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rAKA akantu
material_cohesive_linear_friction.cc
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/**
* @file material_cohesive_linear_friction.cc
*
* @author Mauro Corrado <mauro.corrado@epfl.ch>
*
* @date creation: Tue Jan 12 2016
* @date last modification: Thu Jan 14 2016
*
* @brief Linear irreversible cohesive law of mixed mode loading with
* random stress definition for extrinsic type
*
* @section LICENSE
*
* Copyright (©) 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 "material_cohesive_linear_friction.hh"
#include "solid_mechanics_model_cohesive.hh"
namespace
akantu
{
/* -------------------------------------------------------------------------- */
template
<
UInt
spatial_dimension
>
MaterialCohesiveLinearFriction
<
spatial_dimension
>::
MaterialCohesiveLinearFriction
(
SolidMechanicsModel
&
model
,
const
ID
&
id
)
:
MaterialParent
(
model
,
id
),
residual_sliding
(
"residual_sliding"
,
*
this
),
friction_force
(
"friction_force"
,
*
this
)
{
AKANTU_DEBUG_IN
();
this
->
registerParam
(
"mu"
,
mu_max
,
Real
(
0.
),
_pat_parsable
|
_pat_readable
,
"Maximum value of the friction coefficient"
);
this
->
registerParam
(
"penalty_for_friction"
,
friction_penalty
,
Real
(
0.
),
_pat_parsable
|
_pat_readable
,
"Penalty parameter for the friction behavior"
);
AKANTU_DEBUG_OUT
();
}
/* -------------------------------------------------------------------------- */
template
<
UInt
spatial_dimension
>
void
MaterialCohesiveLinearFriction
<
spatial_dimension
>::
initMaterial
()
{
AKANTU_DEBUG_IN
();
MaterialParent
::
initMaterial
();
friction_force
.
initialize
(
spatial_dimension
);
residual_sliding
.
initialize
(
1
);
residual_sliding
.
initializeHistory
();
AKANTU_DEBUG_OUT
();
}
/* -------------------------------------------------------------------------- */
template
<
UInt
spatial_dimension
>
void
MaterialCohesiveLinearFriction
<
spatial_dimension
>::
computeTraction
(
__attribute__
((
unused
))
const
Array
<
Real
>
&
normal
,
ElementType
el_type
,
GhostType
ghost_type
)
{
AKANTU_DEBUG_IN
();
residual_sliding
.
resize
();
friction_force
.
resize
();
/// define iterators
Array
<
Real
>::
vector_iterator
traction_it
=
this
->
tractions
(
el_type
,
ghost_type
).
begin
(
spatial_dimension
);
Array
<
Real
>::
vector_iterator
traction_end
=
this
->
tractions
(
el_type
,
ghost_type
).
end
(
spatial_dimension
);
Array
<
Real
>::
vector_iterator
opening_it
=
this
->
opening
(
el_type
,
ghost_type
).
begin
(
spatial_dimension
);
/// opening_prec is the opening at the end of the previous step in
/// the Newton-Raphson loop
Array
<
Real
>::
vector_iterator
opening_prec_it
=
this
->
opening_prec
(
el_type
,
ghost_type
).
begin
(
spatial_dimension
);
/// opening_prec_prev is the opening (opening + penetration)
/// referred to the convergence of the previous incremental step
Array
<
Real
>::
vector_iterator
opening_prec_prev_it
=
this
->
opening_prec
.
previous
(
el_type
,
ghost_type
).
begin
(
spatial_dimension
);
Array
<
Real
>::
vector_iterator
contact_traction_it
=
this
->
contact_tractions
(
el_type
,
ghost_type
).
begin
(
spatial_dimension
);
Array
<
Real
>::
vector_iterator
contact_opening_it
=
this
->
contact_opening
(
el_type
,
ghost_type
).
begin
(
spatial_dimension
);
Array
<
Real
>::
const_iterator
<
Vector
<
Real
>>
normal_it
=
this
->
normal
.
begin
(
spatial_dimension
);
Array
<
Real
>::
iterator
<
Real
>
sigma_c_it
=
this
->
sigma_c_eff
(
el_type
,
ghost_type
).
begin
();
Array
<
Real
>::
iterator
<
Real
>
delta_max_it
=
this
->
delta_max
(
el_type
,
ghost_type
).
