MS_axes
MS_AXES - Reorient elasticity matrix for optimal decomposition.
Calculate the principle axes of elasticity tensor C, after:
Browaeys and Chevrot (GJI, v159, 667-678, 2004)
[ CR, ... ] = MS_axes(C)
[CR] = MS_axes(C)
Return a rotated elasticity matrix minimising the number of
distinct elements. This is the orientation which, on further
decomposition using MS_NORMS, will maximise the high symmetry
components of the matrix.
[CR, RR] = MS_axes(C)
In addition, return the rotation matrix, RR, used to perform
the rotation to generate C from CR.
[ ... ] = MS_axes( C, 'nowarn' )
Suppress all warnings.
[ ... ] = MS_axes( C, 'X3_stiff' )
For hexagonal or tetragonal tensors, make X3 the stiffest direction,
not the distinct direction. For triclinic or monoclinic tensors,
align the axes with the axes of the dilational stiffness tensor.
[ ... ] = MS_axes( C, 'debug' )
Enable debugging plots and messages. These are quite messy.
Notes:
If the input matrix has isotropic, hexagonal or tetragonal
symmetry there are multiple orentations of the principle axes.
In the isotropic case CR is not rotated with respect to C (and RR
is the identity matrix). In the hexagonal and tetragonal cases,
X3 is defined by the distinct eigenvalue (see Browaeys and Chevrot)
or, if 'X3_stiff', by the stiffest direction. For the monoclinic or
triclinic cases we have to make a 'best-guess' and following
Browraeys and Chevrot we use the bisectrix of each of the
eigenvectors of d and its closest match in v. Furthermore, in order
to always give the same output orientation for the lowest symmetry
cases, a final rotation is performed to place the maximum P-wave
velocity in the positive quadrent of the output axis system.
References:
Browaeys, J. T. and S. Chevrot (2004) Decomposition of the elastic
tensor and geophysical applications. Geophysical Journal
international v159, 667-678.
Cowin, S. C. and M. M. Mehrabadi (1987) On the identification of
material symmetry for anisotropic elastic materials. Quartely
Journal of Mechanics and Applied Mathematics v40, 451-476.
See also: MS_NORMS, MS_INTERPOLATE, MS_DECOMP