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/**
* @file material.hh
*
* @author Daniel Pino Muñoz <daniel.pinomunoz@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
* @author Marco Vocialta <marco.vocialta@epfl.ch>
*
* @date creation: Fri Jun 18 2010
* @date last modification: Wed Feb 21 2018
*
* @brief Mother class for all materials
*
*
* 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_factory.hh"
#include "aka_voigthelper.hh"
#include "data_accessor.hh"
#include "integration_point.hh"
#include "parsable.hh"
#include "parser.hh"
/* -------------------------------------------------------------------------- */
#include "internal_field.hh"
#include "random_internal_field.hh"
/* -------------------------------------------------------------------------- */
#include "mesh_events.hh"
#include "solid_mechanics_model_event_handler.hh"
/* -------------------------------------------------------------------------- */
#ifndef __AKANTU_MATERIAL_HH__
#define __AKANTU_MATERIAL_HH__
/* -------------------------------------------------------------------------- */
namespace akantu {
class Model;
class SolidMechanicsModel;
class Material;
} // namespace akantu
namespace akantu {
using MaterialFactory =
Factory<Material, ID, UInt, const ID &, SolidMechanicsModel &, const ID &>;
/**
* Interface of all materials
* Prerequisites for a new material
* - inherit from this class
* - implement the following methods:
* \code
* virtual Real getStableTimeStep(Real h, const Element & element =
* ElementNull);
*
* virtual void computeStress(ElementType el_type,
* GhostType ghost_type = _not_ghost);
*
* virtual void computeTangentStiffness(const ElementType & el_type,
* Array<Real> & tangent_matrix,
* GhostType ghost_type = _not_ghost);
* \endcode
*
*/
class Material : public Memory,
public DataAccessor<Element>,
public Parsable,
public MeshEventHandler,
protected SolidMechanicsModelEventHandler {
/* ------------------------------------------------------------------------ */
/* Constructors/Destructors */
/* ------------------------------------------------------------------------ */
public:
Material(const Material & mat) = delete;
Material & operator=(const Material & mat) = delete;
/// Initialize material with defaults
Material(SolidMechanicsModel & model, const ID & id = "");
/// Initialize material with custom mesh & fe_engine
Material(SolidMechanicsModel & model, UInt dim, const Mesh & mesh,
FEEngine & fe_engine, const ID & id = "");
/// Destructor
~Material() override;
protected:
void initialize();
/* ------------------------------------------------------------------------ */
/* Function that materials can/should reimplement */
/* ------------------------------------------------------------------------ */
protected:
/// constitutive law
virtual void computeStress(ElementType /* el_type */,
GhostType /* ghost_type */ = _not_ghost) {
AKANTU_TO_IMPLEMENT();
}
/// compute the tangent stiffness matrix
virtual void computeTangentModuli(const ElementType & /*el_type*/,
Array<Real> & /*tangent_matrix*/,
GhostType /*ghost_type*/ = _not_ghost) {
AKANTU_TO_IMPLEMENT();
}
/// compute the potential energy
virtual void computePotentialEnergy(ElementType el_type);
/// compute the potential energy for an element
virtual void
computePotentialEnergyByElement(ElementType /*type*/, UInt /*index*/,
Vector<Real> & /*epot_on_quad_points*/) {
AKANTU_TO_IMPLEMENT();
}
virtual void updateEnergies(ElementType /*el_type*/) {}
virtual void updateEnergiesAfterDamage(ElementType /*el_type*/) {}
/// set the material to steady state (to be implemented for materials that
/// need it)
virtual void setToSteadyState(ElementType /*el_type*/,
GhostType /*ghost_type*/ = _not_ghost) {}
/// function called to update the internal parameters when the modifiable
/// parameters are modified
virtual void updateInternalParameters() {}
public:
/// extrapolate internal values
virtual void extrapolateInternal(const ID & id, const Element & element,
const Matrix<Real> & points,
Matrix<Real> & extrapolated);
/// compute the p-wave speed in the material
virtual Real getPushWaveSpeed(const Element & /*element*/) const {
AKANTU_TO_IMPLEMENT();
}
/// compute the s-wave speed in the material
virtual Real getShearWaveSpeed(const Element & /*element*/) const {
AKANTU_TO_IMPLEMENT();
}
/// get a material celerity to compute the stable time step (default: is the
/// push wave speed)
virtual Real getCelerity(const Element & element) const {
return getPushWaveSpeed(element);
}
/* ------------------------------------------------------------------------ */
