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rAKA akantu
resolution_penalty.cc
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/**
* @file resolution_penalty.cc
*
* @author Mohit Pundir <mohit.pundir@epfl.ch>
*
* @date creation: Mon Jan 7 2019
* @date last modification: Mon Jan 7 2019
*
* @brief Specialization of the resolution class for the penalty method
*
* @section LICENSE
*
* Copyright (©) 2010-2018 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/>.
*
*/
/* -------------------------------------------------------------------------- */
#include "resolution_penalty.hh"
namespace
akantu
{
/* -------------------------------------------------------------------------- */
ResolutionPenalty
::
ResolutionPenalty
(
ContactMechanicsModel
&
model
,
const
ID
&
id
)
:
Resolution
(
model
,
id
)
{
AKANTU_DEBUG_IN
();
this
->
initialize
();
AKANTU_DEBUG_OUT
();
}
/* -------------------------------------------------------------------------- */
void
ResolutionPenalty
::
initialize
()
{
this
->
registerParam
(
"epsilon_n"
,
epsilon_n
,
Real
(
0.
),
_pat_parsable
|
_pat_modifiable
,
"Normal penalty parameter"
);
this
->
registerParam
(
"epsilon_t"
,
epsilon_t
,
Real
(
0.
),
_pat_parsable
|
_pat_modifiable
,
"Tangential penalty parameter"
);
}
/* -------------------------------------------------------------------------- */
void
ResolutionPenalty
::
computeNormalForce
(
ContactElement
&
element
,
Vector
<
Real
>
&
force
)
{
force
.
clear
();
Real
sigma_n
=
macaulay
(
element
.
gap
)
*
epsilon_n
;
auto
nb_nodes_master
=
Mesh
::
getNbNodesPerElement
(
element
.
master
.
type
);
auto
nb_nodes
=
nb_nodes_master
+
1
;
Vector
<
Real
>
delta_gap
(
nb_nodes
*
spatial_dimension
);
ResolutionUtils
::
firstVariationNormalGap
(
element
,
delta_gap
);
for
(
UInt
i
:
arange
(
force
.
size
()))
force
[
i
]
+=
delta_gap
[
i
]
*
sigma_n
;
}
/* -------------------------------------------------------------------------- */
void
ResolutionPenalty
::
computeTangentialForce
(
ContactElement
&
element
,
Vector
<
Real
>
&
force
)
{
if
(
mu
==
0
)
return
;
UInt
surface_dimension
=
spatial_dimension
-
1
;
Vector
<
Real
>
traction_trial
(
spatial_dimension
);
Vector
<
Real
>
traction_tangential
(
spatial_dimension
);
computeTrialTangentialTraction
(
element
,
traction_trial
);
Real
sigma_n
=
epsilon_n
*
macaulay
(
element
.
gap
);
bool
stick
=
(
traction_trial
.
norm
()
<=
mu
*
sigma_n
)
?
true
:
false
;
if
(
stick
)
computeStickTangentialTraction
(
element
,
traction_trial
,
traction_tangential
);
else
computeSlipTangentialTraction
(
element
,
traction_trial
,
traction_tangential
);
auto
nb_nodes_master
=
Mesh
::
getNbNodesPerElement
(
element
.
master
.
type
);
auto
nb_nodes
=
nb_nodes_master
+
1
;
Array
<
Real
>
delta_xi
(
nb_nodes
*
spatial_dimension
,
surface_dimension
);
ResolutionUtils
::
firstVariationNaturalCoordinate
(
element
,
delta_xi
);
for
(
auto
&&
values
:
zip
(
traction_tangential
,
make_view
(
delta_xi
,
delta_xi
.
size
())))
{
auto
&
t_alpha
=
std
::
get
<
0
>
(
values
);
auto
&
d_alpha
=
std
::
get
<
1
>
(
values
);
force
+=
d_alpha
*
t_alpha
;
}
}
/* -------------------------------------------------------------------------- */
void
ResolutionPenalty
::
computeTrialTangentialTraction
(
ContactElement
&
element
,
Vector
<
Real
>
&
traction
)
{
UInt
spatial_dimension
=
model
.
getMesh
().
