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test_plastic_materials.cc
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rAKA akantu
test_plastic_materials.cc
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/**
* @file test_plastic_materials.cc
*
* @author Guillaume Anciaux <guillaume.anciaux@epfl.ch>
*
* @date creation: Fri Nov 17 2017
* @date last modification: Wed Feb 21 2018
*
* @brief Tests the plastic material
*
*
* Copyright (©) 2016-2018 EPFL (Ecole Polytechnique Fédérale de Lausanne)
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
* Akantu is free software: you can redistribute it and/or modify it under the
* terms of the GNU Lesser General Public License as published by the Free
* Software Foundation, either version 3 of the License, or (at your option) any
* later version.
*
* Akantu 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 Lesser General Public License for more
* details.
*
* You should have received a copy of the GNU Lesser General Public License
* along with Akantu. If not, see <http://www.gnu.org/licenses/>.
*
*/
/* -------------------------------------------------------------------------- */
#include "material_linear_isotropic_hardening.hh"
#include "solid_mechanics_model.hh"
#include "test_material_fixtures.hh"
#include <gtest/gtest.h>
#include <type_traits>
/* -------------------------------------------------------------------------- */
using
namespace
akantu
;
using
mat_types
=
::
testing
::
Types
<
// Traits<MaterialLinearIsotropicHardening, 1>,
// Traits<MaterialLinearIsotropicHardening, 2>,
Traits
<
MaterialLinearIsotropicHardening
,
3
>>
;
/* -------------------------------------------------------------------------- */
template
<>
void
FriendMaterial
<
MaterialLinearIsotropicHardening
<
3
>>::
testComputeStress
()
{
Real
E
=
1.
;
// Real nu = .3;
Real
nu
=
0.
;
Real
rho
=
1.
;
Real
sigma_0
=
1.
;
Real
h
=
0.
;
Real
bulk_modulus_K
=
E
/
3.
/
(
1
-
2.
*
nu
);
Real
shear_modulus_mu
=
0.5
*
E
/
(
1
+
nu
);
setParam
(
"E"
,
E
);
setParam
(
"nu"
,
nu
);
setParam
(
"rho"
,
rho
);
setParam
(
"sigma_y"
,
sigma_0
);
setParam
(
"h"
,
h
);
auto
rotation_matrix
=
getRandomRotation
();
Real
max_strain
=
10.
;
Real
strain_steps
=
100
;
Real
dt
=
max_strain
/
strain_steps
;
std
::
vector
<
double
>
steps
(
strain_steps
);
std
::
iota
(
steps
.
begin
(),
steps
.
end
(),
0.
);
Matrix
<
Real
>
previous_grad_u_rot
(
3
,
3
,
0.
);
Matrix
<
Real
>
previous_sigma
(
3
,
3
,
0.
);
Matrix
<
Real
>
previous_sigma_rot
(
3
,
3
,
0.
);
Matrix
<
Real
>
inelastic_strain_rot
(
3
,
3
,
0.
);
Matrix
<
Real
>
inelastic_strain
(
3
,
3
,
0.
);
Matrix
<
Real
>
previous_inelastic_strain
(
3
,
3
,
0.
);
Matrix
<
Real
>
previous_inelastic_strain_rot
(
3
,
3
,
0.
);
Matrix
<
Real
>
sigma_rot
(
3
,
3
,
0.
);
Real
iso_hardening
=
0.
;
Real
previous_iso_hardening
=
0.
;
// hydrostatic loading (should not plastify)
for
(
auto
&&
i
:
steps
)
{
auto
t
=
i
*
dt
;
auto
grad_u
=
this
->
getHydrostaticStrain
(
t
);
auto
grad_u_rot
=
this
->
applyRotation
(
grad_u
,
rotation_matrix
);
this
->
computeStressOnQuad
(
grad_u_rot
,
previous_grad_u_rot
,
sigma_rot
,
previous_sigma_rot
,
inelastic_strain_rot
,
previous_inelastic_strain_rot
,
iso_hardening
,
previous_iso_hardening
,
0.
,
0.
);
auto
sigma
=
this
->
reverseRotation
(
sigma_rot
,
rotation_matrix
);
Matrix
<
Real
>
sigma_expected
=
t
*
3.
*
bulk_modulus_K
*
Matrix
<
Real
>::
eye
(
3
,
1.
);
Real
stress_error
=
(
sigma
-
sigma_expected
).
norm
<
L_inf
>
();
ASSERT_NEAR
(
stress_error
,
0.