begin
();
Array
<
Real
>::
iterator
<
Real
>
delta_max_prev_it
=
this
->
delta_max
.
previous
(
el_type
,
ghost_type
).
begin
();
Array
<
Real
>::
iterator
<
Real
>
delta_c_it
=
this
->
delta_c_eff
(
el_type
,
ghost_type
).
begin
();
Array
<
Real
>::
iterator
<
Real
>
damage_it
=
this
->
damage
(
el_type
,
ghost_type
).
begin
();
Array
<
Real
>::
vector_iterator
insertion_stress_it
=
this
->
insertion_stress
(
el_type
,
ghost_type
).
begin
(
spatial_dimension
);
Array
<
Real
>::
iterator
<
Real
>
res_sliding_it
=
this
->
residual_sliding
(
el_type
,
ghost_type
).
begin
();
Array
<
Real
>::
iterator
<
Real
>
res_sliding_prev_it
=
this
->
residual_sliding
.
previous
(
el_type
,
ghost_type
).
begin
();
Array
<
Real
>::
vector_iterator
friction_force_it
=
this
->
friction_force
(
el_type
,
ghost_type
).
begin
(
spatial_dimension
);
Array
<
bool
>::
iterator
<
bool
>
reduction_penalty_it
=
this
->
reduction_penalty
(
el_type
,
ghost_type
).
begin
();
Vector
<
Real
>
normal_opening
(
spatial_dimension
);
Vector
<
Real
>
tangential_opening
(
spatial_dimension
);
if
(
!
this
->
model
->
isDefaultSolverExplicit
())
this
->
delta_max
(
el_type
,
ghost_type
)
.
copy
(
this
->
delta_max
.
previous
(
el_type
,
ghost_type
));
/// loop on each quadrature point
for
(;
traction_it
!=
traction_end
;
++
traction_it
,
++
opening_it
,
++
opening_prec_prev_it
,
++
opening_prec_it
,
++
normal_it
,
++
sigma_c_it
,
++
delta_max_it
,
++
delta_c_it
,
++
damage_it
,
++
contact_traction_it
,
++
insertion_stress_it
,
++
contact_opening_it
,
++
delta_max_prev_it
,
++
res_sliding_it
,
++
res_sliding_prev_it
,
++
friction_force_it
,
++
reduction_penalty_it
)
{
Real
normal_opening_norm
,
tangential_opening_norm
;
bool
penetration
;
Real
current_penalty
=
0.
;
this
->
computeTractionOnQuad
(
*
traction_it
,
*
delta_max_it
,
*
delta_max_prev_it
,
*
delta_c_it
,
*
insertion_stress_it
,
*
sigma_c_it
,
*
opening_it
,
*
opening_prec_it
,
*
normal_it
,
normal_opening
,
tangential_opening
,
normal_opening_norm
,
tangential_opening_norm
,
*
damage_it
,
penetration
,
*
reduction_penalty_it
,
current_penalty
,
*
contact_traction_it
,
*
contact_opening_it
);
if
(
penetration
)
{
/// the friction coefficient mu increases with the damage. It
/// equals the maximum value when damage = 1.
// Real damage = std::min(*delta_max_prev_it / *delta_c_it,
// Real(1.));
Real
mu
=
mu_max
;
// * damage;
/// the definition of tau_max refers to the opening
/// (penetration) of the previous incremental step
Real
normal_opening_prev_norm
=
std
::
min
(
opening_prec_prev_it
->
dot
(
*
normal_it
),
Real
(
0.
));
// Vector<Real> normal_opening_prev = (*normal_it);
// normal_opening_prev *= normal_opening_prev_norm;
Real
tau_max
=
mu
*
current_penalty
*
(
std
::
abs
(
normal_opening_prev_norm
));
Real
delta_sliding_norm
=
std
::
abs
(
tangential_opening_norm
-
*
res_sliding_prev_it
);
/// tau is the norm of the friction force, acting tangentially to the
/// surface
Real
tau
=
std
::
min
(
friction_penalty
*
delta_sliding_norm
,
tau_max
);
if
((
tangential_opening_norm
-
*
res_sliding_prev_it
)
<
0.0
)
tau
=
-
tau
;
/// from tau get the x and y components of friction, to be added in the
/// force vector
Vector
<
Real
>
tangent_unit_vector
(
spatial_dimension
);
tangent_unit_vector
=
tangential_opening
/
tangential_opening_norm
;
*
friction_force_it
=
tau
*
tangent_unit_vector
;
/// update residual_sliding
*
res_sliding_it
=
tangential_opening_norm
-
(
std
::
abs
(
tau
)
/
friction_penalty
);
}
else
{
friction_force_it
->
clear
();
}
*
traction_it
+=
*
friction_force_it
;
}
AKANTU_DEBUG_OUT
();
}
/* -------------------------------------------------------------------------- */
template
<
UInt
spatial_dimension
>
void
MaterialCohesiveLinearFriction
<
spatial_dimension
>::
checkDeltaMax
(
GhostType
ghost_type
)
{
AKANTU_DEBUG_IN
();
MaterialParent
::
checkDeltaMax
();
Mesh
&
mesh
=
this
->
fem_cohesive
.