/* Methods */
/* ------------------------------------------------------------------------ */
public:
template <typename T> void registerInternal(InternalField<T> & /*vect*/) {
AKANTU_TO_IMPLEMENT();
}
template <typename T> void unregisterInternal(InternalField<T> & /*vect*/) {
AKANTU_TO_IMPLEMENT();
}
/// initialize the material computed parameter
virtual void initMaterial();
/// compute the residual for this material
// virtual void updateResidual(GhostType ghost_type = _not_ghost);
/// assemble the residual for this material
virtual void assembleInternalForces(GhostType ghost_type);
/// save the stress in the previous_stress if needed
virtual void savePreviousState();
/// restore the stress from previous_stress if needed
virtual void restorePreviousState();
/// compute the stresses for this material
virtual void computeAllStresses(GhostType ghost_type = _not_ghost);
// virtual void
// computeAllStressesFromTangentModuli(GhostType ghost_type = _not_ghost);
virtual void computeAllCauchyStresses(GhostType ghost_type = _not_ghost);
/// set material to steady state
void setToSteadyState(GhostType ghost_type = _not_ghost);
/// compute the stiffness matrix
virtual void assembleStiffnessMatrix(GhostType ghost_type);
/// add an element to the local mesh filter
inline UInt addElement(const ElementType & type, UInt element,
const GhostType & ghost_type);
inline UInt addElement(const Element & element);
/// add many elements at once
void addElements(const Array<Element> & elements_to_add);
/// remove many element at once
void removeElements(const Array<Element> & elements_to_remove);
/// function to print the contain of the class
void printself(std::ostream & stream, int indent = 0) const override;
/**
* interpolate stress on given positions for each element by means
* of a geometrical interpolation on quadrature points
*/
void interpolateStress(ElementTypeMapArray<Real> & result,
const GhostType ghost_type = _not_ghost);
/**
* interpolate stress on given positions for each element by means
* of a geometrical interpolation on quadrature points and store the
* results per facet
*/
void interpolateStressOnFacets(ElementTypeMapArray<Real> & result,
ElementTypeMapArray<Real> & by_elem_result,
const GhostType ghost_type = _not_ghost);
/**
* function to initialize the elemental field interpolation
* function by inverting the quadrature points' coordinates
*/
void initElementalFieldInterpolation(
const ElementTypeMapArray<Real> & interpolation_points_coordinates);
/* ------------------------------------------------------------------------ */
/* Common part */
/* ------------------------------------------------------------------------ */
protected:
/* ------------------------------------------------------------------------ */
inline UInt getTangentStiffnessVoigtSize(UInt spatial_dimension) const;
/// compute the potential energy by element
void computePotentialEnergyByElements();
/// resize the intenals arrays
virtual void resizeInternals();
/* ------------------------------------------------------------------------ */
/* Finite deformation functions */
/* This functions area implementing what is described in the paper of Bathe */
/* et al, in IJNME, Finite Element Formulations For Large Deformation */
/* Dynamic Analysis, Vol 9, 353-386, 1975 */
/* ------------------------------------------------------------------------ */
protected:
/// assemble the residual
template <UInt dim> void assembleInternalForces(GhostType ghost_type);
template <UInt dim>
void computeAllStressesFromTangentModuli(const ElementType & type,
GhostType ghost_type);
template <UInt dim>
void assembleStiffnessMatrix(const ElementType & type, GhostType ghost_type);
/// assembling in finite deformation
template <UInt dim>
void assembleStiffnessMatrixNL(const ElementType & type,
GhostType ghost_type);
template <UInt dim>
void assembleStiffnessMatrixL2(const ElementType & type,
GhostType ghost_type);
/* ------------------------------------------------------------------------ */
/* Conversion functions */
/* ------------------------------------------------------------------------ */
public:
/// Size of the Stress matrix for the case of finite deformation see: Bathe et
/// al, IJNME, Vol 9, 353-386, 1975
inline UInt getCauchyStressMatrixSize(UInt spatial_dimension) const;
/// Sets the stress matrix according to Bathe et al, IJNME, Vol 9, 353-386,
/// 1975
template <UInt dim>
static inline void setCauchyStressMatrix(const Matrix<Real> & S_t,
Matrix<Real> & sigma);
/// write the stress tensor in the Voigt notation.
