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tamaas/examples/nonperiodic.py
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nonperiodic.py
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#!/usr/bin/env python3
#
# Copyright (©) 2016-2023 EPFL (École Polytechnique Fédérale de Lausanne),
# Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
# Copyright (©) 2020-2023 Lucas Frérot
#
# 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 tamaas as tm
import matplotlib.pyplot as plt
from tamaas.utils import publications, hertz_surface
# Surface size
n = 512
# Surface radius
R = 0.1
# Surface generator
surface = hertz_surface([1., 1.], [n, n], R)
plt.imshow(surface)
# Creating model
model = tm.ModelFactory.createModel(tm.model_type.basic_2d, [1., 1.], [n, n])
tm.ModelFactory.registerNonPeriodic(model, 'dcfft')
# Solver
solver = tm.PolonskyKeerRey(model, surface, 1e-12)
solver.setIntegralOperator('dcfft')
# Solve for target pressure
p_target = 1.2
solver.solve(p_target)
# The concact solver always shifts the displacement so that gap >= 0
# To compute the true displacement, one needs to re-evaluate the displacement
model.operators['dcfft'](model.traction, model.displacement)
delta = (9 * p_target**2 / (16 * R * model.E_star**2))**(1/3)
print(f"Hertzian interference = {delta:.4f}, computed = {model.displacement.max():.4f}")
plt.figure()
plt.imshow(model.traction)
plt.title('Contact tractions')
plt.show()
publications()
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