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66c9c8a | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 | # Copyright (c) 2022 NVIDIA CORPORATION. All rights reserved.
# NVIDIA CORPORATION and its licensors retain all intellectual property
# and proprietary rights in and to this software, related documentation
# and any modifications thereto. Any use, reproduction, disclosure or
# distribution of this software and related documentation without an express
# license agreement from NVIDIA CORPORATION is strictly prohibited.
###########################################################################
# Example DEM
#
# Shows how to implement a DEM particle simulation with cohesion between
# particles. Neighbors are found using the wp.HashGrid class, and
# wp.hash_grid_query(), wp.hash_grid_query_next() kernel methods.
#
###########################################################################
import os
import numpy as np
import warp as wp
import warp.render
wp.init()
@wp.func
def contact_force(n: wp.vec3, v: wp.vec3, c: float, k_n: float, k_d: float, k_f: float, k_mu: float):
vn = wp.dot(n, v)
jn = c * k_n
jd = min(vn, 0.0) * k_d
# contact force
fn = jn + jd
# friction force
vt = v - n * vn
vs = wp.length(vt)
if vs > 0.0:
vt = vt / vs
# Coulomb condition
ft = wp.min(vs * k_f, k_mu * wp.abs(fn))
# total force
return -n * fn - vt * ft
@wp.kernel
def apply_forces(
grid: wp.uint64,
particle_x: wp.array(dtype=wp.vec3),
particle_v: wp.array(dtype=wp.vec3),
particle_f: wp.array(dtype=wp.vec3),
radius: float,
k_contact: float,
k_damp: float,
k_friction: float,
k_mu: float,
):
tid = wp.tid()
# order threads by cell
i = wp.hash_grid_point_id(grid, tid)
x = particle_x[i]
v = particle_v[i]
f = wp.vec3()
# ground contact
n = wp.vec3(0.0, 1.0, 0.0)
c = wp.dot(n, x)
cohesion_ground = 0.02
cohesion_particle = 0.0075
if c < cohesion_ground:
f = f + contact_force(n, v, c, k_contact, k_damp, 100.0, 0.5)
# particle contact
neighbors = wp.hash_grid_query(grid, x, radius * 5.0)
for index in neighbors:
if index != i:
# compute distance to point
n = x - particle_x[index]
d = wp.length(n)
err = d - radius * 2.0
if err <= cohesion_particle:
n = n / d
vrel = v - particle_v[index]
f = f + contact_force(n, vrel, err, k_contact, k_damp, k_friction, k_mu)
particle_f[i] = f
@wp.kernel
def integrate(
x: wp.array(dtype=wp.vec3),
v: wp.array(dtype=wp.vec3),
f: wp.array(dtype=wp.vec3),
gravity: wp.vec3,
dt: float,
inv_mass: float,
):
tid = wp.tid()
v_new = v[tid] + f[tid] * inv_mass * dt + gravity * dt
x_new = x[tid] + v_new * dt
v[tid] = v_new
x[tid] = x_new
class Example:
def __init__(self, stage):
self.device = wp.get_device()
self.frame_dt = 1.0 / 60
self.frame_count = 400
self.sim_substeps = 64
self.sim_dt = self.frame_dt / self.sim_substeps
self.sim_steps = self.frame_count * self.sim_substeps
self.sim_time = 0.0
self.point_radius = 0.1
self.k_contact = 8000.0
self.k_damp = 2.0
self.k_friction = 1.0
self.k_mu = 100000.0 # for cohesive materials
self.inv_mass = 64.0
self.renderer = wp.render.UsdRenderer(stage)
self.renderer.render_ground()
self.grid = wp.HashGrid(128, 128, 128)
self.grid_cell_size = self.point_radius * 5.0
self.points = self.particle_grid(32, 128, 32, (0.0, 0.3, 0.0), self.point_radius, 0.1)
self.x = wp.array(self.points, dtype=wp.vec3)
self.v = wp.array(np.ones([len(self.x), 3]) * np.array([0.0, 0.0, 10.0]), dtype=wp.vec3)
self.f = wp.zeros_like(self.v)
self.use_graph = wp.get_device().is_cuda
if self.use_graph:
wp.capture_begin(self.device)
try:
for _ in range(self.sim_substeps):
with wp.ScopedTimer("forces", active=False):
wp.launch(
kernel=apply_forces,
dim=len(self.x),
inputs=[
self.grid.id,
self.x,
self.v,
self.f,
self.point_radius,
self.k_contact,
self.k_damp,
self.k_friction,
self.k_mu,
],
)
wp.launch(
kernel=integrate,
dim=len(self.x),
inputs=[self.x, self.v, self.f, (0.0, -9.8, 0.0), self.sim_dt, self.inv_mass],
)
finally:
self.graph = wp.capture_end(self.device)
def update(self):
with wp.ScopedTimer("simulate", active=True):
if self.use_graph:
with wp.ScopedTimer("grid build", active=False):
self.grid.build(self.x, self.grid_cell_size)
with wp.ScopedTimer("solve", active=False):
wp.capture_launch(self.graph)
self.sim_time += self.frame_dt
else:
with wp.ScopedTimer("grid build", active=False):
self.grid.build(self.x, self.point_radius)
with wp.ScopedTimer("solve", active=False):
for _ in range(self.sim_substeps):
wp.launch(
kernel=apply_forces,
dim=len(self.x),
inputs=[
self.grid.id,
self.x,
self.v,
self.f,
self.point_radius,
self.k_contact,
self.k_damp,
self.k_friction,
self.k_mu,
],
)
wp.launch(
kernel=integrate,
dim=len(self.x),
inputs=[self.x, self.v, self.f, (0.0, -9.8, 0.0), self.sim_dt, self.inv_mass],
)
self.sim_time += self.sim_dt
def render(self, is_live=False):
with wp.ScopedTimer("render", active=True):
time = 0.0 if is_live else self.sim_time
self.renderer.begin_frame(time)
self.renderer.render_points(points=self.x.numpy(), radius=self.point_radius, name="points")
self.renderer.end_frame()
# creates a grid of particles
def particle_grid(self, dim_x, dim_y, dim_z, lower, radius, jitter):
points = np.meshgrid(np.linspace(0, dim_x, dim_x), np.linspace(0, dim_y, dim_y), np.linspace(0, dim_z, dim_z))
points_t = np.array((points[0], points[1], points[2])).T * radius * 2.0 + np.array(lower)
points_t = points_t + np.random.rand(*points_t.shape) * radius * jitter
return points_t.reshape((-1, 3))
if __name__ == "__main__":
stage_path = os.path.join(os.path.dirname(__file__), "outputs/example_dem.usd")
example = Example(stage_path)
for i in range(example.frame_count):
example.update()
example.render()
example.renderer.save()
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