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test_cohesive_intrinsic_tetrahedron.cc
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rAKA akantu
test_cohesive_intrinsic_tetrahedron.cc
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/**
* @file test_cohesive_intrinsic_tetrahedron.cc
*
* @author Marco Vocialta <marco.vocialta@epfl.ch>
*
* @date creation: Tue Aug 27 2013
* @date last modification: Thu Oct 15 2015
*
* @brief Test for cohesive elements
*
* @section LICENSE
*
* Copyright (©) 2014, 2015 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 <fstream>
#include <iostream>
#include <limits>
/* -------------------------------------------------------------------------- */
#include "material_cohesive.hh"
#include "solid_mechanics_model_cohesive.hh"
/* -------------------------------------------------------------------------- */
using
namespace
akantu
;
class
Checker
{
public
:
Checker
(
const
SolidMechanicsModelCohesive
&
model
,
const
Array
<
UInt
>
&
elements
,
ElementType
type
);
void
check
(
const
Vector
<
Real
>
&
opening
,
const
Matrix
<
Real
>
&
rotation
)
{
checkTractions
(
opening
,
rotation
);
checkEquilibrium
();
computeEnergy
(
opening
);
}
void
updateDisplacement
(
const
Vector
<
Real
>
&
increment
);
protected
:
void
checkTractions
(
const
Vector
<
Real
>
&
opening
,
const
Matrix
<
Real
>
&
rotation
);
void
checkEquilibrium
();
void
checkResidual
(
const
Matrix
<
Real
>
&
rotation
);
void
computeEnergy
(
const
Vector
<
Real
>
&
opening
);
private
:
std
::
set
<
UInt
>
nodes_to_check
;
const
SolidMechanicsModelCohesive
&
model
;
ElementType
type
;
//const Array<UInt> & elements;
const
Material
&
mat_cohesive
;
Real
sigma_c
;
const
Real
beta
;
const
Real
G_c
;
const
Real
delta_0
;
const
Real
kappa
;
Real
delta_c
;
const
UInt
spatial_dimension
;
const
ElementType
type_facet
;
const
ElementType
type_cohesive
;
const
Array
<
Real
>
&
traction
;
const
Array
<
Real
>
&
damage
;
const
UInt
nb_quad_per_el
;
const
UInt
nb_element
;
const
Real
beta2_kappa2
;
const
Real
beta2_kappa
;
Vector
<
Real
>
theoretical_traction
;
Vector
<
Real
>
traction_old
;
Vector
<
Real
>
opening_old
;
Real
Ed
;
};
/* -------------------------------------------------------------------------- */
int
main
(
int
argc
,
char
*
argv
[])
{
initialize
(
"material_tetrahedron.dat"
,
argc
,
argv
);
// debug::setDebugLevel(dblDump);
const
UInt
spatial_dimension
=
3
;
const
UInt
max_steps
=
60
;
const
Real
increment_constant
=
0.01
;
Math
::
setTolerance
(
1.e-12
);
const
ElementType
type
=
_tetrahedron_10
;
Mesh
mesh
(
spatial_dimension
);
mesh
.
read
(
"tetrahedron.msh"
);
SolidMechanicsModelCohesive
model
(
mesh
);
/// model initialization
model
.
initFull
();
model
.
limitInsertion
(
_x
,
-
0.01
,
0.01
);
model
.
insertIntrinsicElements
();
Array
<
bool
>
&
boundary
=
model
.
getBlockedDOFs
();
boundary
.
set
(
true
);
UInt
nb_element
=
mesh
.
getNbElement
(
type
);
model
.
setBaseName
(
"intrinsic_tetrahedron"
);
model
.
addDumpFieldVector
(
"displacement"
);
model
.
addDumpField
(
"internal_force"
);
model
.
dump
();
model
.
setBaseNameToDumper
(
"cohesive elements"
,
"cohesive_elements_tetrahedron"
);
model
.
addDumpFieldVectorToDumper
(
"cohesive elements"
,
"displacement"
);
model
.
addDumpFieldToDumper
(
"cohesive elements"
,
"damage"
);
model
.
dump
(
"cohesive elements"
);
/// find elements to displace
Array
<
UInt
>
elements
;
Vector
<
Real
>
bary
(
spatial_dimension
);
for
(
UInt
el
=
0
;
el
<
nb_element
;
++
el
)
{
mesh
.
getBarycenter
(
el
,
type
,
bary
.
storage
());
if
(
bary
(
_x
)
>
0.01
)
elements
.
push_back
(
el
);
}
/// rotate mesh
Real
angle
=
1.
;
// clang-format off
Matrix
<
Real
>
rotation
{
{
std
::
cos
(
angle
),
std
::
sin
(
angle
)
*
-
1.
,
0.
},
{
std
::
sin
(
angle
),
std
::
cos
(
angle
),
0.
},
{
0.
,
0.
,
1.
}};
// clang-format on
Vector
<
Real
>
increment_tmp
{
increment_constant
,
2.
*
increment_constant
,
3.
