tensor.tensor edit page

class representing a material tensor of arbitrary rank

A tensor stores its coefficients in the array M, together with the referenceFrame, respectively the crystal symmetry, they are given with respect to. Rotating a tensor or an orientation acting on it transforms the coefficients accordingly, which is what makes calculations like the elastic properties of a textured aggregate possible.

Tensors of rank 4 come in two flavours of Voigt matrix notation. The flag doubleConvention selects the one where the off diagonal entries carry a factor of two, as is usual for the compliance tensor.

Syntax

T = tensor(M,CS)
T = tensor(M,'rank',r)
T = tensor(M,CS,'name',name,'unit',unit)

Input

M matrix of tensor entries
CS crystal symmetry

Options

rank rank of the tensor
unit physical unit of the entries
name name of the tensor
doubleConvention Voigt notation with a factor of two off the diagonal

Class Properties

M the tensor coefficients
rank tensor rank
CS symmetry the coefficients refer to
frame referenceFrame the tensor is expressed in
how2plot plottingConvention, read only
doubleConvention Voigt convention of a rank 4 tensor
isSymmetric is the tensor symmetric
isSkewSymmetric is the tensor skew symmetric

Derived Classes

stiffnessTensor elastic stiffness
complianceTensor elastic compliance
strainTensor strain
strainRateTensor strain rate
stressTensor stress
deformationGradientTensor deformation gradient
velocityGradientTensor velocity gradient
spinTensor infinitesimal rotation
curvatureTensor lattice curvature
dislocationDensityTensor dislocation density, Nye tensor
ChristoffelTensor Christoffel tensor of a wave direction
refractiveIndexTensor optical refractive index

See also

TensorDefinition 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/tensor.tensor.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.