deformationGradientTensor.deformationGradientTensor edit page

class representing a deformation gradient tensor

The deformation gradient F contains the full information about the local rotation and deformation of the material. It also shows, for example, how a small line segment in the undeformed body, dX, is rotated and stretched into a line segment in the deformed body, dx, since dx = F dX. As F is volume preserving this implies that det F = 1.

Syntax

F = deformationGradientTensor(M)
F = deformationGradientTensor.uniaxial(d,rate)
F = deformationGradientTensor.simpleShear(d,n,e)
F = deformationGradientTensor.pureShear(exp,compr,lambda)

Input

M 3x3 matrix
d, n vector3d
rate, e amount of deformation
exp, compr extension and compression direction, vector3d
lambda stretch

Output

F deformationGradientTensor

Class Properties

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

Example

F = deformationGradientTensor.simpleShear(vector3d.X,vector3d.Z,0.2)
F = deformationGradientTensor (y↓→x)
  rank: 2 (3 x 3)
 
      1      0 0.2027
      0      1      0
      0      0      1

See also

tensor velocityGradientTensor strainTensor

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.deformationGradientTensor.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.