Principal Stretches, Strain and Shape Parameters based on the Orientation Tensor.

Usage

principal_stretch(x, ...)

# Default S3 method
principal_stretch(x, ...)

# S3 method for class 'Vec3'
principal_stretch(x, ...)

# S3 method for class 'Line'
principal_stretch(x, ...)

# S3 method for class 'Ray'
principal_stretch(x, ...)

# S3 method for class 'Plane'
principal_stretch(x, ...)

# S3 method for class 'ortensor'
principal_stretch(x, ...)

# S3 method for class 'ellipsoid'
principal_stretch(x, ...)

principal_strain(x)

shape_params(x, ...)

# Default S3 method
shape_params(x, ...)

# S3 method for class 'spherical'
shape_params(x, ...)

# S3 method for class 'ortensor'
shape_params(x, ...)

# S3 method for class 'ellipsoid'
shape_params(x, ...)

Arguments

x: object of class "ortensor", "ellipsoid", or "Vec3", "Line", "Ray", "Plane", "Pair", or "Fault" where the rows are the observations and the columns are the coordinates.
...: optional parameters passed to ortensor()

Value

list

Details

stretch_ratios: Sqrt of eigenvalue ratios
strain_ratios: Log of stretch ratios
Ramsay: strain symmetry (Ramsay, 1983)
Woodcock: Woodcock shape
Flinn: Flinn strain intensity
Nadai: natural octahedral unit strain and shear (Nadai, 1963)
Lisle_intensity: Intensity index (Lisle, 1985)
Waterson_intensity: strain intensity (Watterson, 1968)
lode: Lode parameter (Lode, 1926)
kind: Descriptive type of ellipsoid: "O" - isotrope, "L" - L-tectonite, "LLS" - oblate L-tectonite, "S" - S-tectonite, "SSL" - prolate S-tectonite
MAD: maximum angular deviation (Kirschvink, 1980)

References

Flinn, Derek.(1963): "On the statistical analysis of fabric diagrams." Geological Journal 3.2: 247-253.

Jelinek, Vit. "Characterization of the magnetic fabric of rocks." Tectonophysics 79.3-4 (1981): T63-T67.

Kirschvink, J. (1980): The least-squares line and plane and the analysis of palaeomagnetic data. Geophysical Journal International, 62(3), 699-718.

Lisle, Richard J. (1985): "The use of the orientation tensor for the description and statistical testing of fabrics." Journal of Structural Geology 7.1: 115-117.

Lode, Walter (1926): "Versuche über den Einfluß der mittleren Hauptspannung auf das Fließen der Metalle Eisen, Kupfer und Nickel“ ("Experiments on the influence of the mean principal stress on the flow of the metals iron, copper and nickel"], Zeitschrift für Physik, vol. 36 (November), pp. 913–939, DOI: 10.1007/BF01400222

Mardia, Kantilal Varichand. (1975): "Statistics of directional data." Journal of the Royal Statistical Society Series B: Statistical Methodology 37.3: 349-371.

Nadai, A., and Hodge, P. G., Jr. (1963): "Theory of Flow and Fracture of Solids, vol. II." ASME. J. Appl. Mech. December 1963; 30(4): 640. https://doi.org/10.1115/1.3636654

Ramsay, John G. (1967): "Folding and fracturing of rocks." Mc Graw Hill Book Company 568.

Vollmer, Frederick W. (1990): "An application of eigenvalue methods to structural domain analysis." Geological Society of America Bulletin 102.6: 786-791.

Vollmer, Frederick W. (2020): "Representing Progressive Fabric Paths on a Triangular Plot Using a Fabric Density Index and Crystal Axes Eigenvector Barycenters." Geological Society of America Abstracts. Vol. 52.

Watterson, Juan. (1968): "Homogeneous deformation of the gneisses of Vesterland, south-west Greenland". No. 78. CA Reitzel.

Woodcock, N. H. (1977): "Specification of fabric shapes using an eigenvalue method." Geological Society of America Bulletin 88.9: 1231-1236.

Examples

set.seed(1)
mu <- Line(120, 50)
x <- rvmf(100, mu = mu, k = 20)
principal_stretch(x)
#>        S1        S2        S3 
#> 0.9511749 0.2220799 0.2143520 
principal_strain(x)
#>          e1          e2          e3 
#> -0.05005729 -1.50471812 -1.54013586 
shape_params(x)
#> $stretch_ratios
#>      Rxy      Ryz      Rxz 
#> 4.283031 1.036052 4.437444 
#> 
#> $strain_ratios
#>        e12        e13        e23 
#> 1.45466083 1.49007857 0.03541774 
#> 
#> $Flinn
#> $Flinn$k
#> [1] 91.0627
#> 
#> $Flinn$d
#> [1] 3.283228
#> 
#> 
#> $Ramsay
#> intensity  symmetry 
#>  2.117293 41.071535 
#> 
#> $Woodcock
#>  strength     shape 
#>  1.490079 41.071535 
#> 
#> $Watterson_intensity
#> [1] 4.319083
#> 
#> $Lisle_intensity
#> [1] 3.67315
#> 
#> $Nadai
#>     goct     eoct 
#> 1.388465 1.202446 
#> 
#> $Lode
#> [1] -0.9524619
#> 
#> $kind
#> [1] "L"
#> 
#> $MAD
#> [1] 17.97803
#> 
#> $Jellinek
#> [1] 5.476767
#>