complianceTensor.shearModulus edit page

shear modulus for an compliance tensor

Description

\[E = \frac{1}{4 S_{ijkl} h_i u_j h_k u_l}\]

Syntax

[GV,GR,GVRH] = shearModulus(S) % the isotropic case
E = shearModulus(S,h,u) % the anisotropic case with plane h and shear direction  u
E = shearModulus(S,[],u)
E = shearModulus(S,h,[])

Input

C elastic stiffnessTensor
h shear plane vector3d
u shear direction vector3d

Output

E shear modulus
GVoigt Voigt effective shear modulus, upper bound
GReuss Reuss effective shear modulus, lower bound
GHill Hill effective shear modulus

See also

complianceTensor.YoungsModulus complianceTensor.volumeCompressibility complianceTensor.ChristoffelTensor

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/complianceTensor.shearModulus.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.