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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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