a tensor of rank R in a reference frame, or a list of them

Syntax

T = tensor(M, cs)

The coefficients in a crystal frame.

T = tensor(M, cs, rank=2, name='strain', unit='%')

The rank, a name and a unit.

T = tensor(v)

A vector as a tensor of rank one.

T = tensor(rot)

A rotation as its matrix, rank two.

C = tensor(V, rank=4)

A 6 x 6 Voigt matrix.

S = tensor(V, rank=4, doubleConvention=True)

With the factors of two of the compliance.

C = tensor(V, rank=4, Kelvin=True)

A matrix in the Kelvin notation.

Description

The coefficients M are an array whose last R indices have dimension three, the dimensions in front of them the shape of the list; the rank, when not given, is the number of trailing dimensions of size three. A 6 x 6 matrix is read as the Voigt matrix of a rank four tensor, a 3 x 6 matrix as that of a rank three one. Rotating the tensor, or an orientation acting on it, ori * T, transforms the coefficients, which is what the texture averages build on.

The frame is a crystalFrame or a specimenFrame, given positionally or as frame=; without one the tensor is in the default specimen frame. T.M gives the coefficients back, T.rank, T.frame (T.CS) and T.isSymmetric what they say. The physical tensors, stiffnessTensor, complianceTensor, strainTensor, stressTensor, …, are subclasses fixing the rank and the Voigt convention.

Input

`M`	array of the coefficients, (…, 3, …, 3), a Voigt matrix (…, 6, 6), a vector3d or a rotation
`cs`	crystalFrame or specimenFrame the coefficients refer to

Keywords

keyword	default	description
`rank`	`None`	the rank of the tensor, read from the shape of M when not given
`doubleConvention`	`None`	read and write a Voigt matrix with the factors of two off the diagonal, as is usual for the compliance
`frame`	`None`	the reference frame of the coefficients, instead of giving it positionally
`density`	`None`	the mass density of the material, carried along (the wave velocities use it)
`unit`	`None`	the physical unit of the coefficients, a string carried along
`name`	`None`	the name of the tensor, carried along
`Kelvin`	`False`	read a 6 x 6 matrix in the Kelvin (Mandel) notation
`dtype`	`None`	the NumPy type of the coefficients

Output

T tensor

Properties

`M`	full Cartesian coefficient array with rank trailing axes of length three
`rank`	number of tensor indices, independent of the number of tensors in a list
`frame`	reference frame of the coefficients
`CS`	alias for the tensor reference frame
`doubleConvention`	Voigt convention used for shear-component factors
`density`	material mass density, when provided
`unit`	physical unit label carried by the tensor
`name`	descriptive tensor label
`shape`	shape of the tensor list, excluding tensor-component axes

Used on

OrientationEmbeddings, TensorArithmetics, TensorDefinition, TensorVisualisation

MATLAB’s tensor.tensor

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/tensor.tensor_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.

tensor.tensor