r"""
Animated torsional-shear loading
--------------------------------

.. topic:: Save an animation of a custom boundary condition.

   * assign non-homogeneous displacements to a boundary condition

   * create an animation

   * export a GIF-movie

   * evaluate the reaction moment on a boundary condition

This example demonstrates how to create a :class:`~felupe.Boundary` for torsional
loading. This is somewhat more complicated than a simple boundary condition with
identical mesh-point values because the values of the mesh-points are different.
However, this is not a problem. FElupe supports arrays to be passed as the ``value``-
argument of a :class:`~felupe.Boundary`. This is even possible in a
:class:`~felupe.Step` with the ``ramp``-argument.
"""

# sphinx_gallery_thumbnail_number = -2
import matplotlib.pyplot as plt
import numpy as np

import felupe as fem

mesh = fem.mesh.Triangle(n=3).expand(n=6)
field = fem.FieldContainer([fem.Field(fem.RegionHexahedron(mesh), dim=3)])

boundaries = {
    "bottom": fem.Boundary(field[0], fz=0),
    "top": fem.Boundary(field[0], fz=1),
}
solid = fem.SolidBody(umat=fem.NeoHookeCompressible(mu=1, lmbda=2), field=field)

angles_deg = fem.math.linsteps([0, -30, 0], num=5)[:-1]
move = []
for phi in angles_deg:
    top = mesh.points[boundaries["top"].points]
    top_rotated = fem.math.rotate_points(
        points=top,
        angle_deg=phi,
        axis=2,
        center=[0, 0, 1],
    )
    move.append(top_rotated - top)


# %%
# The reaction moment on the centerpoint of the right end face is tracked by a custom
# :class:`~felupe.Plugin` during :class:`~felupe.Job` evaluation after each completed
# substep. The animation of the deformation is written to a GIF-file by
# :class:`~felupe.AnimationWriterPlugin`.
class ReactionMoment(fem.Plugin):
    def __init__(self):
        self.values = []

    def after_substep(self, context, state):
        # evaluate the reaction moment at the centerpoint of the right end face
        forces = context.substep.fun
        M = fem.tools.moment(field, forces, boundaries["top"], centerpoint=[0, 0, 1])
        self.values.append(M)


animation = fem.AnimationWriterPlugin(
    items=[field],
    filename="result.gif",
    name="Principal Values of Logarithmic Strain",
    component=0,  # max. principal value of logarithmic strain
    reset_camera=False,
    clim=[0, 0.2],
)
moment = ReactionMoment()
step = fem.Step(items=[solid], ramp={boundaries["top"]: move}, boundaries=boundaries)
job = fem.Job(steps=[step], plugins=[animation, moment]).evaluate()

# %%
# Finally, let's plot the reaction moment vs. torsion angle curve.
fig, ax = plt.subplots()
ax.plot(abs(angles_deg), abs(np.array(moment.values)[:, 2]), "o-")
ax.set_xlabel(r"Torsion Angle $|\phi_3|$ in deg $\rightarrow$")
ax.set_ylabel(r"Torsion Moment $|M_3|$ in Nmm $\rightarrow$")