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conftest.py
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conftest.py
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# -*- coding: utf-8 -*-
# @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/>.
from __future__ import division, print_function
import numpy as np
import tamaas as tm
import pytest
from numpy.linalg import norm
def profile(func, size, mode, amplitude):
x = np.linspace(0, 1, size[0], endpoint=False, dtype=tm.dtype)
y = np.linspace(0, 1, size[1], endpoint=False, dtype=tm.dtype)
x, y = np.meshgrid(x, y, indexing='ij')
surface = amplitude * func(2*np.pi*x*mode[0]) * func(2*np.pi*y*mode[1])
return surface.copy()
@pytest.fixture(scope="session")
def tamaas_fixture():
tm.initialize()
yield None
tm.finalize()
class HertzFixture:
def __init__(self, n, load):
self.domain_size = 1
self.n = n
self.load = load
self.curvature = 0.1
self.radius = 1. / self.curvature
self.e_star = 1.
self.a = (3 * load / (4 * self.curvature * self.e_star))**(1. / 3.)
self.x = np.linspace(-self.domain_size / 2.,
self.domain_size / 2.,
self.n, dtype=tm.dtype)
self.y = self.x.copy()
self.x, self.y = np.meshgrid(self.x, self.y)
self._computeSurface()
self._computePressure()
self._computeDisplacement()
def _computeDisplacement(self):
r = np.sqrt(self.x**2 + self.y**2)
self.displacement = np.zeros_like(r)
contact = r < self.a
self.displacement[contact] = self.surface[contact]
self.displacement[~contact] = \
(self.surface[~contact]
+ self.a / (np.pi * self.radius) * np.sqrt(r[~contact]**2
- self.a**2)
+ (r[~contact]**2 - 2 * self.a**2) / (np.pi * self.radius)
* np.arccos(self.a / r[~contact]))
def _computePressure(self):
r = np.sqrt(self.x**2 + self.y**2)
self.pressure = np.zeros_like(r)
contact = np.where(r < self.a)
self.pressure[contact] = \
2 * self.e_star / (np.pi * self.radius) \
* np.sqrt(self.a**2 - r[contact]**2)
def _computeSurface(self):
self.surface = -1. / (2 * self.radius) * (self.x**2 + self.y**2)
@pytest.fixture(scope="module")
def hertz(tamaas_fixture):
return HertzFixture(1024, 0.00001)
@pytest.fixture(scope="module")
def hertz_coarse(tamaas_fixture):
return HertzFixture(512, 0.0001)
@pytest.fixture(scope="module",
params=[tm.PolonskyKeerRey.pressure])
def pkr(hertz, request):
model = tm.ModelFactory.createModel(tm.model_type.basic_2d,
[hertz.domain_size, hertz.domain_size],
[hertz.n, hertz.n])
model.setElasticity(hertz.e_star, 0)
solver = tm.PolonskyKeerRey(model, hertz.surface, 1e-12,
request.param,
request.param)
solver.solve(hertz.load)
return model, hertz
class WestergaardFixture:
def __init__(self, n, load):
self.domain_size = 1.
self.lamda = 1.
self.delta = 0.1
self.e_star = 1.
self.n = n
self.p_star = np.pi * self.e_star * self.delta / self.lamda
self.load = load * self.p_star
self.a = self.lamda / np.pi \
* np.arcsin(np.sqrt(self.load / self.p_star))
self.x = np.linspace(-self.domain_size / 2.,
self.domain_size / 2.,
self.n, endpoint=False, dtype=tm.dtype)
self._computeSurface()
self._computePressure()
self._computeDisplacement()
def _computeSurface(self):
self.surface = self.delta * np.cos(2 * np.pi * self.x / self.lamda)
def _computePressure(self):
self.pressure = np.zeros_like(self.surface)
contact = np.where(np.abs(self.x) < self.a)
self.pressure[contact] = 2 * self.load \
* (np.cos(np.pi * self.x[contact] / self.lamda)
/ np.sin(np.pi * self.a / self.lamda)**2) \
* np.sqrt(np.sin(np.pi * self.a / self.lamda)**2 -
np.sin(np.pi * self.x[contact] / self.lamda)**2)
def _computeDisplacement(self):
psi = np.pi * np.abs(self.x) / self.lamda
psi_a = np.pi * self.a / self.lamda
with np.errstate(invalid='ignore'): # get some warnings out of the way
self.displacement = (np.cos(2*psi) + 2 * np.sin(psi)
* np.sqrt(np.sin(psi)**2 - np.sin(psi_a)**2)
- 2 * np.sin(psi_a)**2 *
np.log((np.sin(psi) +
np.sqrt(np.sin(psi)**2
- np.sin(psi_a)**2))
/ np.sin(psi_a)))
contact = np.where(np.abs(self.x) < self.a)
self.displacement[contact] = np.cos(2*psi[contact])
self.displacement *= self.load * self.lamda / (np.pi * self.e_star
* np.sin(psi_a)**2)
@pytest.fixture(scope="module")
def westergaard(tamaas_fixture):
return WestergaardFixture(19683, 0.1)
class PatchWestergaard:
def __init__(self, model_type, domain, modes, size):
self.E = 3.
self.nu = 0.
self.e_star = self.E / (1 - self.nu**2)
self.n = size
self.domain = domain
self.model = tm.ModelFactory.createModel(model_type, domain,
size)
self.model.setElasticity(self.E, self.nu)
self.pressure = profile(np.cos, size, modes, 1)
self.solution = profile(np.cos, size, modes,
1 / (np.pi * self.e_star * norm(modes)))
@pytest.fixture(scope="module", params=[tm.model_type.basic_2d])
def patch_westergaard(tamaas_fixture, request):
return PatchWestergaard(request.param, [1., 1.], [3, 1], [6, 6])
class UniformPlasticity:
def __init__(self, model_type, domain, sizes):
self.n = sizes
self.domain = domain
self.model = tm.ModelFactory.createModel(model_type, domain,
sizes)
self.E_h = 0.1
self.sigma_y = 0.01
self.residual = tm.ModelFactory.createResidual(self.model,
sigma_y=self.sigma_y,
hardening=self.E_h)
self.model.E = 1.
self.model.nu = 0.
def solution(self, p):
E, nu = self.model.E, self.model.nu
E_h, sigma_y = self.E_h, self.sigma_y
mu = E / (2 * (1 + nu))
strain = -1 / (mu + E_h) * (p * (3 * mu + E_h) / (2 * mu)
- np.sign(p) * sigma_y)
dep = (2 * mu * np.abs(strain) - sigma_y) / (3 * mu + E_h)
plastic_strain = np.sign(strain) / 2 * dep * np.array([
-1, -1, 2, 0, 0, 0,
], dtype=tm.dtype)
stress = 2 * mu * (np.array([
0, 0, strain, 0, 0, 0
], dtype=tm.dtype) - plastic_strain)
return {
"stress": stress,
"plastic_strain": plastic_strain,
"cumulated_plastic_strain": dep
}, {
"stress": mu,
"plastic_strain": 1,
"cumulated_plastic_strain": 1
}
@pytest.fixture(scope="module", params=[tm.model_type.volume_2d])
def patch_isotropic_plasticity(tamaas_fixture, request):
return UniformPlasticity(request.param, [1., 1., 1.], [4, 4, 4])

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