getSpatialDimension
();
UInt
surface_dimension
=
spatial_dimension
-
1
;
Matrix
<
Real
>
covariant_basis
(
surface_dimension
,
spatial_dimension
);
GeometryUtils
::
covariantBasis
(
model
.
getMesh
(),
model
.
getContactDetector
().
getPositions
(),
element
.
master
,
element
.
projection
,
covariant_basis
);
Matrix
<
Real
>
contravariant_basis
(
surface_dimension
,
spatial_dimension
);
GeometryUtils
::
contravariantBasis
(
covariant_basis
,
contravariant_basis
);
auto
&
contravariant_projection
=
element
.
projection
;
auto
&
covariant_stick
=
element
.
stick_projection
;
Vector
<
Real
>
covariant_projection
(
surface_dimension
);
for
(
auto
&&
values
:
zip
(
covariant_projection
,
contravariant_projection
,
contravariant_basis
.
transpose
()))
{
auto
&
temp
=
std
::
get
<
0
>
(
values
);
Vector
<
Real
>
contravariant
(
std
::
get
<
2
>
(
values
));
temp
=
contravariant
.
dot
(
contravariant
);
temp
*=
std
::
get
<
1
>
(
values
);
}
auto
covariant_slip
=
covariant_projection
-
covariant_stick
;
Matrix
<
Real
>
mat_traction
(
spatial_dimension
,
1
);
//mat_traction.mul<true, false>(contravariant_basis, covariant_slip, epsilon_t);
traction
=
Vector
<
Real
>
(
mat_traction
[
0
]);
}
/* -------------------------------------------------------------------------- */
void
ResolutionPenalty
::
computeStickTangentialTraction
(
ContactElement
&
element
,
Vector
<
Real
>
&
traction_trial
,
Vector
<
Real
>
&
traction_tangential
)
{
traction_tangential
=
traction_trial
;
}
/* -------------------------------------------------------------------------- */
void
ResolutionPenalty
::
computeSlipTangentialTraction
(
ContactElement
&
element
,
Vector
<
Real
>
&
traction_trial
,
Vector
<
Real
>
&
traction_tangential
)
{
auto
slip_vector
=
traction_trial
;
slip_vector
/=
slip_vector
.
norm
();
Real
sigma_n
=
epsilon_n
*
macaulay
(
element
.
gap
);
traction_tangential
=
slip_vector
;
traction_tangential
*=
sigma_n
;
auto
slip
=
macaulay
(
traction_trial
.
norm
()
-
mu
*
sigma_n
);
slip
/=
epsilon_t
;
// slip needs to be multiplied with nodal area
//Vector<Real> slip_covariant;
//GeometryUtils::toCovariantBasis(slip_vector, slip_covariant);
//element.stick_point += slip * slip_covariant;
}
/* -------------------------------------------------------------------------- */
void
ResolutionPenalty
::
computeNormalModuli
(
Matrix
<
Real
>
&
ke
,
Array
<
Real
>
&
n_alpha
,
Array
<
Real
>
&
d_alpha
,
Vector
<
Real
>
&
n
,
ContactElement
&
element
)
{
Real
tn
=
element
.
gap
*
epsilon_n
;
tn
=
macaulay
(
tn
);
Matrix
<
Real
>
n_mat
(
n
.
storage
(),
n
.
size
(),
1
);
ke
.
mul
<
false
,
true
>
(
n_mat
,
n_mat
);
ke
*=
epsilon_n
*
heaviside
(
element
.
