iMechanica - Finite Element Method - 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.

Doubts regarding FEM Analysis of Nanocomposites

nikhil satheesan — Fri, 21 Mar 2008 03:43:44 -0400

Respected Sir

My name is Nikhil S. I am a final year Engg student from T K M College, Kerala, India. I am working on a project about the FEM analysis of Nanocomposites. Sir, I would like to have your advice in this direction.

Steps I have done so far..

1) Wrote a C++ programme to generate the radius,theta and z values of a carbon nanotube with input parameters tube diameter, length and element length.

2) tried to bring it to ansys for analysis .. ( Structural Analysis)

3) Can you tell me how to model a nanocomposite from this situation in Ansys.

Expecting a favourable earliest reply

Thank you

Nikhil S

You may mail me in my email id also..

Difference in fiber reinforce composite and nanocomposites?

Mingji Wang — Tue, 20 Nov 2007 22:00:49 -0500

I am not follwoing recent development in 'nano'-mechanics. I suspect if ABAQUS can help, all classical solutions and analysis developed for fiber/frisk reinforced composites before can be borrowed directly. I will appreciate if someone can give a general description of the key differences in mechanics analysis between the classical fiber/frisk reinforce composites and nanocomposites IF we want to stay in continuum mechanics. Is it just a dimensional change (and some different stress transfer mechanism), or a totally new mechanics area? Thanks ...

Dear Dr. Xu Thank you

Ramin Babaei — Tue, 20 Nov 2007 20:15:22 -0500

Dear Dr. Xu

Thank you very much for your comment and your papers .they are helpful for me.

Best regards,

Ramin

New research topics of mechanics of nanocomposite materials

Luoyu Roy Xu — Tue, 20 Nov 2007 14:34:45 -0500

Dear Ramin,

This review paper is very good but it’s still incomplete (especially mechanics analysis) and not able to report new process from 2005-2007. I’d answer your questions and provide my suggestions based on my previous experience on nanocomposite research.

Q1-what are the important parameters in the modelling of nanostructures which must be considered? A1---- I think the aspect ratio of the nanofiller, stiffness ratio of the nanofiller and matrix should be important parameters.

Q2-what is the main problem of current finite element method to model the nanostructure, especially nanocomposite materials (for example in traditional methods or in ABAQUS program)? A2-----failure modeling should be a major problem. Most of the stiffness problems including the curved nanotubes etc. have been modeled well by previous researchers. Similar to your method, we simulated a simple interfacial stress transferring problem and here is our paper published in Journal of Nanoscience and Nanotechnology(PDF file).

Q3-Can we expand traditional methods like as Rayleigh-Ritz or Least square methods to model and analysis of nanocomposites? A3--- it’ may be very hard since other researchers have solved these easy cases. You may use these classical approaches to solve stiffness related problems.

For new issues of strengths and fracture toughnesses of nanocomposites, you may read my previous article.

The interface may be important

Ying Li — Tue, 20 Nov 2007 08:29:21 -0500

Dear Ramin,

In my view, the interface between the matrix and the additions maybe the important problem. However, the ditrsbution and the orientation of additions are also very imprtant For nanocompostites, I suggest you see the review article"Nanocomposites in context" , which is very impressive.

Lee

Thanks for the notes!

ashokpandey — Sun, 07 Oct 2007 10:46:34 -0400

Thanks for the notes!