velocityGradientTensor.velocityGradientTensor edit page

class representing a velocity gradient tensor

The velocity gradient L is the rank 2 tensor of the spatial derivatives of the velocity field. Its symmetric part is the strainRateTensor, its skew symmetric part the spinTensor. Since solids are not compressible all velocity gradient tensors have trace 0.

Syntax

L = velocityGradientTensor(M)
L = velocityGradientTensor.uniaxial(d,e)
L = velocityGradientTensor.simpleShear(d,n,e)
L = velocityGradientTensor.pureShear(exp,comp,e)

Input

M 3x3 matrix
d, n vector3d
e strain rate
exp extension direction, vector3d
comp compression direction, vector3d

Output

L velocityGradientTensor

Class Properties

M the tensor coefficients
rank always 2
CS symmetry the coefficients refer to

Example

L = velocityGradientTensor.simpleShear(vector3d.X,vector3d.Z)
L = velocityGradientTensor (y↓→x)
  rank: 2 (3 x 3)
 
 0 0 2
 0 0 0
 0 0 0

See also

tensor strainRateTensor spinTensor

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.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.