In civil engineering, we often encounter the material possessing anisotropic characteristic which is difficult to be modelled as most of the finite element modelling were done based on the assumption that the material is isotropic such as in Timoshenko and Euler-Bernoulli theories. Apparently, finite element modeling of anisotropic material is relatively tedious. Is there any possibilities that we could replace an anistropic material to transversely isotrpic material for the sake of simplicity?
Indeed, assumptions in FE are a more complicated question which involve the need of keeping symmetries, a few terms of the strain energy, and so on.
Putting the focus only at the differences between anisotropic, transversely isotropic, and others, one should remember the material constitutive law and its changes/transformations due to rotation of the referential. For who is interested in basic stuff to start I recommend to read the chapter 4 from the free book of Pauli Pedersen (DTU) in http://www.fam.web.mek.dtu.dk/book2.pdf (and may be also some of his papers in the subject). For a more advanced text, look for a good text of soil mechanics.
One may consider several types of anisotropic materials. The most simple anisotropic model is that of a transversely isotropic. I remember a few cases where replacement of an anistropic material by a transversely isotropic material is possible for the sake of simplicity. E.g., some do it with Shales (http://en.wikipedia.org/wiki/Shale) or with periodic thin layers in sedimentary soils.
It gives a small idea. Hope others could give better and more specialized information.
Transverse isotropy is a symmetry assumption considering that the material behaves differently in one direction from the two others.
The simplification comes from this assumption equivalent to saying that some coefficients of your anisotropic material are equal or linearly dependent.
This type of behavior is well suited for some materials, (e.g. extruded components or compressed powders) and is most of the time resulting from a specific manufacturing process.
Anisotropy is not difficult to implement in a finite element code if you are using 3D elements, but the constitutive law needed features a lot of coefficients that can be very difficult to identify experimentally.
Really the anisotropy will require almost 21 material constants for the material definition in an FE software. Then orthotropic materials will need 9 constants in 3 planes of symmetry. A simplified approach is to use transversely isotropic requiring 5 elastic constants. Here, for example, in fiber reinforced composite beam, if the fire direction 1 is along the beam axis, 2 along the width and 3 along the thickness, then it ca be assumed transversely isotropic in planes 2-3 and 1-3. Similar can be taken the case of rcc beam. However, it depends on the material configuration /micro-structure under study. For example in composites with randomly oriented fibers, where there are no planes of symmetry , you will still need anisotropic material constants.
In the study of anisotropy material as well as transversely isotropic material, normally continuum damage mechanic is adopted. Are there any others methods that are suitable in this case? Pls recommend. Thanks all.
For transversely isotropic please watch this video for better understanding
https://www.youtube.com/watch?v=NUwN7iRqg08
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