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test_solid_mechanics_model_work_dynamics.cc
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rAKA akantu
test_solid_mechanics_model_work_dynamics.cc
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/**
* @file test_solid_mechanics_model_work_dynamics.cc
*
* @author Tobias Brink <tobias.brink@epfl.ch>
*
* @date creation: Tue Dec 15 2017
* @date last modification: Dec Nov 15 2017
*
* @brief test work in dynamic simulations
*
* @section description
*
* Assuming that the kinetic energy and the potential energy of the
* linear elastic material are bug free, the work in a dynamic
* simulation must equal the change in internal energy (first law of
* thermodynamics). Work in dynamics is an infinitesimal work Fds,
* thus we need to integrate it and compare at the end. In this test,
* we use one Dirichlet boundary condition (with u = 0.0, 0.01, and
* -0.01) and one Neumann boundary condition for F on the opposite
* side. Then we do a few steps to get reference energies for work and
* internal energy. After more steps, the change in both work and
* internal energy must be equal.
*
* @section LICENSE
*
* Copyright (©) 2017 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 "test_solid_mechanics_model_fixture.hh"
/* -------------------------------------------------------------------------- */
using
namespace
akantu
;
namespace
{
void
test_body
(
SolidMechanicsModel
&
model
,
Mesh
&
mesh
,
AnalysisMethod
analysis_method
,
UInt
steps_needed
)
{
const
auto
spatial_dimension
=
model
.
getSpatialDimension
();
getStaticParser
().
parse
(
"test_solid_mechanics_model_"
"work_material.dat"
);
/// model initialization
model
.
initFull
(
_analysis_method
=
analysis_method
);
model
.
assembleMassLumped
();
/// Create a node group for Neumann BCs.
auto
&
apply_force_grp
=
mesh
.
createNodeGroup
(
"apply_force"
);
auto
&
fixed_grp
=
mesh
.
createNodeGroup
(
"fixed"
);
const
auto
&
pos
=
mesh
.
getNodes
();
auto
&
lower
=
mesh
.
getLowerBounds
();
auto
&
upper
=
mesh
.
getUpperBounds
();
UInt
i
=
0
;
for
(
auto
&&
posv
:
make_view
(
pos
,
spatial_dimension
))
{
if
(
posv
(
_x
)
>
upper
(
_x
)
-
1e-6
)
{
apply_force_grp
.
add
(
i
);
}
else
if
(
posv
(
_x
)
<
lower
(
_x
)
+
1e-6
)
{
fixed_grp
.
add
(
i
);
}
++
i
;
}
mesh
.
createElementGroupFromNodeGroup
(
"el_apply_force"
,
"apply_force"
,
spatial_dimension
-
1
);
mesh
.
createElementGroupFromNodeGroup
(
"el_fixed"
,
"fixed"
,
spatial_dimension
-
1
);
/// set up timestep
auto
time_step
=
model
.
getStableTimeStep
()
*
0.1
;
model
.
setTimeStep
(
time_step
);
/// Do the sim
std
::
vector
<
Real
>
displacements
{
0.00
,
0.01
,
-
0.01
};
for
(
auto
&&
u
:
displacements
)
{
model
.
applyBC
(
BC
::
Dirichlet
::
FixedValue
(
u
,
_x
),
"el_fixed"
);
Vector
<
Real
>
surface_traction
(
spatial_dimension
);
surface_traction
(
_x
)
=
0.5
;
if
(
spatial_dimension
==
1
)
{
//TODO: this is a hack to work
// around non-implemented
// BC::Neumann::FromTraction for 1D
auto
&
force
=
model
.
getForce
();
for
(
auto
&&
pair
:
zip
(
make_view
(
pos
,
spatial_dimension
),
make_view
(
force
,
spatial_dimension
)))
{
auto
&
posv
=
std
::
get
<
0
>
(
pair
);
auto
&
forcev
=
std
::
get
<
1
>
(
pair
);
if
(
posv
(
_x
)
>
upper
(
_x
)
-
1e-6
)
{
forcev
(
_x
)
=
surface_traction
(
_x
);
}
}
}
else
{
model
.
applyBC
(
BC
::
Neumann
::
FromTraction
(
surface_traction
),
"el_apply_force"
);
}
// First, "equilibrate" a bit to get a reference state of total
// energy and work. This is needed when we have a Dirichlet with
// finite displacement on one side.
for
(
UInt
i
=
0
;
i
<
25
;
++
i
)
{
model
.
solveStep
();
}
// Again, work reported by Akantu is infinitesimal (dW) and we
// need to integrate a while to get a decent value.
double
Etot0
=
model
.
getEnergy
(
"potential"
)
+
model
.
getEnergy
(
"kinetic"
);
double
W
=
0.0
;
for
(
UInt
i
=
0
;
i
<
steps_needed
;
++
i
)
{
/// Solve.
model
.
solveStep
();
const
auto
dW
=
model
.
getEnergy
(
"external work"
);
W
+=
dW
;
}
// Finally check.
const
auto
Epot
=
model
.
getEnergy
(
"potential"
);
const
auto
Ekin
=
model
.
getEnergy
(
"kinetic"
);
EXPECT_NEAR
(
W
,
Ekin
+
Epot
-
Etot0
,
5e-2
);
// Sadly not very exact
// for such a coarse mesh.
}
}
/* TODO: this is currently disabled for terrible results and performance
TYPED_TEST(TestSMMFixtureBar, WorkImplicit) {
test_body(*(this->model), *(this->mesh), _implicit_dynamic, 500);
}
*/
TYPED_TEST
(
TestSMMFixtureBar
,
WorkExplicit
)
{
test_body
(
*
(
this
->
model
),
*
(
this
->
mesh
),
_explicit_lumped_mass
,
200
);
}
}
// namespace
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