Rigid-body bounce with IPC contact

This example lets a rigid sphere fall under gravity and bounce on a fixed plane. It illustrates the rigid-body constraint, Newmark time integration, and IPC contact with a deliberately coarse model suitable for the online example gallery.

The longer, higher-resolution demonstration is available in examples/rigid_body/rigid_body_bounce_ipc.py.

import numpy as np
import pyvista as pv

import fedoo as fd

Model

Only the rigid body’s six generalized degrees of freedom are integrated; the surface meshes describe the contact geometry.

gravity = 9.81
mass = 1.0
radius = 0.1
initial_height = 0.4

space = fd.ModelingSpace("3D")
space.new_variable("DispX")
space.new_variable("DispY")
space.new_variable("DispZ")
space.new_vector("Disp", ("DispX", "DispY", "DispZ"))

sphere_mesh = fd.Mesh.from_pyvista(
    pv.Sphere(
        radius=radius,
        center=(0, 0, initial_height),
        theta_resolution=16,
        phi_resolution=16,
    )
)
floor_mesh = fd.Mesh.from_pyvista(
    pv.Plane(
        center=(0, 0, 0),
        direction=(0, 0, 1),
        i_size=1.0,
        j_size=1.0,
        i_resolution=3,
        j_resolution=3,
    ).triangulate(),
    name="Floor",
)

body = fd.constraint.RigidBody(
    sphere_mesh,
    mass=mass,
    inertia_tensor=(2 / 5) * mass * radius**2 * np.eye(3),
    center_of_mass=np.array([0, 0, initial_height]),
)
body.set_force([0, 0, -mass * gravity])
body.set_rayleigh_damping(0.5)
body.set_static_obstacle(floor_mesh, dhat=0.01, kappa=1e8)

Transient solution

The output interval limits the trajectory to a small number of animation frames. The time step is also larger than in the standalone demonstration to keep documentation builds reasonably short.

problem = fd.problem.NonLinear(body.assembly)
problem.set_time_integrator(fd.time.SECOND_ORDER, fd.time.Newmark())
results = problem.add_output(
    "rigid_body_bounce_gallery",
    ["Disp", "RigidDisp", "RigidRot"],
    include_static_obstacles=True,
)

dt = 2e-3
problem.nlsolve(
    dt=dt,
    dt_max=dt,
    tmax=0.8,
    update_dt=True,
    print_info=0,
    interval_output=0.04,
)

Animation

fedoo.MultiFrameDataSet.write_movie() loads and plots the saved frames automatically. Since the output includes static obstacles, the floor is present in the movie without any additional PyVista animation code.

plotter = pv.Plotter(window_size=(640, 480), off_screen=True)
plotter.camera_position = [(0.8, -0.8, 0.55), (0, 0, 0.2), (0, 0, 1)]
results.write_movie(
    "rigid_body_bounce.gif",
    framerate=15,
    plotter=plotter,
    show_edges=True,
)