Velocity gradient gradient tensors

The velocity gradient tensor describes the velocity of particles at any instant during the deformation. Velocity gradient tensor from deformation gradient tensor.

Usage

is.velgrad(x)

as.velgrad(object)

velgrad(x, time, ...)

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

# S3 method for class 'defgrad'
velgrad(x, time = 1, ...)

Source

apsg by O. Lexa: https://apsg.readthedocs.io/

Arguments

x: 3x3 matrix. Deformation gradient tensor.
object: 3x3 "matrix"
time: numeric. Total time (default is 1)
...: parameters passed to function call

Value

3x3 matrix. If steps is > 1, then a list of matrices is returned.

Details

velgrad() calculates the velocity gradient tensor as the matrix logarithm of the deformation gradient tensor divided by given time, and the deformation gradient tensor accumulated after some time.

Examples

d <- defgrad_from_generalshear(k = 2.5, gamma = 0.9)
l <- velgrad(d, time = 10)
d_steps <- defgrad(l, time = 10, steps = 2)

# apply on orientation data
set.seed(20250411)
v <- rvmf(100, mu = Line(0, 90), k = 100)
v_trans <- lapply(d_steps, function(i) {
  transform_linear(v, i)
})

# plot in stereonet
axes <- Vec3(c(1, 0, 0), c(0, 1, 0), c(0, 0, 1))
stereo_path(v_trans, type = "l", add = FALSE)
stereo_path(v_trans, type = "p", col = assign_col(seq_along(v_trans)), pch = 16, cex = .4)
points(axes, pch = 15)
text(axes, labels = c("x", "y", "z"), pos = 1)