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

Usage

principal_stretch(x)

principal_strain(x)

or_shape_params(x)

Arguments

x: numeric. Can be three element vector, three column array, or an object of class "line" or "plane"

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
Vollmer: Point, Girdle, Random, Cylindricity (B), and Uniform Distance (D) Indices (Vollmer 1990; 2020). D is a measure of the "distance" from uniformity, and is linear from R to P, and R to G. End members are: uniform D = 0, girdle D = 0.5, cluster D = 1. The 99% level for a test against uniformity for a sample size of 300 is D = 0.1.
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
MAD: maximum angular deviation (Kirschvink, 1980)
US: Uniformity statistic of Mardia (1972)

References

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

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 
#> 9.511749 2.220799 2.143520 
principal_strain(x)
#>        e1        e2        e3 
#> 2.2525278 0.7978670 0.7624492 
or_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 
#> 
#> $Vollmer
#>          P          G          R          B          C          I          D 
#> 0.85541428 0.00674541 0.13784031 0.86215969 2.98015714 2.45061732 0.85710561 
#> 
#> $Flinn
#> intensity  symmetry 
#>  3.283228 91.062705 
#> 
#> $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_approx
#> [1] 17.97803
#> 
#> $MAD
#> [1] 17.97803
#> 
#> $US
#> [1] 367.315
#>