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material_vreepeerlings_inline_impl.hh
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rAKA akantu
material_vreepeerlings_inline_impl.hh
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/**
* @file material_vreepeerlings_inline_impl.hh
*
* @author Cyprien Wolff <cyprien.wolff@epfl.ch>
*
*
* @brief Specialization of the material class for the VreePeerlings material
*
*
* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
*/
/* -------------------------------------------------------------------------- */
/* -------------------------------------------------------------------------- */
template
<
Int
spatial_dimension
,
template
<
UInt
>
class
MatParent
>
inline
void
MaterialVreePeerlings
<
spatial_dimension
,
MatParent
>::
computeStressOnQuad
(
Matrix
<
Real
>
&
grad_u
,
Matrix
<
Real
>
&
sigma
,
Real
&
dam
,
Real
&
Equistrain
,
Real
&
Equistrain_rate
,
Real
&
Kapaq
,
Real
dt
,
Matrix
<
Real
>
&
strain_rate_vrplgs
,
Real
&
FullDam_ValStrain
,
Real
&
FullDam_ValStrain_rate
,
Real
&
Nb_damage
)
{
Real
I1
=
0.
;
/// trace initialization of the strain tensor
Real
J2
=
0.
;
/// J2 [J2=1/6(3 strain:strain - I1*I1)] initialization
Real
I1rate
=
0.
;
/// trace initialization of the strain rate tensor
Real
J2rate
=
0.
;
/// J2 [J2=1/3(3 strain:strainrate - I1*I1rate)] initialization
if
(
spatial_dimension
==
1
)
{
I1
=
grad_u
.
trace
();
J2
=
.5
*
grad_u
(
0
,
0
)
*
grad_u
(
0
,
0
)
-
I1
*
I1
/
6.
;
I1rate
=
strain_rate_vrplgs
.
trace
();
J2rate
=
grad_u
(
0
,
0
)
*
strain_rate_vrplgs
(
0
,
0
)
-
I1
*
I1rate
/
6.
;
}
else
{
// if(this->plane_stress) {
// Real tmp = this->nu/(this->nu - 1);
// tmp *= tmp;
// I1 = (grad_u(0,0) + grad_u(1,1))*(1 - 2*this->nu)/(1 - this->nu);
// J2 = .5*(grad_u(0,0)*grad_u(0,0) +
// grad_u(1,1)*grad_u(1,1) +
// tmp*(grad_u(0,0) + grad_u(1,1))*(grad_u(0,0) + grad_u(1,1)) +
// .5*(grad_u(0,1) + grad_u(1,0))*(grad_u(0,1) + grad_u(1,0))) -
// I1*I1/6.;
// I1rate = (strain_rate_vrplgs(0,0) + strain_rate_vrplgs(1,1))*(1 -
// 2*this->nu)/(1 - this->nu);
// J2rate = (grad_u(0,0)*strain_rate_vrplgs(0,0) +
// grad_u(1,1)*strain_rate_vrplgs(1,1) +
// tmp*(grad_u(0,0) + grad_u(1,1))*(strain_rate_vrplgs(0,0) +
// strain_rate_vrplgs(1,1)) +
// (grad_u(0,1)*strain_rate_vrplgs(1,0)) +
// (grad_u(0,1)*strain_rate_vrplgs(1,0))) -
// I1*I1rate/3.;
// }
// else {
I1
=
grad_u
.
trace
();
for
(
UInt
i
=
0
;
i
<
spatial_dimension
;
++
i
)
for
(
UInt
j
=
i
;
j
<
spatial_dimension
;
++
j
)
J2
+=
0.5
*
((
i
==
j
)
*
grad_u
(
i
,
i
)
*
grad_u
(
i
,
i
)
+
0.5
*
(
1
-
(
i
==
j
))
*
((
grad_u
(
i
,
j
)
+
grad_u
(
j
,
i
))
*
(
grad_u
(
i
,
j
)
+
grad_u
(
j
,
i
))));
J2
-=
I1
*
I1
/
6.
;
I1rate
=
strain_rate_vrplgs
.
trace
();
bool
is3D
=
spatial_dimension
==
3
;
J2rate
=
(
grad_u
(
0
,
0
)
*
strain_rate_vrplgs
(
0
,
0
)
+
grad_u
(
1
,
1
)
*
strain_rate_vrplgs
(
1
,
1
)
+
is3D
*
grad_u
(
2
,
2
)
*
strain_rate_vrplgs
(
2
,
2
)
+
(
grad_u
(
0
,
1
)
*
strain_rate_vrplgs
(
1
,
0
))
+
(
grad_u
(
0
,
1
)
*
strain_rate_vrplgs
(
1
,
0
))
+
is3D
*
(
grad_u
(
1
,
2
)
*
strain_rate_vrplgs
(
2
,
1
))
+
is3D
*
(
grad_u
(
1
,
2
)
*
strain_rate_vrplgs
(
2
,
1
))
+
is3D
*
(
grad_u
(
2
,
0
)
*
strain_rate_vrplgs
(
0
,
2
))
+
is3D
*
(
grad_u
(
2
,
0
)
*
strain_rate_vrplgs
(
0
,
2
)))
-
I1
*
I1rate
/
3.
