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stresses.py
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Fri, May 17, 21:17

stresses.py
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#!/usr/bin/env python3
# @file
# @section LICENSE
#
# Copyright (©) 2016-2020 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 numpy as np
import tamaas as tm
import argparse
from tamaas.dumpers import UVWDumper
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")
args = parser.parse_args()
tm.initialize()
# Definition of modeled domain
model_type = tm.model_type.volume_2d
discretization = [127, 127, 127]
system_size = [1., 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)
# 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.getTraction()
traction[r < a, 2] = p_0 * np.sqrt(1 - (r[r < a] / a)**2)
# Array references
displacement = model.getDisplacement()
stress = residual.getStress()
gradient = residual.getVector()
# Applying operator
boussinesq = model.getIntegralOperator("boussinesq")
boussinesq_gradient = model.getIntegralOperator("boussinesq_gradient")
boussinesq.apply(traction, displacement)
boussinesq_gradient.apply(traction, gradient)
model.applyElasticity(stress, gradient)
# Dumper
dumper_helper = UVWDumper(args.name, 'stress')
model.addDumper(dumper_helper)
model.dump()
print("Done")
tm.finalize()

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