the elastic Christoffel tensor for a wave propagation direction

Syntax

E = ChristoffelTensor(C, n)
E = ChristoffelTensor(M, cs)

Description

For stiffness C and a unit direction n, the rank-two tensor is E[i, k] = C[i, j, k, l] n[j] n[l], summed over j and l. Its eigenvectors give the polarisation directions of the three elastic waves. Dividing its eigenvalues by the material density gives squared wave speeds when consistent physical units are used. The velocity function handles the supported stiffness and density units.

It can also be constructed from a 3-by-3 matrix using the tensor constructor options. When constructed from C, the crystal frame and density are carried from C.

Input

`M`	stiffnessTensor or complianceTensor, or a 3-by-3 Christoffel matrix; compliance is inverted to stiffness before contraction
`args`	propagation direction n when M is elastic stiffness or compliance; otherwise the reference frame and other positional tensor arguments
`kwargs`	tensor constructor options for direct matrix input

Output

`E`	ChristoffelTensor

Properties

`M`	numeric tensor coefficients, with trailing dimensions (3, 3)
`rank`	2
`frame`	coordinate frame of the coefficients
`density`	material density carried from the elastic tensor

Signature

complianceTensor.ChristoffelTensor(M, *args, **kwargs)

MATLAB’s complianceTensor.ChristoffelTensor

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/complianceTensor.ChristoffelTensor_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.

complianceTensor.ChristoffelTensor