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Patrick Jaap
dune-elasticity
Commits
a057b8c3
Commit
a057b8c3
authored
12 years ago
by
akbib
Committed by
akbib@FU-BERLIN.DE
12 years ago
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Material class for Neo-Hookean materials
[[Imported from SVN: r11295]]
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dune/elasticity/materials/neohookeanmaterial.hh
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a057b8c3
#ifndef NEO_HOOKIAN_MATERIAL
#define NEO_HOOKIAN_MATERIAL
#include
<dune/fufem/quadraturerules/quadraturerulecache.hh>
#include
<dune/fufem/symmetrictensor.hh>
#include
<dune/fufem/functions/virtualgridfunction.hh>
#include
<dune/fufem/functions/basisgridfunction.hh>
#include
<dune/elasticity/assemblers/neohookefunctionalassembler.hh>
#include
<dune/elasticity/assemblers/neohookeoperatorassembler.hh>
/** \brief Class representing a hyperelastic Neo-hookian material.
*
* \tparam Basis Global basis that is used for the spatial discretization.
* (This is not nice but I need a LocalFiniteElement for the local Hessian assembler :-( )
*/
template
<
class
Basis
>
class
NeoHookeMaterial
{
public:
typedef
typename
Basis
::
GridView
::
Grid
GridType
;
typedef
typename
Basis
::
LocalFiniteElement
Lfe
;
typedef
NeoHookeFunctionalAssembler
<
GridType
>
LocalLinearization
;
typedef
NeoHookeOperatorAssembler
<
GridType
,
Lfe
,
Lfe
>
LocalHessian
;
typedef
Basis
GlobalBasis
;
private:
typedef
typename
GridType
::
ctype
ctype
;
static
const
int
dim
=
GridType
::
dimension
;
static
const
int
dimworld
=
GridType
::
dimensionworld
;
typedef
typename
GridType
::
template
Codim
<
0
>
::
Geometry
::
LocalCoordinate
LocalCoordinate
;
typedef
typename
GridType
::
template
Codim
<
0
>
::
LeafIterator
ElementIterator
;
public:
NeoHookeMaterial
()
:
lambda_
(
1.0
),
mu_
(
0.3
)
{}
NeoHookeMaterial
(
const
Basis
&
basis
,
ctype
E
,
ctype
nu
)
:
basis_
(
basis
)
{
lambda_
=
E
*
nu
/
((
1
+
nu
)
*
(
1
-
2
*
nu
));
mu_
=
E
/
(
2
*
(
1
+
nu
));
localLinearization_
=
Dune
::
shared_ptr
<
LocalLinearization
>
(
new
LocalLinearization
(
lambda_
,
mu_
));
localHessian_
=
Dune
::
shared_ptr
<
LocalHessian
>
(
new
LocalHessian
(
lambda_
,
mu_
));
}
void
setup
(
ctype
E
,
ctype
nu
,
const
Basis
&
basis
)
{
lambda_
=
E
*
nu
/
((
1
+
nu
)
*
(
1
-
2
*
nu
));
mu_
=
E
/
(
2
*
(
1
+
nu
));
if
(
localLinearization_
)
localLinearization_
.
reset
();
if
(
localHessian_
)
localHessian_
.
reset
();
localLinearization_
=
Dune
::
shared_ptr
<
LocalLinearization
>
(
new
LocalLinearization
(
lambda_
,
mu_
));
localHessian_
=
Dune
::
shared_ptr
<
LocalHessian
>
(
new
LocalHessian
(
lambda_
,
mu_
));
basis_
=
&
basis
;
}
//! Evaluate the strain energy
template
<
class
CoeffType
>
ctype
energy
(
const
CoeffType
&
coeff
)
{
// make grid function
BasisGridFunction
<
Basis
,
CoeffType
>
configuration
(
*
basis_
,
coeff
);
ctype
energy
=
0
;
const
GridType
&
grid
=
configuration
.
grid
();
ElementIterator
eIt
=
grid
.
template
leafbegin
<
0
>();
ElementIterator
eItEnd
=
grid
.
template
leafend
<
0
>();
for
(;
eIt
!=
eItEnd
;
++
eIt
)
{
// TODO Get proper quadrature rule
// get quadrature rule
const
int
order
=
(
eIt
->
type
().
isSimplex
())
?