;
// }
}
Real
tmp_1
=
(
Kct
-
1
)
/
(
1
-
2
*
this
->
nu
);
Real
tmp_2
=
(
12
*
Kct
)
/
((
1
+
this
->
nu
)
*
(
1
+
this
->
nu
));
Equistrain
=
tmp_1
*
I1
/
(
2
*
Kct
)
+
1.
/
(
2
*
Kct
)
*
std
::
sqrt
(
tmp_1
*
tmp_1
*
I1
*
I1
+
tmp_2
*
J2
);
if
(
I1
*
I1rate
>
0
||
J2rate
>
0
)
{
Equistrain_rate
=
tmp_1
*
std
::
abs
(
I1rate
)
/
(
2
*
Kct
)
+
1.
/
(
4
*
Kct
)
*
(
2
*
tmp_1
*
tmp_1
*
I1
*
I1rate
+
tmp_2
*
J2rate
)
/
std
::
sqrt
(
tmp_1
*
tmp_1
*
I1
*
I1
+
tmp_2
*
J2
);
}
else
{
AKANTU_ERROR
(
"This instruction here was commented but has to be checked"
);
// Equistrain_rate = Equistrain_rate;
}
if
(
!
this
->
is_non_local
)
{
computeDamageAndStressOnQuad
(
sigma
,
dam
,
Equistrain
,
Equistrain_rate
,
Kapaq
,
dt
,
FullDam_ValStrain
,
FullDam_ValStrain_rate
,
Nb_damage
);
}
}
/* -------------------------------------------------------------------------- */
template
<
Int
spatial_dimension
,
template
<
UInt
>
class
MatParent
>
inline
void
MaterialVreePeerlings
<
spatial_dimension
,
MatParent
>::
computeDamageAndStressOnQuad
(
Matrix
<
Real
>
&
sigma
,
Real
&
dam
,
Real
&
Equistrain
,
Real
&
Equistrain_rate
,
Real
&
Kapaq
,
Real
dt
,
Real
&
FullDam_ValStrain
,
Real
&
FullDam_ValStrain_rate
,
Real
&
Nb_damage
)
{
//---------------------------------------------------------------------------------------
// rate-dependence model
//
//---------------------------------------------------------------------------------------
Real
Kapao
=
Crate
*
(
1.
+
(
std
::
pow
(
std
::
abs
(
Equistrain_rate
)
*
Arate
,
Brate
)))
*
(
1.
-
Kapao_randomness
)
+
Kapao_randomness
*
Kapaq
;
Real
Kapac_99
=
Kapac
*
.99
;
Real
Kapaodyn
=
0
;
if
(
Kapao
>
Kapaoi
)
{
if
(
Kapao
<
Kapac_99
)
{
Kapaodyn
=
Kapao
;
}
else
{
Kapaodyn
=
Kapac_99
;
}
}
else
{
Kapaodyn
=
Kapaoi
;
}
Real
Fd1
=
Equistrain
-
Kapaoi
;
if
(
Fd1
>
0
)
{
Real
dam1
=
1.
-
Kapaodyn
/
Equistrain
*
((
Kapac
-
Equistrain
)
/
(
Kapac
-
Kapaodyn
));
if
(
dam1
>
dam
)
{
dam
=
std
::
min
(
dam1
,
1.
);
Nb_damage
=
Nb_damage
+
1.
;
if
(
dam
>=
1.
)
{
FullDam_ValStrain
=
Equistrain
;
FullDam_ValStrain_rate
=
Equistrain_rate
;
}
}
}
//---------------------------------------------------------------------------------------
// delayed damage (see Marions thesis page 68)
//---------------------------------------------------------------------------------------
// Real viscosity = 10.;
// Real damRateInfini = 10000000.;
// Real gequi = 1. - Kapaq/Equistrain * ((Kapac-Equistrain)/(Kapac -
// Kapaq));
// if (gequi - dam > 0){
//
// Real damRate = damRateInfini * (1. - std::exp(-1*viscosity * (gequi -
// dam)));
// if (damrate > 0){
//
// if (dam < 1.){
// dam = dam + damRate*dt;
// } else {
// dam = 1.;
// }
// }
// }
//
//---------------------------------------------------------------------------------------
sigma
*=
1
-
dam
;
}
/* -------------------------------------------------------------------------- */
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