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material_viscoelastic_maxwell.hh
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rAKA akantu
material_viscoelastic_maxwell.hh
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/**
* @file material_viscoelastic_maxwell.hh
*
* @author Emil Gallyamov <emil.gallyamov@epfl.ch>
*
* @date creation: Tue May 08 2018
* @date last modification: Tue May 08 2018
*
* @brief Material Visco-elastic, based on Maxwell chain,
* see
* [] R. de Borst and A.H. van den Boogaard "Finite-element modeling of
* deformation and cracking in early-age concrete", J.Eng.Mech., 1994
* as well as
* [] Manual of DIANA FEA Theory manual v.10.2 Section 37.6
*
*
* 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 "aka_common.hh"
#include "aka_voigthelper.hh"
#include "material_elastic.hh"
/* -------------------------------------------------------------------------- */
#ifndef AKANTU_MATERIAL_VISCOELASTIC_MAXWELL_HH_
#define AKANTU_MATERIAL_VISCOELASTIC_MAXWELL_HH_
namespace
akantu
{
/**
* Material Viscoelastic based on Maxwell chain
*
*
* @verbatim
E_0
------|\/\/\|-------
| |
---| |---
| |
----|\/\/\|--[|-----
| E_v1 \Eta_1|
---| |---
| |
----|\/\/\|--[|-----
| E_v2 \Eta_2 |
---| |---
| |
----|\/\/\|--[|----
E_vN \Eta_N
@endverbatim
*
* keyword : viscoelastic_maxwell
*
* parameters in the material files :
* - N : number of Maxwell elements
* - Einf : one spring element stiffness
* - Ev1 : stiffness of the 1st viscous element
* - Eta1: viscosity of the 1st Maxwell element
* ...
* - Ev<N> : stiffness of the Nst viscous element
* - Eta<N>: viscosity of the Nst Maxwell element
*/
template
<
UInt
spatial_dimension
>
class
MaterialViscoelasticMaxwell
:
public
MaterialElastic
<
spatial_dimension
>
{
/* ------------------------------------------------------------------------ */
/* Constructors/Destructors */
/* ------------------------------------------------------------------------ */
public
:
MaterialViscoelasticMaxwell
(
SolidMechanicsModel
&
model
,
const
ID
&
id
=
""
);
~
MaterialViscoelasticMaxwell
()
override
=
default
;
/* ------------------------------------------------------------------------ */
/* Methods */
/* ------------------------------------------------------------------------ */
public
:
/// initialize the material computed parameter
void
initMaterial
()
override
;
/// recompute the lame coefficient and effective tangent moduli
void
updateInternalParameters
()
override
;
/// update internal variable on a converged Newton
void
afterSolveStep
(
bool
converged
)
override
;
/// update internal variable based on previous and current strain values
void
updateIntVariables
();
/// update the internal variable sigma_v on quadrature point
void
updateIntVarOnQuad
(
const
Matrix
<
Real
>
&
grad_u
,
const
Matrix
<
Real
>
&
previous_grad_u
,
Tensor3
<
Real
>
&
sigma_v
,
Tensor3
<
Real
>
&
epsilon_v
);
/// constitutive law for all element of a type
void
computeStress
(
ElementType
el_type
,
GhostType
ghost_type
=
_not_ghost
)
override
;
/// compute the tangent stiffness matrix for an element type
void
computeTangentModuli
(
ElementType
el_type
,
Array
<
Real
>
&
tangent_matrix
,
GhostType
ghost_type
=
_not_ghost
)
override
;
/// save previous stress and strain values into "previous" arrays
void
savePreviousState
()
override
;
/// change flag of updateIntVar to true
void
forceUpdateVariable
();
/// change flag of updateIntVar to false
void
forceNotUpdateVariable
();
/// compute the elastic potential energy
void
computePotentialEnergy
(
ElementType
el_type
)
override
;
protected
:
void
computePotentialEnergyOnQuad
(
const
Matrix
<
Real
>
&
grad_u
,
Real
&
epot
,
Tensor3
<
Real
>
&
sigma_v
,
Tensor3
<
Real
>
&
epsilon_v
);
/// update the dissipated energy, is called after the stress have been
/// computed
void
updateDissipatedEnergy
(
ElementType
el_type
);
void
updateDissipatedEnergyOnQuad
(
const
Matrix
<
Real
>
&
grad_u
,
const
Matrix
<
Real
>
&
previous_grad_u
,
const
Matrix
<
Real
>
&
sigma
,
const
Matrix
<
Real
>
&
previous_sigma
,
Real
&
dis_energy
,
Real
&
mech_work
,
const
Real
&
pot_energy
);
/// compute stresses on a quadrature point
void
computeStressOnQuad
(
const
Matrix
<
Real
>
&
grad_u
,
const
Matrix
<
Real
>
&
previous_grad_u
,
Matrix
<
Real
>
&
sigma
,
Tensor3
<
Real
>
&
sigma_v
,
const
Real
&
sigma_th
);
/// compute tangent moduli on a quadrature point
void
computeTangentModuliOnQuad
(
Matrix
<
Real
>
&
tangent
);
bool
hasStiffnessMatrixChanged
()
override
{
Real
dt
=
this
->
model
.
getTimeStep
();
return
((
this
->
previous_dt
==
dt
)
?
(
!
(
this
->
previous_dt
==
dt
))
*
(
this
->
was_stiffness_assembled
)
:
(
!
(
this
->
previous_dt
==
dt
)));
// return (!(this->previous_dt == dt));
}
MatrixType
getTangentType
()
override
{
return
_symmetric
;
}
/* ------------------------------------------------------------------------ */
/* Accessors */
/* ------------------------------------------------------------------------ */
public
:
/// give the dissipated energy
Real
getDissipatedEnergy
()
const
;
Real
getDissipatedEnergy
(
ElementType
type
,
UInt
index
)
const
;
/// get the potential energy
Real
getPotentialEnergy
()
const
;
Real
getPotentialEnergy
(
ElementType
type
,
UInt
index
)
const
;
/// get the potential energy
Real
getMechanicalWork
()
const
;
Real
getMechanicalWork
(
ElementType
type
,
UInt
index
)
const
;
/// get the energy using an energy type string for the time step
Real
getEnergy
(
const
std
::
string
&
type
)
override
;
Real
getEnergy
(
const
std
::
string
&
energy_id
,
ElementType
type
,
UInt
index
)
override
;
/* ------------------------------------------------------------------------ */
/* Class Members */
/* ------------------------------------------------------------------------ */
protected
:
using
voigt_h
=
VoigtHelper
<
spatial_dimension
>
;
/// Vectors of viscosity, viscous elastic modulus, one spring element elastic
/// modulus
Vector
<
Real
>
Eta
;
Vector
<
Real
>
Ev
;
Real
Einf
;
/// time step from previous solveStep
Real
previous_dt
;
/// Stiffness matrix template
Matrix
<
Real
>
C
;
/// Compliance matrix template
Matrix
<
Real
>
D
;
/// Internal variable: viscous_stress
InternalField
<
Real
>
sigma_v
;
/// Internal variable: spring strain in Maxwell element
InternalField
<
Real
>
epsilon_v
;
/// Dissipated energy
InternalField
<
Real
>
dissipated_energy
;
/// Mechanical work
InternalField
<
Real
>
mechanical_work
;
/// Update internal variable after solve step or not
bool
update_variable_flag
;
};
}
// namespace akantu
#endif
/* AKANTU_MATERIAL_VISCOELASTIC_MAXWELL_HH_ */
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