gap
);
/* for (auto && values : zip(make_view(n_alpha, n_alpha.size()),
make_view(d_alpha, d_alpha.size()))) {
auto & n_s = std::get<0>(values);
auto & d_s = std::get<1>(values);
Matrix<Real> ns_mat(n_s.storage(), n_s.size(), 1);
Matrix<Real> ds_mat(d_s.storage(), d_s.size(), 1);
Matrix<Real> tmp1(n_s.size(), n_s.size());
tmp1.mul<false, true>(ns_mat, ds_mat);
Matrix<Real> tmp2(n_s.size(), n_s.size());
tmp2.mul<false, true>(ds_mat, ns_mat);
ke -= (tmp1 + tmp2) * tn;
}
auto surface_dimension = spatial_dimension - 1;
Matrix<Real> m_alpha_beta(surface_dimension, surface_dimension);
ResolutionUtils::computeMetricTensor(m_alpha_beta, element.tangents);
for (auto && values :
zip(arange(surface_dimension), make_view(n_alpha, n_alpha.size()))) {
auto & s = std::get<0>(values);
auto & n_s = std::get<1>(values);
Matrix<Real> ns_mat(n_s.storage(), n_s.size(), 1);
for (auto && tuple :
zip(arange(surface_dimension), make_view(n_alpha, n_alpha.size()))) {
auto & t = std::get<0>(tuple);
auto & n_t = std::get<1>(tuple);
Matrix<Real> nt_mat(n_t.storage(), n_t.size(), 1);
Matrix<Real> tmp3(n_s.size(), n_s.size());
tmp3.mul<false, true>(ns_mat, nt_mat);
tmp3 *= m_alpha_beta(s, t) * tn * element.gap;
ke += tmp3;
}
}*/
}
/* -------------------------------------------------------------------------- */
void
ResolutionPenalty
::
computeFrictionalModuli
(
Matrix
<
Real
>
&
/*ke*/
,
Array
<
Real
>
&
t_alpha_beta
,
Array
<
Real
>
&
n_alpha_beta
,
Array
<
Real
>
&
/*n_alpha*/
,
Array
<
Real
>
&
d_alpha
,
Matrix
<
Real
>
&
phi
,
Vector
<
Real
>
&
n
,
ContactElement
&
element
)
{
auto
k_common
=
computeCommonModuli
(
t_alpha_beta
,
n_alpha_beta
,
d_alpha
,
n
,
element
);
const
auto
&
type
=
element
.
master
.
type
;
const
auto
&
conn
=
element
.
connectivity
;
auto
surface_dimension
=
Mesh
::
getSpatialDimension
(
type
);
auto
spatial_dimension
=
surface_dimension
+
1
;
Matrix
<
Real
>
m_alpha_beta
(
surface_dimension
,
surface_dimension
);
ResolutionUtils
::
computeMetricTensor
(
m_alpha_beta
,
element
.
tangents
);
Array
<
Real
>
g_alpha
(
conn
.
size
()
*
spatial_dimension
,
surface_dimension
);
ResolutionUtils
::
computeGalpha
(
g_alpha
,
t_alpha_beta
,
d_alpha
,
phi
,
element
);
/*Matrix<Real> k_t;
bool stick = computeFrictionalTraction(m_alpha_beta, element);
if(stick)
k_t = computeStickModuli(g_alpha, d_alpha, m_alpha_beta);
else
k_t = computeSlipModuli(g_alpha, d_alpha, m_alpha_beta, element);*/
}
/* -------------------------------------------------------------------------- */
Array
<
Real
>
ResolutionPenalty
::
computeCommonModuli
(
Array
<
Real
>
&
/*t_alpha_beta*/
,
Array
<
Real
>
&
/*n_alpha_beta*/
,
Array
<
Real
>
&
d_alpha
,
Vector
<
Real
>
&
/*n*/
,
ContactElement
&
/*element*/
)
{
Array
<
Real
>
kt_alpha
(
spatial_dimension
-
1
,
d_alpha
.
size
()
*
d_alpha
.
