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mindlin.cpp
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rTAMAAS tamaas
mindlin.cpp
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/**
* @file
*
* @author Lucas Frérot <lucas.frerot@epfl.ch>
*
* @section LICENSE
*
* Copyright (©) 2017 EPFL (Ecole Polytechnique Fédérale de
* Lausanne) Laboratory (LSMS - Laboratoire de Simulation en Mécanique des
* Solides)
*
* Tamaas 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.
*
* Tamaas 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 Tamaas. If not, see <http://www.gnu.org/licenses/>.
*
*/
/* -------------------------------------------------------------------------- */
#include "mindlin.hh"
#include "elasto_plastic_model.hh"
#include "influence.hh"
#include "kelvin_helper.hh"
/* -------------------------------------------------------------------------- */
namespace
tamaas
{
/* -------------------------------------------------------------------------- */
namespace
detail
{
template
<
model_type
type
,
typename
T
>
class
MindlinBoussinesqHelper
{
using
boussinesq_t
=
T
;
using
trait
=
model_type_traits
<
type
>
;
static
constexpr
UInt
dim
=
trait
::
dimension
;
static
constexpr
UInt
bdim
=
trait
::
boundary_dimension
;
public
:
MindlinBoussinesqHelper
(
const
T
&
boussinesq
,
const
influence
::
ElasticHelper
<
dim
>&
el
,
Real
y_3
,
Real
cutoff
)
:
boussinesq
(
boussinesq
),
el
(
el
),
y_3
(
y_3
),
cutoff
(
cutoff
)
{}
inline
void
applyIntegral
(
GridHermitian
<
Real
,
bdim
>&
out
,
GridHermitian
<
Real
,
bdim
>&
surface_gradients
,
GridHermitian
<
Real
,
bdim
>&
source_stresses
,
const
Grid
<
Real
,
bdim
>&
wavevectors
)
const
{
using
k_out
=
typename
KelvinTrait
<
T
>::
out_t
;
using
m_type
=
MatrixProxy
<
Complex
,
dim
,
dim
>
;
using
v_type
=
VectorProxy
<
const
Real
,
bdim
>
;
Loop
::
loop
(
[
&
](
typename
KelvinTrait
<
T
>::
out_t
out_local
,
MatrixProxy
<
Complex
,
dim
,
dim
>
surface_gradient
,
MatrixProxy
<
Complex
,
dim
,
dim
>
source_stress
,
VectorProxy
<
const
Real
,
bdim
>
q
)
{
// No cutoff
// if (-q.l2norm() * std::abs(y_3) < std::log(cutoff))
// return;
Vector
<
Real
,
dim
>
normal
{{{
0
,
0
,
1
}}};
auto
traction
=
el
(
surface_gradient
)
*
normal
;
// computing strains from gradu
traction
-=
source_stress
*
normal
;
// subtracting source stresses
out_local
+=
boussinesq
.
applyU0
(
traction
,
q
)
*
influence
::
KelvinIntegrator
<
0
>::
g0
<
true
>
(
q
.
l2norm
()
*
y_3
);
out_local
+=
(
boussinesq
.
applyU1
(
traction
,
q
)
*
influence
::
KelvinIntegrator
<
0
>::
g1
<
true
>
(
q
.
l2norm
()
*
y_3
));
},
range
<
k_out
>
(
out
),
range
<
m_type
>
(
surface_gradients
),
range
<
m_type
>
(
source_stresses
),
range
<
v_type
>
(
wavevectors
));
}
inline
void
applyConstantTerm
(
typename
KelvinTrait
<
T
>::
out_t
&
out
,
Vector
<
Complex
,
dim
>&
/*source*/
,
const
influence
::
ElasticHelper
<
dim
>&
/*el*/
)
const
{
out
=
0
;
}
protected
:
const
T
&
boussinesq
;
const
influence
::
ElasticHelper
<
dim
>&
el
;
const
Real
y_3
,
cutoff
;
};
template
<>
inline
void
MindlinBoussinesqHelper
<
model_type
::
volume_2d
,
influence
::
Boussinesq
<
3
,
1
>>::
applyConstantTerm
(
typename
KelvinTrait
<
influence
::
Boussinesq
<
3
,
1
>>::
out_t
&
out
,
Vector
<
Complex
,
dim
>&
source
,
const
influence
::
ElasticHelper
<
dim
>&
el
)
const
{
out
=
0
;
out
(
2
,
0
)
=
-
source
(
0
)
/
el
.
mu
;
out
(
2
,
1
)
=
-
source
(
1
)
/
el
.
