a velocity gradient tensor L, the rank two tensor of the spatial derivatives of the velocity

Syntax

L = velocityGradientTensor(M)

By its 3 x 3 matrix.

L = velocityGradientTensor.uniaxial(d, q)

A uniaxial flow along d.

L = velocityGradientTensor.simpleShear(d, n, e)

Simple shear along d on the plane n.

Description

Its symmetric part is the strain rate, strainRate(L), its skew symmetric part the spin, spin(L). A solid does not compress, so every velocity gradient of one has trace zero.

Input

M 3 x 3 matrix, or an array (…, 3, 3) of them
d, n vector3d, the flow direction and the shear plane normal
q the share of the contraction across the second axis, 0.5 for an axially symmetric flow
e the strain rate

Keywords

keyword default description
rank None the rank of the tensor; for this class always two
doubleConvention None read and write a Voigt matrix with the factors of two off the diagonal
frame None the reference frame of the coefficients, instead of giving it positionally
density None the mass density of the material, carried along
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

L velocityGradientTensor

See also

tensor, strainRateTensor, spinTensor, deformationGradientTensor

MATLAB’s velocityGradientTensor.velocityGradientTensor

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/velocityGradientTensor.velocityGradientTensor_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.