A method of stiffnessTensor.

the Poisson ratio of the tension direction x and the transverse direction y, minus the transverse over the longitudinal strain, -S_ijkl x_i x_j y_k y_l / S_mnop x_m x_n x_o x_p; MATLAB’s PoissonRatio

Syntax

nu = PoissonRatio(C, x, y)

Of the tension along x, the contraction along y.

nu = PoissonRatio(C, x)

The function of the transverse direction.

nu = PoissonRatio(C, None, y) # the function of the tension direction

nu = PoissonRatio(C)

The isotropic ratio.

Description

Without directions the ratio of an isotropic polycrystal, that of the compliance tensor averaged over uniformly distributed orientations: (3K - 2G) / (2 (3K + G)) with the Reuss bounds of the bulk and the shear modulus.

Input

C stiffnessTensor or complianceTensor, a stiffness tensor is inverted first
x vector3d or Miller, the tension direction
y vector3d or Miller, the transverse direction, perpendicular to x

Output

nu the Poisson ratio, or an S2Fun of the transverse or the tension direction

See also

YoungsModulus, shearModulus, bulkModulus

Signature

stiffnessTensor.PoissonRatio(T, x=None, y=None)

MATLAB’s stiffnessTensor.PoissonRatio

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/stiffnessTensor.PoissonRatio_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.