4
:
4
*
dim
;
const
Dune
::
template
QuadratureRule
<
ctype
,
dim
>
&
quad
=
QuadratureRuleCache
<
ctype
,
dim
>::
rule
(
order
);
// loop over quadrature points
for
(
size_t
pt
=
0
;
pt
<
quad
.
size
();
++
pt
)
{
// get quadrature point
const
LocalCoordinate
&
quadPos
=
quad
[
pt
].
position
();
// get integration factor
const
ctype
integrationElement
=
eIt
->
geometry
().
integrationElement
(
quadPos
);
// evaluate displacement gradient at the quadrature point
typename
BasisGridFunction
<
Basis
,
CoeffType
>::
DerivativeType
localConfGrad
;
if
(
configuration
.
isDefinedOn
(
*
eIt
))
configuration
.
evaluateDerivativeLocal
(
*
eIt
,
quadPos
,
localConfGrad
);
else
configuration
.
evaluateDerivative
(
eIt
->
geometry
().
global
(
quadPos
),
localConfGrad
);
SymmetricTensor
<
dim
>
strain
;
computeStrain
(
localConfGrad
,
strain
);
// the trace
ctype
trE
(
0
);
for
(
int
i
=
0
;
i
<
dim
;
i
++
)
trE
+=
strain
(
i
,
i
);
// make deformation gradient out of the discplacement
for
(
int
i
=
0
;
i
<
dim
;
i
++
)
localConfGrad
[
i
][
i
]
+=
1
;
// evaluate the derminante of the deformation gradient
const
ctype
J
=
localConfGrad
.
determinant
();
ctype
z
=
quad
[
pt
].
weight
()
*
integrationElement
;
#ifdef LAURSEN
energy
+=
z
*
(
0.25
*
lambda_
*
(
J
*
J
-
1
)
-
(
lambda_
*
0.5
+
mu_
)
*
std
::
log
(
J
)
+
mu_
*
trE
);
#else
energy
+=
z
*
(
0.5
*
lambda_
*
(
J
-
1
)
*
(
J
-
1
)
-
2
*
mu_
*
std
::
log
(
J
)
+
mu_
*
trE
);
#endif
}
}
return
0.5
*
energy
;
}
//! Return the local assembler of the first derivative of the strain energy
LocalLinearization
&
firstDerivative
()
{
return
*
localLinearization_
;}
//! Return the local assembler of the second derivative of the strain energy
LocalHessian
&
secondDerivative
()
{
return
*
localHessian_
;}
//! Return the global basis
const
Basis
&
basis
()
{
return
*
basis_
;}
private
:
//! First derivative of the strain energy
Dune
::
shared_ptr
<
LocalLinearization
>
localLinearization_
;
//! Second derivative of the strain energy
Dune
::
shared_ptr
<
LocalHessian
>
localHessian_
;
//! Global basis used for the spatial discretization
const
Basis
*
basis_
;
//! Lame constant
ctype
lambda_
;
//! Lame constant
ctype
mu_
;
//! Compute nonlinear strain tensor from the deformation gradient.
void
computeStrain
(
const
Dune
::
FieldMatrix
<
ctype
,
dim
,
dim
>&
grad
,
SymmetricTensor
<
dim
>&
strain
)
const
{
strain
=
0
;
for
(
int
i
=
0
;
i
<
dim
;
++
i
)
{
strain
(
i
,
i
)
+=
grad
[
i
][
i
];
for
(
int
k
=
0
;
k
<
dim
;
++
k
)
strain
(
i
,
i
)
+=
0.5
*
grad
[
k
][
i
]
*
grad
[
k
][
i
];
for
(
int
j
=
i
+
1
;
j
<
dim
;
++
j
)
{
strain
(
i
,
j
)
+=
0.5
*
(
grad
[
i
][
j
]
+
grad
[
j
][
i
]);
for
(
int
k
=
0
;
k
<
dim
;
++
k
)
strain
(
i
,
j
)
+=
0.5
*
grad
[
k
][
i
]
*
grad
[
k
][
j
];
}
}
}
};
#endif
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