getMesh
();
Mesh
::
type_iterator
it
=
mesh
.
firstType
(
spatial_dimension
,
ghost_type
,
_ek_cohesive
);
Mesh
::
type_iterator
last_type
=
mesh
.
lastType
(
spatial_dimension
,
ghost_type
,
_ek_cohesive
);
for
(;
it
!=
last_type
;
++
it
)
{
Array
<
UInt
>
&
elem_filter
=
this
->
element_filter
(
*
it
,
ghost_type
);
UInt
nb_element
=
elem_filter
.
size
();
if
(
nb_element
==
0
)
continue
;
ElementType
el_type
=
*
it
;
/// define iterators
Array
<
Real
>::
iterator
<
Real
>
delta_max_it
=
this
->
delta_max
(
el_type
,
ghost_type
).
begin
();
Array
<
Real
>::
iterator
<
Real
>
delta_max_end
=
this
->
delta_max
(
el_type
,
ghost_type
).
end
();
Array
<
Real
>::
iterator
<
Real
>
res_sliding_it
=
this
->
residual_sliding
(
el_type
,
ghost_type
).
begin
();
Array
<
Real
>::
iterator
<
Real
>
res_sliding_prev_it
=
this
->
residual_sliding
.
previous
(
el_type
,
ghost_type
).
begin
();
/// loop on each quadrature point
for
(;
delta_max_it
!=
delta_max_end
;
++
delta_max_it
,
++
res_sliding_it
,
++
res_sliding_prev_it
)
{
/**
* in case convergence is not reached, set "residual_sliding"
* for the friction behaviour to the value referred to the
* previous incremental step
*/
*
res_sliding_it
=
*
res_sliding_prev_it
;
}
}
}
/* -------------------------------------------------------------------------- */
template
<
UInt
spatial_dimension
>
void
MaterialCohesiveLinearFriction
<
spatial_dimension
>::
computeTangentTraction
(
const
ElementType
&
el_type
,
Array
<
Real
>
&
tangent_matrix
,
__attribute__
((
unused
))
const
Array
<
Real
>
&
normal
,
GhostType
ghost_type
)
{
AKANTU_DEBUG_IN
();
/// define iterators
Array
<
Real
>::
matrix_iterator
tangent_it
=
tangent_matrix
.
begin
(
spatial_dimension
,
spatial_dimension
);
Array
<
Real
>::
matrix_iterator
tangent_end
=
tangent_matrix
.
end
(
spatial_dimension
,
spatial_dimension
);
Array
<
Real
>::
const_vector_iterator
normal_it
=
this
->
normal
.
begin
(
spatial_dimension
);
Array
<
Real
>::
vector_iterator
opening_it
=
this
->
opening
(
el_type
,
ghost_type
).
begin
(
spatial_dimension
);
Array
<
Real
>::
vector_iterator
opening_prec_prev_it
=
this
->
opening_prec
.
previous
(
el_type
,
ghost_type
).
begin
(
spatial_dimension
);
/**
* NB: delta_max_it points on delta_max_previous, i.e. the
* delta_max related to the solution of the previous incremental
* step
*/
Array
<
Real
>::
iterator
<
Real
>
delta_max_it
=
this
->
delta_max
.
previous
(
el_type
,
ghost_type
).
begin
();
Array
<
Real
>::
iterator
<
Real
>
sigma_c_it
=
this
->
sigma_c_eff
(
el_type
,
ghost_type
).
begin
();
Array
<
Real
>::
iterator
<
Real
>
delta_c_it
=
this
->
delta_c_eff
(
el_type
,
ghost_type
).
