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tamaas/examples/stresses.py
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stresses.py
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#!/usr/bin/env python3
#
# Copyright (©) 2016-2021 EPFL (École Polytechnique Fédérale de Lausanne),
# Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
#
# This program is free software: you can redistribute it and/or modify
# it under the terms of the GNU Affero General Public License as published
# by the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# This program is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Affero General Public License for more details.
#
# You should have received a copy of the GNU Affero General Public License
# along with this program. If not, see <https://www.gnu.org/licenses/>.
import argparse
import os
import numpy as np
import tamaas as tm
from tamaas.dumpers import H5Dumper as Dumper
from tamaas.dumpers._helper import hdf5toVTK
parser = argparse.ArgumentParser(
description="Hertzian tractios applied on elastic half-space")
parser.add_argument("radius", type=float, help="Radius of sphere")
parser.add_argument("load", type=float, help="Applied normal force")
parser.add_argument("name", help="Output file name")
parser.add_argument("--plots", help='Show surface normal stress',
action="store_true")
args = parser.parse_args()
# Definition of modeled domain
model_type = tm.model_type.volume_2d
discretization = [32, 127, 127]
system_size = [0.25, 1., 1.]
# Material contants
E = 1. # Young's modulus
nu = 0.3 # Poisson's ratio
E_star = E/(1-nu**2) # Hertz modulus
# Creation of model
model = tm.ModelFactory.createModel(model_type,
system_size,
discretization)
model.E = E
model.nu = nu
# Setup for integral operators
residual = tm.ModelFactory.createResidual(model, 0, 0)
# Coordinates
x = np.linspace(0, system_size[1], discretization[1], endpoint=False)
y = np.linspace(0, system_size[2], discretization[2], endpoint=False)
x, y = np.meshgrid(x, y, indexing='ij')
center = [0.5, 0.5]
r = np.sqrt((x-center[0])**2 + (y-center[1])**2)
# Span of local data
local_size = model.boundary_shape
local_offset = tm.mpi.local_offset(r.shape)
local_slice = np.s_[local_offset:local_offset+local_size[0], :]
# Sphere
R = args.radius
P = args.load
# Contact area
a = (3*P*R/(4*E_star))**(1/3)
p_0 = 3 * P / (2 * np.pi * a**2)
# Pressure definition
traction = model.traction
hertz_traction = np.zeros(discretization[1:])
hertz_traction[r < a] = p_0 * np.sqrt(1 - (r[r < a] / a)**2)
traction[..., 2] = hertz_traction[local_slice]
# Array references
displacement = model.displacement
stress = model['stress']
gradient = np.zeros_like(stress)
# Getting integral operators
boussinesq = model.operators["boussinesq"]
boussinesq_gradient = model.operators["boussinesq_gradient"]
# Applying operators
boussinesq(traction, displacement)
boussinesq_gradient(traction, gradient)
model.operators["hooke"](gradient, stress)
# Dumper
dumper_helper = Dumper(args.name, 'stress')
model.addDumper(dumper_helper)
model.dump()
# Converting HDF dump to VTK
with tm.mpi.sequential():
if tm.mpi.rank() == 0:
hdf5toVTK(os.path.join('hdf5', 'stress_0000.h5'), args.name)
if args.plots:
import matplotlib.pyplot as plt # noqa
fig, ax = plt.subplots(1, 2)
fig.suptitle("Rank {}".format(tm.mpi.rank()))
ax[0].set_title("Traction")
ax[1].set_title("Normal Stress")
ax[0].imshow(traction[..., 2])
ax[1].imshow(stress[0, ..., 2])
fig.tight_layout()
plt.show()
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