Syntax

% decompose into symmetric portions
[Tiso, T1, T2, T3] = symmetricDecomposition(T,cs1,cs2,cs3)

Input

`T`	`tensor`
`cs1, cs2, cs3`	`symmetry`

Output

T1, T2, T3 tensor

Example

cs = crystalSymmetry('222',[18 8.8 5.2],'mineral','Enstatite');

T = stiffnessTensor([
225 54 72 0 0 0
54 214 53 0 0 0
72 53 178 0 0 0
0 0 0 78 0 0
0 0 0 0 82 0
0 0 0 0 0 76],cs);

csHex = crystalSymmetry('622','mineral','Enstatite');
csTet = crystalSymmetry('422','mineral','Enstatite');

[Tiso, THex, TTet, TOrt] = symmetricDecomposition(T,csHex,csTet)

Tiso = stiffnessTensor (Enstatite)
  unit: GPa              
  rank: 4 (3 x 3 x 3 x 3)
 
  tensor in Voigt matrix representation:
 210.2  57.4  57.4     0     0     0
  57.4 210.2  57.4     0     0     0
  57.4  57.4 210.2     0     0     0
     0     0     0  76.4     0     0
     0     0     0     0  76.4     0
     0     0     0     0     0  76.4
 
THex = stiffnessTensor (Enstatite)
  unit: GPa              
  rank: 4 (3 x 3 x 3 x 3)
 
  tensor in Voigt matrix representation:
  5.92 -0.02   5.1     0     0     0
 -0.02  5.92   5.1     0     0     0
   5.1   5.1 -32.2     0     0     0
     0     0     0   3.6     0     0
     0     0     0     0   3.6     0
     0     0     0     0     0  2.97
 
TTet = stiffnessTensor (Enstatite)
  unit: GPa              
  rank: 4 (3 x 3 x 3 x 3)
 
  tensor in Voigt matrix representation:
  3.375 -3.375      0      0      0      0
 -3.375  3.375      0      0      0      0
      0      0      0      0      0      0
      0      0      0      0      0      0
      0      0      0      0      0      0
      0      0      0      0      0 -3.375
 
TOrt = stiffnessTensor (Enstatite)
  unit: GPa              
  rank: 4 (3 x 3 x 3 x 3)
 
  tensor in Voigt matrix representation:
  5.5    0  9.5    0    0    0
    0 -5.5 -9.5    0    0    0
  9.5 -9.5    0    0    0    0
    0    0    0   -2    0    0
    0    0    0    0    2    0
    0    0    0    0    0    0

References

Decomposition of the elastic tensor and geophysical applications J.T. Browaeys, S. Chevrot, Geophysical Journal International (2004).

Citing this page. This page is part of the documentation of MTEX, a free and open source MATLAB toolbox for analyzing and modeling crystallographic textures. It was written by The MTEX Developers and is published at https://mtex-toolbox.github.io/tensor.symmetricDecomposition.html. If you use MTEX, or reuse text or figures from this page, in your research, please cite

F. Bachmann, R. Hielscher, H. Schaeben: Texture Analysis with MTEX - Free and Open Source Software Toolbox, Solid State Phenomena 160 (2010), 63-68. 10.4028/www.scientific.net/SSP.160.63

BibTeX

@article{bachmann2010mtex,
  author  = {F. Bachmann and R. Hielscher and H. Schaeben},
  title   = {Texture Analysis with MTEX - Free and Open Source Software Toolbox},
  journal = {Solid State Phenomena},
  volume  = {160},
  pages   = {63-68},
  year    = {2010},
  doi     = {10.4028/www.scientific.net/SSP.160.63},
  url     = {https://doi.org/10.4028/www.scientific.net/SSP.160.63}
}

Other papers describing specific MTEX methods are listed under Publications — please cite the one that best fits your application. The MTEX source code is licensed under the GNU General Public License v2.0; the text and figures of this documentation are licensed under CC BY 4.0, which permits reuse — including by automated systems — provided The MTEX Developers and this page are credited.