Hi,
I am calculating the elastic properties of composite using finite element method.
The value of longitudinal modulus calculated using analytical and FEM approach are matching, but the transverse Modulus values of the analytical and FEM approach are not matching. I am attaching the paper which i am following. It will be great if any body tell the reason
Hi
I have never worked this problem myself but I had a look out of curiosity and, for what it is worth, can make some guesses to your question
- The analytical volume mixture model mixes material based on volume fraction, i.e. ignores the specific shape of the composite mixture, which is accounted for in the FE model. It appears that this assumption, i.e. ignoring geometry, is more robust for the longitudinal modulus than is the case for the transverse modulus.
- The Halpin-Tsai model is semi-empirical, i.e. a best fit from experiments likely is used to overcome the above limitations.
- The periodic microstructure model accounts for geometry using Fourier series. A Fourier series never explicityly match the exact function as it is energy correct, i.e. it will always err somewhere but pinpoints the total energy. In any case, from my glancing the paper, it seems to me that the match is better between FE and this model, though the match is better for some shapes than other shapes. The difference in match between shapes may be related to how well the Fourier series works for the particular geometry, e.g. a Fouries series can never catch a square wave (see the Gibb's phenomenon) but has an easier job capturing circular geometry.
http://en.wikipedia.org/wiki/Gibbs_phenomenon
All in all, using FE would be the general method. The FE approach might be less good than analytical models for random fiber mixes, i.e. where angle, diameter etc is varied. I would expect FE to outperform other methods for explicit composite arrangements, i.e. arrangements with low variation of microstructure geometry.
Just my 2 cents.
Claes
The calculations based on FEM will be better than the analytical computations, because they can take into account some nonlinear affects, and also the anisotropy can be
included more exactly than by analytical computation. But it will be necessary to
have a good FEM code and an FEM mesh which is fine enough.
The rules of mixtures and inverse rules of mixtures are not very robust. Christensen even labeled them as the 'meaingless rules of mixtures' in his 1990 'A critical evaluation for a class of micro-mechanics models'
As stated before, Halpin-Tsai is a fitting model so it needs the right parameters. A well designed FE model should provide good estimations.
Dear Rayudu,
mixture rules can give some indications with a certain confidence level only for some effective elastic constants. The micro mechanical approach proposed in the paper you refer to is too much rough. A better estimation of effective constitutive response can be obtained by using numerical procedures, as for instance based on FEM. The most used procedures involve the use of theorems of average strain or average stress on a representative volume element (RVE). The critical aspects of these procedures are mainly related to the proper choice of the RVE, and to the applied boundary conditions. Usually uniform strains or uniform stresses are involved, although good computational performaces can be obtained by recurring to periodic startegies. You may refer as a first starting point to, for example,
http://www.sciencedirect.com/science/article/pii/S0377042709005536
Even if, you find a large amount of papers on this topic.
let me know. Regards
GVairo
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