Animated torsional-shear loading

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 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 Boundary. This is even possible in a Step with the ramp-argument.

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 Plugin during Job evaluation after each completed substep. The animation of the deformation is written to a GIF-file by 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 $\rightarrow$")