*
increment_constant
};
Vector
<
Real
>
increment
=
rotation
*
increment_tmp
;
auto
&
position
=
mesh
.
getNodes
();
auto
position_it
=
position
.
begin
(
spatial_dimension
);
auto
position_end
=
position
.
end
(
spatial_dimension
);
for
(;
position_it
!=
position_end
;
++
position_it
)
{
auto
&
pos
=
*
position_it
;
pos
=
rotation
*
pos
;
}
model
.
dump
();
model
.
dump
(
"cohesive elements"
);
/// find nodes to check
Checker
checker
(
model
,
elements
,
type
);
checker
.
updateDisplacement
(
increment
);
Real
theoretical_Ed
=
0
;
Vector
<
Real
>
opening
(
spatial_dimension
,
0.
);
Vector
<
Real
>
opening_old
(
spatial_dimension
,
0.
);
/// Main loop
for
(
UInt
s
=
1
;
s
<=
max_steps
;
++
s
)
{
model
.
solveStep
();
model
.
dump
();
model
.
dump
(
"cohesive elements"
);
opening
+=
increment_tmp
;
checker
.
check
(
opening
,
rotation
);
checker
.
updateDisplacement
(
increment
);
}
model
.
dump
();
model
.
dump
(
"cohesive elements"
);
Real
Ed
=
model
.
getEnergy
(
"dissipated"
);
theoretical_Ed
*=
4.
;
std
::
cout
<<
Ed
<<
" "
<<
theoretical_Ed
<<
std
::
endl
;
if
(
!
Math
::
are_float_equal
(
Ed
,
theoretical_Ed
)
||
std
::
isnan
(
Ed
))
{
std
::
cout
<<
"The dissipated energy is incorrect"
<<
std
::
endl
;
finalize
();
return
EXIT_FAILURE
;
}
finalize
();
std
::
cout
<<
"OK: test_cohesive_intrinsic_tetrahedron was passed!"
<<
std
::
endl
;
return
EXIT_SUCCESS
;
}
/* -------------------------------------------------------------------------- */
void
Checker
::
updateDisplacement
(
const
Vector
<
Real
>
&
increment
)
{
Mesh
&
mesh
=
model
.
getFEEngine
().
getMesh
();
const
auto
&
connectivity
=
mesh
.
getConnectivity
(
type
);
auto
&
displacement
=
model
.
getDisplacement
();
Array
<
bool
>
update
(
displacement
.
size
());
update
.
clear
();
auto
conn_it
=
connectivity
.
begin
(
connectivity
.
getNbComponent
());
auto
conn_end
=
connectivity
.
begin
(
connectivity
.
getNbComponent
());
for
(;
conn_it
!=
conn_end
;
++
conn_it
)
{
const
auto
&
conn
=
*
conn_it
;
for
(
UInt
n
=
0
;
n
<
conn
.
size
();
++
n
)
{
UInt
node
=
conn
(
n
);
if
(
!
update
(
node
))
{
Vector
<
Real
>
node_disp
(
displacement
.
storage
()
+
node
*
spatial_dimension
,
spatial_dimension
);
node_disp
+=
increment
;
update
(
node
)
=
true
;
}
}
}
}
/* -------------------------------------------------------------------------- */
Checker
::
Checker
(
const
SolidMechanicsModelCohesive
&
model
,
const
Array
<
UInt
>
&
elements
,
ElementType
type
)
:
model
(
model
),
type
(
std
::
move
(
type
)),
//elements(elements),
mat_cohesive
(
model
.
getMaterial
(
1
)),
sigma_c
(
mat_cohesive
.
get
(
"sigma_c"
)),
beta
(
mat_cohesive
.
get
(
"beta"
)),
G_c
(
mat_cohesive
.
get
(
"G_c"
)),
delta_0
(
mat_cohesive
.
get
(
"delta_0"
)),
kappa
(
mat_cohesive
.
get
(
"kappa"
)),
spatial_dimension
(
model
.
getSpatialDimension
()),
type_facet
(
Mesh
::
getFacetType
(
type
)),
type_cohesive
(
FEEngine
::
getCohesiveElementType
(
type_facet
)),
traction
(
mat_cohesive
.
getArray
<
Real
>
(
"tractions"
,
type_cohesive
)),
damage
(
mat_cohesive
.
getArray
<
Real
>
(
"damage"
,
type_cohesive
)),
nb_quad_per_el
(
model
.
getFEEngine
(
"CohesiveFEEngine"
)
.
getNbIntegrationPoints
(
type_cohesive
)),
nb_element
(
model
.
getMesh
().
getNbElement
(
type_cohesive
)),
beta2_kappa2
(
beta
*
beta
/
kappa
/
kappa
),
beta2_kappa
(
beta
*
beta
/
kappa
)
{
const
Mesh
&
mesh
=
model
.
getMesh
();
const
auto
&
connectivity
=
mesh
.
getConnectivity
(
type
);
const
auto
&
position
=
mesh
.
getNodes
();
auto
conn_it
=
connectivity
.
begin
(
connectivity
.
getNbComponent
());
for
(
const
auto
&
element
:
elements
)
{
Vector
<
UInt
>
conn_el
(
conn_it
[
element
]);
for
(
UInt
n
=
0
;
n
<
conn_el
.
size
();
++
n
)
{
UInt
node
=
conn_el
(
n
);
if
(
Math
::
are_float_equal
(
position
(
node
,
_x
),
0.
