a deformation gradient tensor F, the rank two tensor carrying a line segment dX of the undeformed body into dx = F dX of the deformed one
Syntax
F = deformationGradientTensor(M)
By its 3 x 3 matrix.
F = deformationGradientTensor.uniaxial(d, rate)
A uniaxial deformation along d.
F = deformationGradientTensor.simpleShear(d, n, e)
Simple shear along d on the plane n.
F = deformationGradientTensor.pureShear(ex, comp, lam) # pure shear, extension along ex
Description
The deformation gradient holds the full local rotation and stretch of the material; a volume preserving deformation has det F = 1. Its strains are F.GreenStrain() and F.CauchyStrain().
Input
M |
3 x 3 matrix, or an array (…, 3, 3) of them |
d, n |
vector3d, the shear direction and the shear plane normal |
rate, e |
the amount of deformation |
ex, comp |
vector3d, the extension and the compression direction |
lam |
the stretch |
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
F |
deformationGradientTensor |
See also
tensor, velocityGradientTensor, strainTensor
Members
| CauchyStrain | compute the small-strain approximation from a deformation gradient |
| deformationGradientTensor | a deformation gradient tensor F, the rank two tensor carrying a line segment dX of the undeformed body into dx = F dX of the deformed one |
| GreenStrain | compute the Green–Lagrange finite strain of a deformation gradient |
| logm | the matrix logarithm of a rank two tensor, or of a rank four one through its Kelvin matrix, the class kept |
| pureShear | the deformation gradient of a pure shear, stretched by lam along ext and shortened by 1 / lam along comp |
| simpleShear | the deformation gradient of a simple shear along d on the plane n by the angle gamma, I + tan(gamma) d n^T |
| uniaxial | the deformation gradient of a uniaxial stretch along d, the volume kept |
MATLAB’s deformationGradientTensor_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/deformationGradientTensor_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.