template <UInt dim>
static inline decltype(auto) stressToVoigt(const Matrix<Real> & stress) {
return VoigtHelper<dim>::matrixToVoigt(stress);
}
/// write the strain tensor in the Voigt notation.
template <UInt dim>
static inline decltype(auto) strainToVoigt(const Matrix<Real> & strain) {
return VoigtHelper<dim>::matrixToVoigtWithFactors(strain);
}
/// write a voigt vector to stress
template <UInt dim>
static inline void voigtToStress(const Vector<Real> & voigt,
Matrix<Real> & stress) {
VoigtHelper<dim>::voigtToMatrix(voigt, stress);
}
/// Computation of Cauchy stress tensor in the case of finite deformation from
/// the 2nd Piola-Kirchhoff for a given element type
template <UInt dim>
void StoCauchy(ElementType el_type, GhostType ghost_type = _not_ghost);
/// Computation the Cauchy stress the 2nd Piola-Kirchhoff and the deformation
/// gradient
template <UInt dim>
inline void StoCauchy(const Matrix<Real> & F, const Matrix<Real> & S,
Matrix<Real> & sigma, const Real & C33 = 1.0) const;
template <UInt dim>
static inline void gradUToF(const Matrix<Real> & grad_u, Matrix<Real> & F);
template <UInt dim>
static inline decltype(auto) gradUToF(const Matrix<Real> & grad_u);
static inline void rightCauchy(const Matrix<Real> & F, Matrix<Real> & C);
static inline void leftCauchy(const Matrix<Real> & F, Matrix<Real> & B);
template <UInt dim>
static inline void gradUToEpsilon(const Matrix<Real> & grad_u,
Matrix<Real> & epsilon);
template <UInt dim>
static inline decltype(auto) gradUToEpsilon(const Matrix<Real> & grad_u);
template <UInt dim>
static inline void gradUToE(const Matrix<Real> & grad_u,
Matrix<Real> & epsilon);
template <UInt dim>
static inline decltype(auto) gradUToE(const Matrix<Real> & grad_u);
static inline Real stressToVonMises(const Matrix<Real> & stress);
protected:
/// converts global element to local element
inline Element convertToLocalElement(const Element & global_element) const;
/// converts local element to global element
inline Element convertToGlobalElement(const Element & local_element) const;
/// converts global quadrature point to local quadrature point
inline IntegrationPoint
convertToLocalPoint(const IntegrationPoint & global_point) const;
/// converts local quadrature point to global quadrature point
inline IntegrationPoint
convertToGlobalPoint(const IntegrationPoint & local_point) const;
/* ------------------------------------------------------------------------ */
/* DataAccessor inherited members */
/* ------------------------------------------------------------------------ */
public:
inline UInt getNbData(const Array<Element> & elements,
const SynchronizationTag & tag) const override;
inline void packData(CommunicationBuffer & buffer,
const Array<Element> & elements,
const SynchronizationTag & tag) const override;
inline void unpackData(CommunicationBuffer & buffer,
const Array<Element> & elements,
const SynchronizationTag & tag) override;
template <typename T>
inline void packElementDataHelper(const ElementTypeMapArray<T> & data_to_pack,
CommunicationBuffer & buffer,
const Array<Element> & elements,
const ID & fem_id = ID()) const;
template <typename T>
inline void unpackElementDataHelper(ElementTypeMapArray<T> & data_to_unpack,
CommunicationBuffer & buffer,
const Array<Element> & elements,
const ID & fem_id = ID());
/* ------------------------------------------------------------------------ */
/* MeshEventHandler inherited members */
