tensor.symmetricDecomposition edit page

decomposes the tensor into

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