,
1e-13
);
ASSERT_NEAR
(
inelastic_strain_rot
.
norm
<
L_inf
>
(),
0.
,
1e-13
);
previous_grad_u_rot
=
grad_u_rot
;
previous_sigma_rot
=
sigma_rot
;
previous_inelastic_strain_rot
=
inelastic_strain_rot
;
previous_iso_hardening
=
iso_hardening
;
}
// deviatoric loading (should plastify)
// stress at onset of plastication
Real
beta
=
sqrt
(
42
);
Real
t_P
=
sigma_0
/
2.
/
shear_modulus_mu
/
beta
;
Matrix
<
Real
>
sigma_P
=
sigma_0
/
beta
*
this
->
getDeviatoricStrain
(
1.
);
for
(
auto
&&
i
:
steps
)
{
auto
t
=
i
*
dt
;
auto
grad_u
=
this
->
getDeviatoricStrain
(
t
);
auto
grad_u_rot
=
this
->
applyRotation
(
grad_u
,
rotation_matrix
);
Real
iso_hardening
,
previous_iso_hardening
;
this
->
computeStressOnQuad
(
grad_u_rot
,
previous_grad_u_rot
,
sigma_rot
,
previous_sigma_rot
,
inelastic_strain_rot
,
previous_inelastic_strain_rot
,
iso_hardening
,
previous_iso_hardening
,
0.
,
0.
);
auto
sigma
=
this
->
reverseRotation
(
sigma_rot
,
rotation_matrix
);
auto
inelastic_strain
=
this
->
reverseRotation
(
inelastic_strain_rot
,
rotation_matrix
);
if
(
t
<
t_P
)
{
Matrix
<
Real
>
sigma_expected
=
shear_modulus_mu
*
(
grad_u
+
grad_u
.
transpose
());
Real
stress_error
=
(
sigma
-
sigma_expected
).
norm
<
L_inf
>
();
ASSERT_NEAR
(
stress_error
,
0.
,
1e-13
);
ASSERT_NEAR
(
inelastic_strain_rot
.
norm
<
L_inf
>
(),
0.
,
1e-13
);
}
else
if
(
t
>
t_P
+
dt
)
{
// skip the transition from non plastic to plastic
auto
delta_lambda_expected
=
dt
/
t
*
previous_sigma
.
doubleDot
(
grad_u
+
grad_u
.
transpose
())
/
2.
;
auto
delta_inelastic_strain_expected
=
delta_lambda_expected
*
3.
/
2.
/
sigma_0
*
previous_sigma
;
auto
inelastic_strain_expected
=
delta_inelastic_strain_expected
+
previous_inelastic_strain
;
ASSERT_NEAR
((
inelastic_strain
-
inelastic_strain_expected
).
norm
<
L_inf
>
(),
0.
,
1e-13
);
auto
delta_sigma_expected
=
2.
*
shear_modulus_mu
*
(
0.5
*
dt
/
t
*
(
grad_u
+
grad_u
.
transpose
())
-
delta_inelastic_strain_expected
);
auto
delta_sigma
=
sigma
-
previous_sigma
;
ASSERT_NEAR
((
delta_sigma_expected
-
delta_sigma
).
norm
<
L_inf
>
(),
0.
,
1e-13
);
}
previous_sigma
=
sigma
;
previous_sigma_rot
=
sigma_rot
;
previous_grad_u_rot
=
grad_u_rot
;
previous_inelastic_strain
=
inelastic_strain
;
previous_inelastic_strain_rot
=
inelastic_strain_rot
;
}
}
namespace
{
template
<
typename
T
>
class
TestPlasticMaterialFixture
:
public
::
TestMaterialFixture
<
T
>
{};
TYPED_TEST_SUITE
(
TestPlasticMaterialFixture
,
mat_types
,
);
TYPED_TEST
(
TestPlasticMaterialFixture
,
ComputeStress
)
{
this
->
material
->
testComputeStress
();
}
TYPED_TEST
(
TestPlasticMaterialFixture
,
DISABLED_EnergyDensity
)
{
this
->
material
->
testEnergyDensity
();
}
TYPED_TEST
(
TestPlasticMaterialFixture
,
DISABLED_ComputeTangentModuli
)
{
this
->
material
->
testComputeTangentModuli
();
}
TYPED_TEST
(
TestPlasticMaterialFixture
,
DISABLED_ComputeCelerity
)
{
this
->
material
->
testCelerity
();
}
}
// namespace
/*****************************************************************/
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