3d anisotropic material stiffness matrix

[Angel Sedano]

Hello group:

I have a characterization of one material througth experimental test. In this characterization I have 15 constants defined: 3 Young modulus, 6 poisson, and 6 shear modulus (xy term and yx term are not the same).

The matrix of elastic coeficients for an anisotropic material (Hooke´s law) has to have 21 independent terms (it is simetric). However, I have read in MSC/NASTRAN documentation (linear static user guide from page 145) a formulation for anisotropic materials where only 9 terms are defined (the other terms are null). I think that these terms define an orthotropic material but not an anisotropic material. Besides, in and orthotropic material: E1*nu21=E2*nu12; E2*nu32=E3*nu23; E3*nu13=E1*nu31. So the elastic coeficients matrix for an orthotropic material is:

<<ole0.bmp>>


My problem now is to obtain a similar matrix but for anisotropic materials. Does it exists? I hope so.

Thanks in advance,

Ángel Sedano
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[gausson]

Post by Angel Sedano
I have a characterization of one material througth experimental test. In this characterization I have 15 constants defined: 3 Young modulus, 6 poisson, and 6 shear modulus (xy term and yx term are not the same).
...

If I remember well, the case of general anisotropy in terms of engineering constants
(moduli, Poisson ctes., etc.) has:
3 Young moduli Exx,Eyy,Ezz
+ 3 shear moduli Gxy,Gxz,Gyz (BTW, Gxy=Gyx, otherwise the matrix is not symmetric --
though, this statement may vary depending on the nomenclature system employed)
+ 3 Poisson ctes. NUxy,NUxz,NUyz =>=> 3x3=9
+ the rest -- ctes. of mutual influence of the 1st and 2nd kind which have 3- or
4-indice notations, something like MUxyyz, ETAxyx.
Though, it seems to be proved that independent of them are 18 at utmost.
For more details look for a good book on anisotropic elasticity, e.g., by Lekhnitskii
(I'm not sure about spelling).

Just a curiosity: what kind of engineering material can have the general anisotropy with
21 ctes.?

Regards,
V.Gato
USAL

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