A method of stiffnessTensor.

the shear modulus of the plane h and the shear direction u, 1 / (4 S_ijkl h_i u_j h_k u_l); MATLAB’s shearModulus

Syntax

G = shearModulus(C, h, u)

Of the plane h along u.

G = shearModulus(C, h)

The function of the shear direction.

G = shearModulus(C, None, u)

The function of the shear plane.

G = shearModulus(C)

The Voigt bound of an isotropic polycrystal.

G = shearModulus(C, 'Reuss')

The Reuss bound, ‘Hill’ the mean of the two.

GV, GR, GH = shearModulus(C, 'all') # all three

Description

With the plane and the direction the anisotropic modulus of the single crystal; with the plane alone the function on the sphere of the shear direction, with the direction alone the function of the shear plane. Without both, or with a bound’s name in place of the plane, the isotropic shear modulus of a polycrystal of uniformly distributed orientations: the Voigt upper bound, the Reuss lower bound or their mean, Hill’s; ‘all’ returns the three as a named tuple (voigt, reuss, hill), MATLAB’s three outputs.

Input

C stiffnessTensor or complianceTensor, a stiffness tensor is inverted first
h vector3d or Miller, the shear plane; or ‘Voigt’, ‘Reuss’, ‘Hill’, ‘all’
u vector3d or Miller, the shear direction

Output

G the shear modulus, an S2Fun of the direction or the plane, or the bounds

See also

YoungsModulus, PoissonRatio, bulkModulus, isotropicShearModulus

Signature

stiffnessTensor.shearModulus(T, h=None, u=None, *args)

MATLAB’s stiffnessTensor.shearModulus

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.shearModulus_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.