))
nodes_to_check
.
insert
(
node
);
}
}
delta_c
=
2
*
G_c
/
sigma_c
;
sigma_c
*=
delta_c
/
(
delta_c
-
delta_0
);
}
/* -------------------------------------------------------------------------- */
void
Checker
::
checkTractions
(
const
Vector
<
Real
>
&
opening
,
const
Matrix
<
Real
>
&
rotation
)
{
auto
normal_opening
=
opening
*
Vector
<
Real
>
{
1.
,
0.
,
0.
};
auto
tangential_opening
=
opening
-
normal_opening
;
const
Real
normal_opening_norm
=
normal_opening
.
norm
();
const
Real
tangential_opening_norm
=
tangential_opening
.
norm
();
const
Real
delta
=
std
::
max
(
std
::
sqrt
(
tangential_opening_norm
*
tangential_opening_norm
*
beta2_kappa2
+
normal_opening_norm
*
normal_opening_norm
),
0.
);
Real
theoretical_damage
=
std
::
min
(
delta
/
delta_c
,
1.
);
theoretical_traction
=
(
tangential_opening
*
beta2_kappa
+
normal_opening
)
*
sigma_c
/
delta
*
(
1.
-
theoretical_damage
);
// adjust damage
theoretical_damage
=
std
::
max
((
delta
-
delta_0
)
/
(
delta_c
-
delta_0
),
0.
);
theoretical_damage
=
std
::
min
(
theoretical_damage
,
1.
);
Vector
<
Real
>
theoretical_traction_rotated
=
rotation
*
theoretical_traction
;
std
::
for_each
(
traction
.
begin
(
spatial_dimension
),
traction
.
end
(
spatial_dimension
),
[
&
theoretical_traction_rotated
](
auto
&&
traction
)
{
Real
diff
=
Vector
<
Real
>
(
theoretical_traction_rotated
-
traction
).
norm
<
L_inf
>
();
if
(
diff
>
1e-14
)
throw
std
::
domain_error
(
"Tractions are incorrect"
);
});
std
::
for_each
(
damage
.
begin
(),
damage
.
end
(),
[
&
theoretical_damage
](
auto
&&
damage
)
{
if
(
not
Math
::
are_float_equal
(
theoretical_damage
,
damage
))
throw
std
::
domain_error
(
"Damage is incorrect"
);
});
}
/* -------------------------------------------------------------------------- */
void
Checker
::
computeEnergy
(
const
Vector
<
Real
>
&
opening
)
{
/// compute energy
auto
Do
=
opening
-
opening_old
;
auto
Dt
=
traction_old
+
theoretical_traction
;
Ed
+=
.5
*
Do
.
dot
(
Dt
);
opening_old
=
opening
;
traction_old
=
theoretical_traction
;
}
/* -------------------------------------------------------------------------- */
void
Checker
::
checkEquilibrium
()
{
Vector
<
Real
>
residual_sum
(
spatial_dimension
,
0.
);
const
auto
&
residual
=
model
.
getInternalForce
();
auto
res_it
=
residual
.
begin
(
spatial_dimension
);
auto
res_end
=
residual
.
end
(
spatial_dimension
);
for
(;
res_it
!=
res_end
;
++
res_it
)
residual_sum
+=
*
res_it
;
if
(
!
Math
::
are_float_equal
(
residual_sum
.
norm
<
L_inf
>
(),
0.
))
throw
std
::
domain_error
(
"System is not in equilibrium!"
);
}
/* -------------------------------------------------------------------------- */
void
Checker
::
checkResidual
(
const
Matrix
<
Real
>
&
rotation
)
{
Vector
<
Real
>
total_force
(
spatial_dimension
,
0.
);
const
auto
&
residual
=
model
.
getInternalForce
();
for
(
auto
node
:
nodes_to_check
)
{
Vector
<
Real
>
res
(
residual
.
begin
(
spatial_dimension
)[
node
]);
total_force
+=
res
;
}
Vector
<
Real
>
theoretical_total_force
(
spatial_dimension
);
theoretical_total_force
.
mul
<
false
>
(
rotation
,
theoretical_traction
);
theoretical_total_force
*=
-
1
*
2
*
2
;
for
(
UInt
s
=
0
;
s
<
spatial_dimension
;
++
s
)
{
if
(
!
Math
::
are_float_equal
(
total_force
(
s
),
theoretical_total_force
(
s
)))
{
std
::
cout
<<
"Total force isn't correct!"
<<
std
::
endl
;
std
::
terminate
();
}
}
}
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