Deformation Gradient Tensor

Usage

is.defgrad(x)

as.defgrad(object)

defgrad(x, ...)

defgrad_from_ratio(Rxy = 1, Ryz = 1)

# S3 method for class 'Pair'
defgrad(x, ...)

defgrad_from_vectors(v1, v2)

defgrad_from_axisangle(axis, angle)

defgrad_from_comp(
  xx = 1,
  xy = 0,
  xz = 0,
  yx = 0,
  yy = 1,
  yz = 0,
  zx = 0,
  zy = 0,
  zz = 1
)

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

# S3 method for class 'velgrad'
defgrad(x, time, steps)

Arguments

x: object of class "Pair", "velgrad" or 3x3 "matrix"
object: 3x3 "matrix"
...: parameters passed to function call
Rxy, Ryz: numeric. the XY and YZ strain ratio to create a strain tensor with axial stretches.Values must be greater than or equal to 1.
v1, v2: spherical objects. Deformation gradient results from the rotation around axis perpendicular to both vectors to rotate v1 to v2.
axis, angle: rotation axis and angle, axis can be an object of class "Vec3", "Line", "Ray", or "Plane", or a three-element vector. Angle in degrees when axis is a object of class "Line", "Ray", or "Plane", and radians otherwise.
xx, xy, xz, yx, yy, yz, zx, zy, zz: numeric. Directly specify components of the tensor. Identity matrix by default.
time: numeric. Total time (default is 1)
steps: numeric. Time increments (default is 1)

Value

3x3 matrix.

Examples

defgrad_from_ratio(2, 3)
#>          [,1]     [,2]      [,3]
#> [1,] 2.289428 0.000000 0.0000000
#> [2,] 0.000000 1.144714 0.0000000
#> [3,] 0.000000 0.000000 0.3815714
#> attr(,"class")
#> [1] "matrix"  "array"   "defgrad"
defgrad_from_axisangle(Line(120, 50), 60)
#>            [,1]       [,2]      [,3]
#> [1,]  0.8798642 -0.4069917 0.2453504
#> [2,]  0.3590528  0.9075417 0.2178283
#> [3,] -0.3113200 -0.1035655 0.9446449
#> attr(,"class")
#> [1] "matrix"  "array"   "defgrad"
defgrad_from_vectors(Line(120, 50), Line(270, 80))
#>             [,1]       [,2]       [,3]
#> [1,]  0.86775875 0.01649708  0.2175641
#> [2,]  0.08991349 0.77796344 -0.4437182
#> [3,] -0.19880103 0.45243581  0.7540121
#> attr(,"class")
#> [1] "matrix"  "array"   "defgrad"
defgrad(Pair(40, 20, 75, 16))
#>           [,1]       [,2]       [,3]
#> [1,] 0.2487928 -0.9331095 -0.2620026
#> [2,] 0.9285075  0.3060065 -0.2198463
#> [3,] 0.2756374 -0.1885752  0.9396926
#> attr(,"class")
#> [1] "matrix"  "array"   "defgrad"