the elastic compliance S = inv(C), its Voigt matrix carrying the factors of the double convention

Input

M 6-by-6 compliance matrix in engineering Voigt notation, full rank-four coefficients, or another tensor
args optional reference frame
kwargs tensor constructor options; unit defaults to ‘1/GPa’ and doubleConvention to True

Members

bulkModulus the bulk modulus of an isotropic polycrystal, the Voigt and Reuss bounds
ChristoffelTensor the elastic Christoffel tensor for a wave propagation direction
colon the double contraction A : B, the last two indices of A against the first two of B, MATLAB’s A:B
complianceTensor the elastic compliance S = inv(C), its Voigt matrix carrying the factors of the double convention
hashinShtrikmanBounds the Hashin-Shtrikman bounds of the isotropic moduli, the tightest pair for a quasihomogeneous polycrystal: (lower=(K, G), upper=(K, G)), each the extreme estimate over the references whose residual is semidefinite, found on the boundary of that convex set by a golden section over the shear and a bisection over the bulk modulus
inv the inverse: rank two by the matrix, rank four through the Voigt matrix, which swaps the convention and with it the class, a stiffness inverting to a compliance
linearCompressibility the linear compressibility, the length change per pressure in the direction v, S_ijkk v_i v_j
mtimes scale a tensor, multiply rank-two tensors, or contract an elastic tensor with a strain
PoissonRatio 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
rand a random tensor with the symmetries its class and frame ask for
shearModulus the shear modulus of the plane h and the shear direction u, 1 / (4 S_ijkl h_i u_j h_k u_l)
velocity the speeds of the three elastic plane waves in a direction and their polarisations, the eigenvalues and eigenvectors of the Christoffel tensor
volumeCompressibility the volume change per pressure, S_iikk
YoungsModulus Young’s modulus in the direction v, the reciprocal of S_ijkl v_i v_j v_k v_l

Used on

IsotropicTheory

MATLAB’s complianceTensor_index

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_index_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.