(F,C)/dC? Thank you very much fro your time.

hydrogel experiments

Rui Huang — Thu, 17 Jan 2008 11:05:37 -0500

Dear Wei and Zhigang,

Thank you for your responses and for pointing to your recent works on hydrogels. Indeed, I have been following your works (quietly so far). I have several experiments in mind and try to develop models, with little success so far. One particular experiment involves patterned hydrogel lines constrained by a substrate. The swelling and deformation in this case is highly inhomogeneous and anisotropic. What caught my attention at the beginning is that these lines buckle into wavy structures. The question here is how to relate the buckling phenomenon to the material and geometry properties of the hydrogel lines.

Relate the theory of hydrogels to experimental observations

Zhigang Suo — Thu, 17 Jan 2008 09:23:12 -0500

Dear Rui: Thank you very much for your interest, and for going through the calculation. We have since made a number of applications, which have been posted at

Working through these specific problems, we are trying to learn about applications of hydrogels, and to connect the theory to experimental observations. The experimental literature on hydrogels is huge, and will take many theoreticians many years to sort out.

They are just typos

Wei Hong — Wed, 16 Jan 2008 21:17:43 -0500

Hi Rui,

Thank you for reading our paper so carefully and pointing out the errors.

Actually these were just typos we had on the first version of our manuscript. We have corrected them on the later versions.

Besides the two places you have identified, there are more:
1) the chi number we used should be 0.2 instead of 0.1
2) the lambda value sould be 3.215 instead of 3.125

I am uploading the new version. Please take a look at this version and sorry for the misleading typos.
You can also check on the final version on JMPS website at http://dx.doi.org/10.1016/j.jmps.2007.11.010

Thanks,

Wei

a question for Wei Hong

Rui Huang — Wed, 16 Jan 2008 18:01:08 -0500

Hi Wei,

I am reading your paper, "A theory of coupled diffusion and large deformation in polymeric gels", which I like very much. I am trying to do some simple calculations myself, which leads to a minor question here. For the uniaxial creep problem, I reached an equation similar to Eq. (32) in your paper, but different for the second last term on the right hand side. Instead of 1, I have 1/lambda3. Solving this nonlinear equation for s = 0 with Matlab, I could not get the same stretch, lambda = 3.125. With your equation, I got 1.294, and with my equation I got 3.390. I wonder if I have missed something somewhere. I would appreciate it if you can check your equation and solution to let me know.

Thanks.

Assumptions for isotropic tension/reversibility/cotinuum

Wei Hong — Wed, 02 Jan 2008 11:17:39 -0500

Hi Dr. Li,

Let me try to answer your questions:

(1) The gel is assumed to be bonded to both the rods and the substrate. Constrained in all directions, the gel is just like in a cage, and it simply can not deform (except for tilting which involves additional thredshold as described in the paper). When dried, the gel has an natural tendency to reduce in volume. If without the constraints, the gel would shrink freely. However, it is now constrained in a cage. The only thing it can do before tilting is building up an internal stress against shrinking. As both the initial condition and the constained are assumed to be isotropic, the tensile stress within can only be isotropic.

(2) The process is reversible is that it can shrink when dried or swell back when hydrated. Not as the "reversible process" in thermodynamics terminology, such a process does dissipates energy. Zhigang, shall we consider another word here?

(3) I think the assumption necessary is that the size of the nanostructure is still larger than the microstructure of the material itself. In this case, for example, the assumption should be that the nanorods are still way bigger than the polymer molecules.

Finite deformation Biot references

Sanjay Govindjee — Wed, 02 Jan 2008 09:17:36 -0500

Just to add more completeness to the referencing, here are two interesting citations of Biot's which deal with finite deformation.

M. Biot, Theory of Finite Deformations of Pourous Solids, Indiana Univ. Math. J. 21 No. 7 (1972), 597–620

M. A. Biot, Variational Lagrangian-thermodynamics of nonisothermal finite strain mechanics of porous solids and thermomolecular diffusion, International Journal of Solids and StructuresVolume 13, Issue 6, , 1977, Pages 579-597.

Prof. Dr. Sanjay Govindjee
University of California, Berkeley