mu
;
out
(
2
,
2
)
=
-
source
(
2
)
/
(
el
.
lambda
+
2
*
el
.
mu
);
}
}
// namespace detail
template
<
model_type
type
,
UInt
order
>
void
Mindlin
<
type
,
order
>::
applyIf
(
GridBase
<
Real
>&
source
,
GridBase
<
Real
>&
out
,
filter_t
pred
)
const
{
Real
nu
=
this
->
model
->
getPoissonRatio
(),
mu
=
this
->
model
->
getShearModulus
();
constexpr
UInt
derivative
=
order
-
2
;
influence
::
Kelvin
<
trait
::
dimension
,
derivative
>
kelvin
(
mu
,
nu
);
influence
::
Kelvin
<
trait
::
dimension
,
2
>
kelvin_strain
(
mu
,
nu
);
influence
::
Boussinesq
<
trait
::
dimension
,
derivative
-
1
>
boussinesq
(
mu
,
nu
);
influence
::
ElasticHelper
<
trait
::
dimension
>
elasticity
(
mu
,
nu
);
auto
apply
=
[
&
](
UInt
node
,
decltype
(
this
->
source_buffers
)
&
source_buffers
,
decltype
(
this
->
disp_buffer
)
&
out_buffer
)
{
const
Real
L
=
this
->
model
->
getSystemSize
().
front
();
const
UInt
N
=
this
->
model
->
getDiscretization
().
front
();
const
Real
dl
=
L
/
(
N
-
1
);
const
Real
xi
=
node
*
dl
;
// this should only be used when node == xi == 0
detail
::
LinearElement
<
type
,
decltype
(
kelvin_strain
)
>
strain_element
{
thrust
::
make_pair
(
node
,
xi
),
kelvin_strain
,
source_buffers
,
surface_strains
,
this
->
wavevectors
};
detail
::
LinearElement
<
type
,
decltype
(
kelvin
)
>
element
{
thrust
::
make_pair
(
node
,
xi
),
kelvin
,
source_buffers
,
out_buffer
,
this
->
wavevectors
};
out_buffer
=
0
;
// Simple condition to ensure correct integration
auto
filter_out_elem
=
[
&
pred
](
UInt
e
)
{
return
not
pred
(
e
)
and
not
pred
(
e
+
1
);
};
/// Compute surface strains only once (dirty)
if
(
node
==
0
)
{
surface_strains
=
0
;
for
(
UInt
e
:
Loop
::
range
(
N
-
1
))
{
if
(
filter_out_elem
(
e
))
continue
;
const
auto
node_positions
=
thrust
::
make_pair
(
e
*
dl
,
(
e
+
1
)
*
dl
);
strain_element
.
integrateElement
(
e
,
node_positions
);
}
}
// Apply Kelvin operator
for
(
UInt
e
:
Loop
::
range
(
N
-
1
))
{
if
(
filter_out_elem
(
e
))
continue
;
const
auto
node_positions
=
thrust
::
make_pair
(
e
*
dl
,
(
e
+
1
)
*
dl
);
element
.
integrateElement
(
e
,
node_positions
);
}
// Correcting for the tractions on the surface
detail
::
MindlinBoussinesqHelper
<
type
,
decltype
(
boussinesq
)
>
helper
(
boussinesq
,
elasticity
,
xi
,
1e-3
);
helper
.
applyIntegral
(
out_buffer
,
surface_strains
,
source_buffers
.
front
(),
this
->
wavevectors
);
typename
detail
::
KelvinTrait
<
decltype
(
boussinesq
)
>::
out_t
out_fundamental
(
out_buffer
(
0
));
typename
detail
::
KelvinTrait
<
decltype
(
kelvin
)
>::
source_t
source_fundamental
(
source_buffers
[
node
](
0
));
Vector
<
Real
,
trait
::
dimension
>
e3
;
e3
=
0
;
e3
(
trait
::
dimension
-
1
)
=
-
1
;
auto
in_fundamental
=
source_fundamental
*
e3
;
// Uniform shift in case of gradient computation
helper
.
applyConstantTerm
(
out_fundamental
,
in_fundamental
,
elasticity
);
};
this
->
fourierApplyIf
(
apply
,
source
,
out
,
pred
);
}
/* -------------------------------------------------------------------------- */
/* Template instanciation */
/* -------------------------------------------------------------------------- */
template
class
Mindlin
<
model_type
::
volume_2d
,
3
>
;
template
class
Mindlin
<
model_type
::
volume_2d
,
4
>
;
/* -------------------------------------------------------------------------- */
}
// namespace tamaas
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