convert tensor coefficients to orthonormal Kelvin (Mandel) notation

Syntax

K = Kelvin(T)

Description

The pair order is (11, 22, 33, 23, 13, 12), as in Voigt notation, with a factor sqrt(2) for each off-diagonal pair. A rank-four tensor gives a 6-by-6 matrix. These factors preserve the Euclidean inner product of symmetric tensors and are used for tensor matrix functions. Leading array dimensions are retained.

Input

T tensor of rank 2, 3 or 4

Output

K numeric coefficient array in Kelvin notation

See also

Voigt, tensor.expm, tensor.logm

Signature

Kelvin(T)
source

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/Kelvin_py.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.