size
(),
"k_T_alpha"
);
// auto t_alpha_beta_size = t_alpha_beta.size() * (spatial_dimension - 1);
// auto & tangents = element.tangents;
/*for(auto && values :
zip(tangents.transpose(),
make_view(kt_alpha, kt_alpha.size()),
make_view(t_alpha_beta, t_alpha_beta_size),
make_view(n_alpha_beta, n_alpha_beta_size))) {
auto & tangent_s = std::get<0>(values);
auto & kt_s = std::get<1>(values);
auto & t_alpha_s = std::get<2>(values);
auto & n_alpha_s = std::get<3>(values);
Matrix<Real> kt_s_mat(kt_s.storage(), d_alpha.size(), d_alpha.size());
// loop over beta
for(auto && tuple :
zip(make_view(d_alpha, d_alpha.size()),
make_view(n_alpha_ ))) {
auto & d_s = std::get<0>(tuple);
Matrix<Real> tmp(d_s.size(), d_s.size());
// loop over gamma
for(auto && entry :
make_view(d_alpha, d_alpha.size())) {
auto & d_t = std::get<0>(entry);
// compute constant
Matrix<Real> tmp2(d_t.size(), d_t.size());
tmp2.mul<false, true>(d_s, d_t);
kt_s_mat += tmp2;
}
}
}*/
return
kt_alpha
;
}
/* -------------------------------------------------------------------------- */
Matrix
<
Real
>
ResolutionPenalty
::
computeStickModuli
(
Array
<
Real
>
&
g_alpha
,
Array
<
Real
>
&
d_alpha
,
Matrix
<
Real
>
&
m_alpha_beta
)
{
Matrix
<
Real
>
k_stick
(
d_alpha
.
size
(),
d_alpha
.
size
());
for
(
auto
&&
values
:
zip
(
arange
(
d_alpha
.
getNbComponent
()),
make_view
(
d_alpha
,
d_alpha
.
size
()),
make_view
(
g_alpha
,
g_alpha
.
size
())))
{
auto
&
s
=
std
::
get
<
0
>
(
values
);
auto
&
d_s
=
std
::
get
<
1
>
(
values
);
auto
&
g_s
=
std
::
get
<
2
>
(
values
);
Matrix
<
Real
>
ds_mat
(
d_s
.
storage
(),
d_s
.
size
(),
1
);
Matrix
<
Real
>
gs_mat
(
g_s
.
storage
(),
g_s
.
size
(),
1
);
Matrix
<
Real
>
tmp1
(
d_s
.
size
(),
d_s
.
size
());
tmp1
.
mul
<
false
,
true
>
(
ds_mat
,
gs_mat
);
k_stick
+=
tmp1
;
for
(
auto
&&
tuple
:
enumerate
(
make_view
(
d_alpha
,
d_alpha
.
size
())))
{
auto
&
t
=
std
::
get
<
0
>
(
tuple
);
auto
&
d_t
=
std
::
get
<
1
>
(
tuple
);
Matrix
<
Real
>
dt_mat
(
d_t
.
storage
(),
d_t
.
size
(),
1
);
Matrix
<
Real
>
tmp2
(
d_t
.
size
(),
d_t
.
size
());
tmp2
.
mul
<
false
,
true
>
(
ds_mat
,
dt_mat
);
k_stick
+=
tmp2
*
m_alpha_beta
(
s
,
t
);
}
}
k_stick
*=
epsilon_t
;
return
k_stick
;
}
/* -------------------------------------------------------------------------- */
Matrix
<
Real
>
ResolutionPenalty
::
computeSlipModuli
(
Array
<
Real
>
&
/*g_alpha*/
,
Array
<
Real
>
&
d_alpha
,
Matrix
<
Real
>
&
/*m_alpha_beta*/
,
ContactElement
&
/*element*/
)
{
/*Real tn = element.gap * epsilon;
tn = macaulay(tn);
Real factor;
factor = epsilon_t * mu * tn;
auto p_t = element.traction;
p_t /= p_t.norm();*/
Matrix
<
Real
>
k_slip
(
d_alpha
.
size
(),
d_alpha
.
size
());
/*
// loop for alpha
for(auto && value :
make_view(d_alpha, d_alpha.size())) {
auto & d_s = std::get<0>(value);
// loop for beta
for(auto && tuple :
zip(arange(spatial_dimension - 1),
make_view(d_alpha, d_alpha.size()),
make_view(g_alpha, g_alpha.size()))) {
auto & beta = std::get<0>(tuple);
auto & d_beta = std::get<1>(tuple);
auto & g_beta = std::get<2>(tuple);
// loop for gamma
for(auto && entry :
zip(arange(spatial_dimension - 1),
make_view(d_alpha, d_alpha.size()))) {
auto & gamma = std::get<0>(entry);
auto & d_gamma = std::get<1>(entry);
}
}
}*/
return
k_slip
;
}
INSTANTIATE_RESOLUTION
(
penalty
,
ResolutionPenalty
);
}
// namespace akantu
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