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Ellipsoid class

Source: R/ellipsoid.R
ellipsoid-class.Rd

In deformation analysis, the quadratic forms of the three-dimensional stretches are represented by the ellipsoid class. It can be used to represents either ellipsoid objects or finite strain ellipsoids.

Usage

is.ellipsoid(x)

as.ellipsoid(x)

ellipsoid(x, left, ...)

# Default S3 method
ellipsoid(x, left = NULL, ...)

# S3 method for class 'defgrad'
ellipsoid(x, left = TRUE, ...)

Arguments

x

Either a matrix or a "defgrad" object

left

logical. TRUE for left Cauchy–Green deformation tensor (or Finger deformation tensor, the default), FALSE for for right Cauchy–Green deformation tensor (or Green’s deformation tensor)

...

optional parameters passed to function call.

Value

is.ellipsoid returns TRUE if x is an "ellipsoid" object, and FALSE otherwise.

as.ellipsoid coerces a 3x3 matrix into an "ellipsoid" object.

Details

The eigenvalues \(\lambda\) of the deformation matrix are the quadratic forms of the principal stretches \(s\) (\(s = 1 + \epsilon = l/l_0\)).

See also

ortensor()

Other ellipsoid: ellipsoid-params, ellipsoid_from_stretch()

Examples

test <- as.ellipsoid(diag(3))
is.ellipsoid(test)
#> [1] TRUE

R <- defgrad_from_ratio(2, 3)
ellipsoid(R)
#> Ellipsoid tensor
#>          [,1]     [,2]      [,3]
#> [1,] 5.241483 0.000000 0.0000000
#> [2,] 0.000000 1.310371 0.0000000
#> [3,] 0.000000 0.000000 0.1455967