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resolution_penalty_quadratic.cc
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rAKA akantu
resolution_penalty_quadratic.cc
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/**
* Copyright (©) 2019-2023 EPFL (Ecole Polytechnique Fédérale de Lausanne)
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
* This file is part of Akantu
*
* 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 "resolution_penalty_quadratic.hh"
#include "element_class_helper.hh"
/* -------------------------------------------------------------------------- */
namespace
akantu
{
/* -------------------------------------------------------------------------- */
ResolutionPenaltyQuadratic
::
ResolutionPenaltyQuadratic
(
ContactMechanicsModel
&
model
,
const
ID
&
id
)
:
Parent
(
model
,
id
)
{
AKANTU_DEBUG_IN
();
this
->
initialize
();
AKANTU_DEBUG_OUT
();
}
/* -------------------------------------------------------------------------- */
Real
ResolutionPenaltyQuadratic
::
computeNormalTraction
(
const
Real
&
gap
)
const
{
return
epsilon_n
*
(
macaulay
(
gap
)
*
macaulay
(
gap
)
+
macaulay
(
gap
));
}
/* -------------------------------------------------------------------------- */
void
ResolutionPenaltyQuadratic
::
computeNormalModuli
(
const
ContactElement
&
element
,
Matrix
<
Real
>
&
stiffness
)
{
auto
surface_dimension
=
spatial_dimension
-
1
;
auto
&
gaps
=
model
.
getGaps
();
Real
gap
(
gaps
.
begin
()[
element
.
slave
]);
auto
&
projections
=
model
.
getProjections
();
Vector
<
Real
>
projection
(
projections
.
begin
(
surface_dimension
)[
element
.
slave
]);
auto
&
nodal_areas
=
model
.
getNodalArea
();
auto
&
nodal_area
=
nodal_areas
.
begin
()[
element
.
slave
];
auto
&
normals
=
model
.
getNormals
();
Vector
<
Real
>
normal
(
normals
.
begin
(
spatial_dimension
)[
element
.
slave
]);
// method from Schweizerhof and A. Konyukhov, K. Schweizerhof
// DOI 10.1007/s00466-004-0616-7 and DOI 10.1007/s00466-003-0515-3
// construct A matrix
auto
A
=
ResolutionUtils
::
computeShapeFunctionMatrix
(
element
,
projection
);
// construct the main part of normal matrix
Matrix
<
Real
>
k_main
(
A
.
cols
(),
A
.
cols
());
Matrix
<
Real
>
n_outer_n
(
spatial_dimension
,
spatial_dimension
);
n_outer_n
=
normal
*
normal
.
transpose
();
k_main
=
(
A
.
transpose
()
*
n_outer_n
*
A
)
*
epsilon_n
*
heaviside
(
gap
)
*
(
2
*
gap
+
1
)
*
nodal_area
;
// construct the rotational part of the normal matrix
auto
&
tangents
=
model
.
getTangents
();
auto
&&
covariant_basis
=
tangents
.
begin
(
spatial_dimension
,
surface_dimension
)[
element
.
slave
];
auto
contravariant_metric_tensor
=
GeometryUtils
::
contravariantMetricTensor
(
covariant_basis
);
// consists of 2 rotational parts
Matrix
<
Real
>
k_rot1
(
A
.
cols
(),
A
.
cols
());
Matrix
<
Real
>
k_rot2
(
A
.
cols
(),
A
.
cols
());
k_rot1
.
zero
();
k_rot2
.
zero
();
auto
Ajs
=
ResolutionUtils
::
computeDerivativeShapeFunctionMatrix
(
element
,
projection
);
for
(
auto
&&
[
alpha
,
tangent
]
:
enumerate
(
covariant_basis
))
{
auto
n_outer_t
=
normal
*
tangent
.
transpose
();
// auto t_outer_n = tangent * normal.transpose();
for
(
auto
&&
[
beta
,
Aj
]
:
enumerate
(
Ajs
))
{
// construct Aj from shape function wrt to jth natural
// coordinate
k_rot1
+=
(
Aj
.
transpose
()
*
n_outer_t
*
A
)
*
contravariant_metric_tensor
(
alpha
,
beta
);
k_rot2
+=
(
A
.
transpose
()
*
n_outer_t
*
Aj
)
*
contravariant_metric_tensor
(
alpha
,
beta
);
}
}
k_rot1
*=
-
epsilon_n
*
heaviside
(
gap
)
*
(
gap
*
gap
+
gap
)
*
nodal_area
;
k_rot2
*=
-
epsilon_n
*
heaviside
(
gap
)
*
(
gap
*
gap
+
gap
)
*
nodal_area
;
stiffness
+=
k_main
+
k_rot1
+
k_rot2
;
}
INSTANTIATE_RESOLUTION
(
penalty_quadratic
,
ResolutionPenaltyQuadratic
);
}
// namespace akantu
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