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material_reinforcement.hh
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rAKA akantu
material_reinforcement.hh
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/**
* @file material_reinforcement.hh
*
* @author Lucas Frérot <lucas.frerot@epfl.ch>
*
* @date creation: Thu Mar 12 2015
* @date last modification: Thu Mar 12 2015
*
* @brief Reinforcement material
*
* @section LICENSE
*
* Copyright (©) 2010-2012, 2014 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/>.
*
*/
/* -------------------------------------------------------------------------- */
#ifndef __AKANTU_MATERIAL_REINFORCEMENT_HH__
#define __AKANTU_MATERIAL_REINFORCEMENT_HH__
#include "aka_common.hh"
#include "material.hh"
#include "embedded_interface_model.hh"
#include "embedded_internal_field.hh"
/* -------------------------------------------------------------------------- */
__BEGIN_AKANTU__
/**
* @brief Material used to represent embedded reinforcements
*
* This class is used for computing the reinforcement stiffness matrix
* along with the reinforcement residual. Room is made for constitutive law,
* but actual use of contitutive laws is made in MaterialReinforcementTemplate.
*/
template
<
UInt
dim
>
class
MaterialReinforcement
:
virtual
public
Material
{
/* ------------------------------------------------------------------------ */
/* Constructors/Destructors */
/* ------------------------------------------------------------------------ */
public
:
/// Constructor
MaterialReinforcement
(
SolidMechanicsModel
&
model
,
const
ID
&
id
=
""
);
/// Destructor
virtual
~
MaterialReinforcement
();
/* ------------------------------------------------------------------------ */
/* Methods */
/* ------------------------------------------------------------------------ */
public
:
/// Init the material
virtual
void
initMaterial
();
/// Init the background shape derivatives
void
initBackgroundShapeDerivatives
();
/// Init the cosine matrices
void
initDirectingCosines
();
/// Assemble stiffness matrix
virtual
void
assembleStiffnessMatrix
(
GhostType
ghost_type
);
/// Update the residual
virtual
void
updateResidual
(
GhostType
ghost_type
=
_not_ghost
);
/// Assembled the residual
virtual
void
assembleResidual
(
GhostType
ghost_type
);
/// Compute all the stresses !
virtual
void
computeAllStresses
(
GhostType
ghost_type
);
/// Compute the stiffness parameter for elements of a type
virtual
void
computeTangentModuli
(
const
ElementType
&
type
,
Array
<
Real
>
&
tangent
,
GhostType
ghost_type
)
=
0
;
virtual
Real
getEnergy
(
std
::
string
id
);
virtual
void
flattenInternal
(
const
std
::
string
&
field_id
,
ElementTypeMapArray
<
Real
>
&
internal_flat
,
const
GhostType
ghost_type
=
_not_ghost
,
ElementKind
element_kind
=
_ek_not_defined
);
/* ------------------------------------------------------------------------ */
/* Protected methods */
/* ------------------------------------------------------------------------ */
protected
:
/// Allocate the background shape derivatives
void
allocBackgroundShapeDerivatives
();
/// Compute the directing cosines matrix for one element type
void
computeDirectingCosines
(
const
ElementType
&
type
,
GhostType
ghost_type
);
/**
* @brief Compute the directing cosines matrix on quadrature points.
*
* The structure of the directing cosines matrix is :
* \f{eqnarray*}{
* C_{1,\cdot} & = & (l^2, m^2, n^2, lm, mn, ln) \\
* C_{i,j} & = & 0
* \f}
*
* with :
* \f[
* (l, m, n) = \frac{1}{\|\frac{\mathrm{d}\vec{r}(s)}{\mathrm{d}s}\|} \cdot \frac{\mathrm{d}\vec{r}(s)}{\mathrm{d}s}
* \f]
*/
inline
void
computeDirectingCosinesOnQuad
(
const
Matrix
<
Real
>
&
nodes
,
Matrix
<
Real
>
&
cosines
);
/// Assemble the stiffness matrix for an element type (typically _segment_2)
void
assembleStiffnessMatrix
(
const
ElementType
&
type
,
GhostType
ghost_type
);
/**
* @brief Assemble the stiffness matrix for background & interface types
*
* Computes the reinforcement stiffness matrix (Gomes & Awruch, 2001)
* \f[
* \mathbf{K}_e = \sum_{i=1}^R{A_i\int_{S_i}{\mathbf{B}^T
* \mathbf{C}_i^T \mathbf{D}_{s, i} \mathbf{C}_i \mathbf{B}\,\mathrm{d}s}}
* \f]
*/
void
assembleStiffnessMatrix
(
const
ElementType
&
interface_type
,
const
ElementType
&
background_type
,
GhostType
interface_ghost
,
GhostType
background_ghost
);
/// Compute the background shape derivatives for a type
void
computeBackgroundShapeDerivatives
(
const
ElementType
&
type
,
GhostType
ghost_type
);
/// Filter elements crossed by interface of a type
void
filterInterfaceBackgroundElements
(
Array
<
UInt
>
&
filter
,
const
ElementType
&
type
,
const
ElementType
&
interface_type
,
GhostType
ghost_type
,
GhostType
interface_ghost_type
);
/// Assemble the residual of one type of element (typically _segment_2)
void
assembleResidual
(
const
ElementType
&
type
,
GhostType
ghost_type
);
/**
* @brief Assemble the residual for a pair of elements
*
* Computes and assemble the residual. Residual in reinforcement is computed as :
* \f[
* \vec{r} = A_s \int_S{\mathbf{B}^T\mathbf{C}^T \vec{\sigma_s}\,\mathrm{d}s}
* \f]
*/
void
assembleResidual
(
const
ElementType
&
interface_type
,
const
ElementType
&
background_type
,
GhostType
interface_ghost
,
GhostType
background_ghost
);
// TODO figure out why voigt size is 4 in 2D
inline
void
stressTensorToVoigtVector
(
const
Matrix
<
Real
>
&
tensor
,
Vector
<
Real
>
&
vector
);
inline
void
strainTensorToVoigtVector
(
const
Matrix
<
Real
>
&
tensor
,
Vector
<
Real
>
&
vector
);
/// Compute gradu on the interface quadrature points
virtual
void
computeGradU
(
const
ElementType
&
type
,
GhostType
ghost_type
);
/* ------------------------------------------------------------------------ */
/* Class Members */
/* ------------------------------------------------------------------------ */
protected
:
/// Embedded model
EmbeddedInterfaceModel
*
model
;
/// grad_u
EmbeddedInternalField
<
Real
>
gradu
;
/// stress
EmbeddedInternalField
<
Real
>
stress
;
/// C matrix on quad
EmbeddedInternalField
<
Real
>
directing_cosines
;
/// Prestress on quad
EmbeddedInternalField
<
Real
>
pre_stress
;
/// Cross-sectional area
Real
area
;
/// Background mesh shape derivatives
ElementTypeMap
<
ElementTypeMapArray
<
Real
>
*
>
shape_derivatives
;
};
#include "material_reinforcement_inline_impl.cc"
__END_AKANTU__
#endif
// __AKANTU_MATERIAL_REINFORCEMENT_HH__
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