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test_solid_mechanics_model_linear_elastic_potential_energy.cc
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rAKA akantu
test_solid_mechanics_model_linear_elastic_potential_energy.cc
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/**
* @file test_solid_mechanics_model_linear_elastic_potential_energy.cc
*
* @author Tobias Brink <tobias.brink@epfl.ch>
*
* @date creation: Tue Nov 14 2017
* @date last modification: Fri Jan 26 2018
*
* @brief test potential energy of the linear elasticity model
*
*
* 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/>.
*
* @section description
*
* This test uses a linear elastic material with density = 1, Young's
* modulus = 1, and Poisson's ratio = 0 and applies a linear
* displacement from 0 to ε in x direction. The resulting potential
* energy density should be 0.5*Y*ε² = ε²/2. Since the mesh always has
* a volume of 1, the energy density equals the total energy. We test
* 3 different strains.
*
*/
/* -------------------------------------------------------------------------- */
#include "../test_solid_mechanics_model_fixture.hh"
#include "sparse_matrix.hh"
/* -------------------------------------------------------------------------- */
using
namespace
akantu
;
namespace
{
TYPED_TEST
(
TestSMMFixture
,
LinearElasticPotentialEnergy
)
{
const
auto
spatial_dimension
=
this
->
spatial_dimension
;
this
->
initModel
(
"test_solid_mechanics_model_linear_elastic_"
"potential_energy_material.dat"
,
_static
);
const
auto
&
lower
=
this
->
mesh
->
getLowerBounds
();
const
auto
&
upper
=
this
->
mesh
->
getUpperBounds
();
auto
length
=
upper
(
_x
)
-
lower
(
_x
);
const
auto
&
pos
=
this
->
mesh
->
getNodes
();
auto
&
disp
=
this
->
model
->
getDisplacement
();
auto
&
boun
=
this
->
model
->
getBlockedDOFs
();
std
::
vector
<
Real
>
strains
{
0.0
,
0.1
,
0.2
,
0.3
};
for
(
auto
&&
eps
:
strains
)
{
/// boundary conditions
for
(
auto
&&
pair
:
zip
(
make_view
(
pos
,
spatial_dimension
),
make_view
(
disp
,
spatial_dimension
),
make_view
(
boun
,
spatial_dimension
)))
{
const
auto
&
posv
=
std
::
get
<
0
>
(
pair
);
auto
&
dispv
=
std
::
get
<
1
>
(
pair
);
auto
&
bounv
=
std
::
get
<
2
>
(
pair
);
auto
reduced_x
=
(
posv
(
_x
)
-
lower
(
_x
))
/
length
;
dispv
(
_x
)
=
reduced_x
*
eps
;
bounv
(
_x
)
=
true
;
if
(
posv
(
_x
)
<
(
lower
(
_x
)
+
1e-6
))
{
if
((
spatial_dimension
>
1
)
and
(
posv
(
_y
)
<
(
lower
(
_y
)
+
1e-6
)))
{
bounv
(
_y
)
=
true
;
if
((
spatial_dimension
>
2
)
and
(
posv
(
_z
)
<
(
lower
(
_z
)
+
1e-6
)))
{
bounv
(
_z
)
=
true
;
}
}
}
}
if
(
this
->
dump_paraview
)
{
this
->
model
->
dump
();
}
/// "solve" a step (solution is imposed)
try
{
this
->
model
->
solveStep
();
}
catch
(...)
{
const
auto
&
A
=
this
->
model
->
getDOFManager
().
getMatrix
(
"J"
);
auto
prank
=
this
->
mesh
->
getCommunicator
().
whoAmI
();
A
.
saveMatrix
(
"solver_mumps"
+
std
::
to_string
(
prank
)
+
".mtx"
);
throw
;
}
if
(
this
->
dump_paraview
)
{
const
auto
&
A
=
this
->
model
->
getDOFManager
().
getMatrix
(
"J"
);
auto
prank
=
this
->
mesh
->
getCommunicator
().
whoAmI
();
A
.
saveMatrix
(
"solver_mumps"
+
std
::
to_string
(
prank
)
+
".mtx"
);
}
/// compare energy to analytical solution
auto
E_ref
=
0.5
*
eps
*
eps
;
auto
E_pot
=
this
->
model
->
getEnergy
(
"potential"
);
EXPECT_NEAR
(
E_ref
,
E_pot
,
1e-8
);
}
}
}
// namespace
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