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material_igfem_elastic_inline_impl.hh
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Tue, Aug 27, 16:22
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rAKA akantu
material_igfem_elastic_inline_impl.hh
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/**
* @file material_igfem_elastic_inline_impl.hh
*
* @author Aurelia Isabel Cuba Ramos <aurelia.cubaramos@epfl.ch>
*
*
* @brief Implementation of the inline functions of the material igfem elastic
*
*
* Copyright (©) 2010-2012, 2014 EPFL (Ecole Polytechnique Fédérale de Lausanne)
* Laboratory (LSMS - Laboratoire de Simulation en Mécanique des Solides)
*
*/
/* -------------------------------------------------------------------------- */
/* -------------------------------------------------------------------------- */
template
<
UInt
spatial_dimension
>
inline
void
MaterialIGFEMElastic
<
spatial_dimension
>::
computeStressOnQuad
(
const
Matrix
<
Real
>
&
grad_u
,
Matrix
<
Real
>
&
sigma
,
const
Real
lambda
,
const
Real
mu
)
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
));
}
}
}
/* -------------------------------------------------------------------------- */
template
<>
inline
void
MaterialIGFEMElastic
<
1
>::
computeStressOnQuad
(
const
Matrix
<
Real
>
&
grad_u
,
Matrix
<
Real
>
&
sigma
,
const
Real
lambda
,
const
Real
mu
)
const
{
sigma
(
0
,
0
)
=
2
*
mu
*
grad_u
(
0
,
0
);
}
/* -------------------------------------------------------------------------- */
template
<
UInt
spatial_dimension
>
inline
void
MaterialIGFEMElastic
<
spatial_dimension
>::
computeTangentModuliOnQuad
(
Matrix
<
Real
>
&
tangent
,
const
Real
lambda
,
const
Real
mu
)
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
)
=
3
*
mu
;
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
MaterialIGFEMElastic
<
dim
>::
computePotentialEnergyOnQuad
(
const
Matrix
<
Real
>
&
grad_u
,
const
Matrix
<
Real
>
&
sigma
,
Real
&
epot
)
{
AKANTU_DEBUG_TO_IMPLEMENT
();
/// epot = .5 * sigma.doubleDot(grad_u);
}
/* -------------------------------------------------------------------------- */
template
<>
inline
void
MaterialIGFEMElastic
<
1
>::
computeTangentModuliOnQuad
(
Matrix
<
Real
>
&
tangent
,
const
Real
lambda
,
const
Real
mu
)
const
{
tangent
(
0
,
0
)
=
2
*
mu
;
}
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