stiffnessTensor.stiffnessTensor edit page

class representing the elastic stiffness tensor

The stiffness tensor C is the rank 4 tensor relating stress and strain by sigma = C : epsilon. It is usually given as a 6x6 Voigt matrix, in GPa and without the factor of two of the double convention. The constructor warns if the matrix is not symmetric or not positive definite.

Syntax

C = stiffnessTensor(M,cs)
C = stiffnessTensor(M,cs,'unit','GPa')

Input

`M`	`6x6 Voigt matrix or 3x3x3x3 array`
`cs`	`crystal symmetry`

Output

`C`	`stiffnessTensor`

Options

unit physical unit of the entries, GPa by default

Class Properties

`M`	`the tensor coefficients`
`rank`	`always 4`
`CS`	`symmetry the coefficients refer to`

Example

cs = crystalSymmetry('m-3m');
C = stiffnessTensor(diag([230 230 230 117 117 117]),cs)

C = stiffnessTensor (crystal)
  unit: GPa              
  rank: 4 (3 x 3 x 3 x 3)
 
  tensor in Voigt matrix representation:
 230   0   0   0   0   0
   0 230   0   0   0   0
   0   0 230   0   0   0
   0   0   0 117   0   0
   0   0   0   0 117   0
   0   0   0   0   0 117

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/stiffnessTensor.stiffnessTensor.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.

stiffnessTensor.stiffnessTensor