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material_elastic_inline_impl.cc
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rAKA akantu
material_elastic_inline_impl.cc
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/**
* @file material_elastic_inline_impl.cc
*
* @author Lucas Frerot <lucas.frerot@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
*
* @date creation: Wed Aug 04 2010
* @date last modification: Fri Dec 16 2016
*
* @brief Implementation of the inline functions of the material elastic
*
* @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 "material_elastic.hh"
/* -------------------------------------------------------------------------- */
#ifndef __AKANTU_MATERIAL_ELASTIC_INLINE_IMPL_CC__
#define __AKANTU_MATERIAL_ELASTIC_INLINE_IMPL_CC__
namespace
akantu
{
/* -------------------------------------------------------------------------- */
template
<
UInt
spatial_dimension
>
inline
void
MaterialElastic
<
spatial_dimension
>::
computeStressOnQuad
(
const
Matrix
<
Real
>
&
grad_u
,
Matrix
<
Real
>
&
sigma
,
const
Real
sigma_th
)
const
{
Real
trace
=
grad_u
.
trace
();
// trace = (\nabla u)_{kk}
// \sigma_{ij} = \lambda * (\nabla u)_{kk} * \delta_{ij} + \mu * (\nabla
// u_{ij} + \nabla u_{ji})
for
(
UInt
i
=
0
;
i
<
spatial_dimension
;
++
i
)
{
for
(
UInt
j
=
0
;
j
<
spatial_dimension
;
++
j
)
{
sigma
(
i
,
j
)
=
(
i
==
j
)
*
lambda
*
trace
+
mu
*
(
grad_u
(
i
,
j
)
+
grad_u
(
j
,
i
))
+
(
i
==
j
)
*
sigma_th
;
}
}
}
/* -------------------------------------------------------------------------- */
template
<>
inline
void
MaterialElastic
<
1
>::
computeStressOnQuad
(
const
Matrix
<
Real
>
&
grad_u
,
Matrix
<
Real
>
&
sigma
,
Real
sigma_th
)
const
{
sigma
(
0
,
0
)
=
this
->
E
*
grad_u
(
0
,
0
)
+
sigma_th
;
}
/* -------------------------------------------------------------------------- */
template
<
UInt
spatial_dimension
>
inline
void
MaterialElastic
<
spatial_dimension
>::
computeTangentModuliOnQuad
(
Matrix
<
Real
>
&
tangent
)
const
{
UInt
n
=
tangent
.
cols
();
// Real Ep = E/((1+nu)*(1-2*nu));
Real
Miiii
=
lambda
+
2
*
mu
;
Real
Miijj
=
lambda
;
Real
Mijij
=
mu
;
if
(
spatial_dimension
==
1
)
tangent
(
0
,
0
)
=
this
->
E
;
else
tangent
(
0
,
0
)
=
Miiii
;
// test of dimension should by optimized out by the compiler due to the
// template
if
(
spatial_dimension
>=
2
)
{
tangent
(
1
,
1
)
=
Miiii
;
tangent
(
0
,
1
)
=
Miijj
;
tangent
(
1
,
0
)
=
Miijj
;
tangent
(
n
-
1
,
n
-
1
)
=
Mijij
;
}
if
(
spatial_dimension
==
3
)
{
tangent
(
2
,
2
)
=
Miiii
;
tangent
(
0
,
2
)
=
Miijj
;
tangent
(
1
,
2
)
=
Miijj
;
tangent
(
2
,
0
)
=
Miijj
;
tangent
(
2
,
1
)
=
Miijj
;
tangent
(
3
,
3
)
=
Mijij
;
tangent
(
4
,
4
)
=
Mijij
;
}
}
/* -------------------------------------------------------------------------- */
template
<
UInt
dim
>
inline
void
MaterialElastic
<
dim
>::
computePotentialEnergyOnQuad
(
const
Matrix
<
Real
>
&
grad_u
,
const
Matrix
<
Real
>
&
sigma
,
Real
&
epot
)
{
epot
=
.5
*
sigma
.
doubleDot
(
grad_u
);
}
/* -------------------------------------------------------------------------- */
template
<>
inline
void
MaterialElastic
<
1
>::
computeTangentModuliOnQuad
(
Matrix
<
Real
>
&
tangent
)
const
{
tangent
(
0
,
0
)
=
E
;
}
}
// namespace akantu
#endif
/* __AKANTU_MATERIAL_ELASTIC_INLINE_IMPL_CC__ */
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