Deformation Gradient Tensor

Usage

defgrad_from_ratio(Rxy = 1, Ryz = 1)

defgrad_from_pair(p)

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
)

Arguments

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.
p: object of class pair
v1, v2: objects of class "spherical" or three-element vector. 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 "spherical" (incl. "line" and "plane") or a three-element vector. Angle in degrees when axis is a object of class "spherical", and radians otherwise.
xx, xy, xz, yx, yy, yz, zx, zy, zz: numeric. Directly specify components of the tensor. Identity matrix by default.

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
defgrad_from_axisangle(Line(120, 30), 45)
#>            [,1]       [,2]      [,3]
#> [1,]  0.7620243 -0.4486733 0.4669168
#> [2,]  0.2584335  0.8718592 0.4160212
#> [3,] -0.5937433 -0.1963513 0.7803301
defgrad_from_vectors(Line(120, 30), Line(210, 60))
#>             [,1]       [,2]       [,3]
#> [1,]  0.97419453 -0.1931138  0.1168422
#> [2,]  0.22291137  0.9044366 -0.3637374
#> [3,] -0.03543362  0.3803964  0.9241445
defgrad_from_pair(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