ChristoffelTensor.ChristoffelTensor edit page

class representing the Christoffel tensor of a wave direction

The Christoffel tensor E(n) = n * C * n is the rank 2 tensor a stiffnessTensor C induces for a propagation direction n. Its eigenvalues give the elastic wave velocities in that direction, its eigenvectors the corresponding polarization directions.

Syntax

E = ChristoffelTensor(M,cs)

Input

M 3x3 matrix
cs crystal symmetry

Output

E ChristoffelTensor

Class Properties

M the tensor coefficients
rank always 2
CS symmetry the coefficients refer to

Example

fname = fullfile(mtexDataPath,'tensor','Olivine1997PC.GPa');
C = stiffnessTensor.load(fname);
E = ChristoffelTensor(C,vector3d.X)
E = ChristoffelTensor (y↓→x)
  rank: 2 (3 x 3)
 
 320.5     0     0
     0  78.7     0
     0     0    77

See also

tensor stiffnessTensor

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/ChristoffelTensor.ChristoffelTensor.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.