Hi,
I would like to get the necessary conditions if a isotropize the elastic tensor.
Normally each elastic tensor depends on the symmetry of the considered material.
For example, for the cubic symmetry tensor, there are 3 elastic constants in this tensor: c11, c12 and c44.
I would like to know how it is possible to get the isotropic condition: c11=c12+2.c44.
And second, if i take an another symmetry,how it is possible to get the isotopic conditons of each symmetry.
Tahnak you, Ravi
Polycrystal with random crystallographic texture.
Michael Dahms
Maybe you should try the library.
Physical properties of crystals: Their representatives by tensors and matrices (Unknown Binding) by John Frederick Nye (Author) Clarendon Press (1967)
What Michael Dahms has told you about randomly oriented polycrystalline metals being isotropic - such as zinc, beryllium, cadmium ...... and more .... is described in here too.
Most of the classic issues of matrix and tensor representation of material properties is all covered in this classic reference.
Good luck.
Don't forget that cubic crystals are also elastically anisotropic. In order to obtain isotropic elasticity, you need a random texture as well. To be precise: The 2nd- and 4th-order terms of the ODF (orientation distribution function) must be zero.
Michael Dahms
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