begin
();
Array
<
Real
>::
iterator
<
Real
>
damage_it
=
this
->
damage
(
el_type
,
ghost_type
).
begin
();
Array
<
Real
>::
iterator
<
Vector
<
Real
>>
contact_opening_it
=
this
->
contact_opening
(
el_type
,
ghost_type
).
begin
(
spatial_dimension
);
Array
<
Real
>::
iterator
<
Real
>
res_sliding_prev_it
=
this
->
residual_sliding
.
previous
(
el_type
,
ghost_type
).
begin
();
Array
<
bool
>::
iterator
<
bool
>
reduction_penalty_it
=
this
->
reduction_penalty
(
el_type
,
ghost_type
).
begin
();
Vector
<
Real
>
normal_opening
(
spatial_dimension
);
Vector
<
Real
>
tangential_opening
(
spatial_dimension
);
for
(;
tangent_it
!=
tangent_end
;
++
tangent_it
,
++
normal_it
,
++
opening_it
,
++
opening_prec_prev_it
,
++
delta_max_it
,
++
sigma_c_it
,
++
delta_c_it
,
++
damage_it
,
++
contact_opening_it
,
++
res_sliding_prev_it
,
++
reduction_penalty_it
)
{
Real
normal_opening_norm
,
tangential_opening_norm
;
bool
penetration
;
Real
current_penalty
=
0.
;
this
->
computeTangentTractionOnQuad
(
*
tangent_it
,
*
delta_max_it
,
*
delta_c_it
,
*
sigma_c_it
,
*
opening_it
,
*
normal_it
,
normal_opening
,
tangential_opening
,
normal_opening_norm
,
tangential_opening_norm
,
*
damage_it
,
penetration
,
*
reduction_penalty_it
,
current_penalty
,
*
contact_opening_it
);
if
(
penetration
)
{
// Real damage = std::min(*delta_max_it / *delta_c_it, Real(1.));
Real
mu
=
mu_max
;
// * damage;
Real
normal_opening_prev_norm
=
std
::
min
(
opening_prec_prev_it
->
dot
(
*
normal_it
),
Real
(
0.
));
// Vector<Real> normal_opening_prev = (*normal_it);
// normal_opening_prev *= normal_opening_prev_norm;
Real
tau_max
=
mu
*
current_penalty
*
(
std
::
abs
(
normal_opening_prev_norm
));
Real
delta_sliding_norm
=
std
::
abs
(
tangential_opening_norm
-
*
res_sliding_prev_it
);
// tau is the norm of the friction force, acting tangentially to the
// surface
Real
tau
=
std
::
min
(
friction_penalty
*
delta_sliding_norm
,
tau_max
);
if
(
tau
<
tau_max
&&
tau_max
>
Math
::
getTolerance
())
{
Matrix
<
Real
>
I
(
spatial_dimension
,
spatial_dimension
);
I
.
eye
(
1.
);
Matrix
<
Real
>
n_outer_n
(
spatial_dimension
,
spatial_dimension
);
n_outer_n
.
outerProduct
(
*
normal_it
,
*
normal_it
);
Matrix
<
Real
>
nn
(
n_outer_n
);
I
-=
nn
;
*
tangent_it
+=
I
*
friction_penalty
;
}
}
// check if the tangential stiffness matrix is symmetric
// for (UInt h = 0; h < spatial_dimension; ++h){
// for (UInt l = h; l < spatial_dimension; ++l){
// if (l > h){
// Real k_ls = (*tangent_it)[spatial_dimension*h+l];
// Real k_us = (*tangent_it)[spatial_dimension*l+h];
// // std::cout << "k_ls = " << k_ls << std::endl;
// // std::cout << "k_us = " << k_us << std::endl;
// if (std::abs(k_ls) > 1e-13 && std::abs(k_us) > 1e-13){
// Real error = std::abs((k_ls - k_us) / k_us);
// if (error > 1e-10){
// std::cout << "non symmetric cohesive matrix" << std::endl;
// // std::cout << "error " << error << std::endl;
// }
// }
// }
// }
// }
}
AKANTU_DEBUG_OUT
();
}
/* -------------------------------------------------------------------------- */
INSTANTIATE_MATERIAL
(
cohesive_linear_friction
,
MaterialCohesiveLinearFriction
);
}
// akantu
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