a rank two symmetric stress tensor, or a list of them

Syntax

sigma = stressTensor(M)

By its 3 x 3 matrix.

sigma = stressTensor.uniaxial(vector3d.X)

The uniaxial tension along a direction.

sigma = stressTensor.uniaxial(v, 2)

Of a given magnitude.

Description

The stress is a symmetric tensor of rank two in the frame given, by default the specimen frame; the resolved shear stress on a slip system, SchmidFactor, and the equivalent stress are computed from it.

Input

`M`	3 x 3 symmetric matrix, or an array (…, 3, 3) of them
`v`	vector3d, the direction of a uniaxial tension

Keywords

keyword	default	description
`rank`		the rank of the tensor; for this class always two
`doubleConvention`		read and write a Voigt matrix with the factors of two off the diagonal
`frame`		the reference frame of the coefficients, instead of giving it positionally
`density`		the mass density of the material, carried along
`unit`		the physical unit of the coefficients, a string carried along
`name`		the name of the tensor, carried along
`Kelvin`		read a 6 x 6 matrix in the Kelvin (Mandel) notation
`dtype`		the NumPy type of the coefficients

Output

sigma stressTensor

Members

calcShearStress	resolve a stress tensor on slip systems and identify the most highly stressed system
deviatoricStress	remove the isotropic part of a rank-two stress or strain tensor
equivalentStress	compute the von Mises equivalent stress
meanStress	compute the mean normal stress, trace(sigma) / 3
normalize	the tensors divided by their Frobenius norms
stressTensor	a rank two symmetric stress tensor, or a list of them
uniaxial	the stress of a uniaxial tension along v, sigma v v^T

Used on

IsotropicTheory

MATLAB’s stressTensor_index

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/stressTensor_index_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.

The class stressTensor