/* ------------------------------------------------------------------------ */
public:
/* ------------------------------------------------------------------------ */
void onNodesAdded(const Array<UInt> &, const NewNodesEvent &) override{};
void onNodesRemoved(const Array<UInt> &, const Array<UInt> &,
const RemovedNodesEvent &) override{};
void onElementsAdded(const Array<Element> & element_list,
const NewElementsEvent & event) override;
void onElementsRemoved(const Array<Element> & element_list,
const ElementTypeMapArray<UInt> & new_numbering,
const RemovedElementsEvent & event) override;
void onElementsChanged(const Array<Element> &, const Array<Element> &,
const ElementTypeMapArray<UInt> &,
const ChangedElementsEvent &) override{};
/* ------------------------------------------------------------------------ */
/* SolidMechanicsModelEventHandler inherited members */
/* ------------------------------------------------------------------------ */
public:
virtual void beforeSolveStep();
virtual void afterSolveStep(bool converged = true);
void onDamageIteration() override;
void onDamageUpdate() override;
void onDump() override;
/* ------------------------------------------------------------------------ */
/* Accessors */
/* ------------------------------------------------------------------------ */
public:
AKANTU_GET_MACRO(Name, name, const std::string &);
AKANTU_GET_MACRO(Model, model, const SolidMechanicsModel &)
AKANTU_GET_MACRO(ID, Memory::getID(), const ID &);
AKANTU_GET_MACRO(Rho, rho, Real);
AKANTU_SET_MACRO(Rho, rho, Real);
AKANTU_GET_MACRO(SpatialDimension, spatial_dimension, UInt);
/// return the potential energy for the subset of elements contained by the
/// material
Real getPotentialEnergy();
/// return the potential energy for the provided element
Real getPotentialEnergy(ElementType & type, UInt index);
/// return the energy (identified by id) for the subset of elements contained
/// by the material
virtual Real getEnergy(const std::string & energy_id);
/// return the energy (identified by id) for the provided element
virtual Real getEnergy(const std::string & energy_id, ElementType type,
UInt index);
AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(ElementFilter, element_filter, UInt);
AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(GradU, gradu, Real);
AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(Stress, stress, Real);
AKANTU_GET_MACRO_BY_ELEMENT_TYPE_CONST(PotentialEnergy, potential_energy,
Real);
AKANTU_GET_MACRO(GradU, gradu, const ElementTypeMapArray<Real> &);
AKANTU_GET_MACRO(Stress, stress, const ElementTypeMapArray<Real> &);
AKANTU_GET_MACRO(ElementFilter, element_filter,
const ElementTypeMapArray<UInt> &);
AKANTU_GET_MACRO(FEEngine, fem, FEEngine &);
bool isNonLocal() const { return is_non_local; }
template <typename T>
const Array<T> & getArray(const ID & id, const ElementType & type,
const GhostType & ghost_type = _not_ghost) const;
template <typename T>
Array<T> & getArray(const ID & id, const ElementType & type,
const GhostType & ghost_type = _not_ghost);
template <typename T>
const InternalField<T> & getInternal(const ID & id) const;
template <typename T> InternalField<T> & getInternal(const ID & id);
template <typename T>
inline bool isInternal(const ID & id, const ElementKind & element_kind) const;
template <typename T>
ElementTypeMap<UInt>
getInternalDataPerElem(const ID & id, const ElementKind & element_kind) const;
bool isFiniteDeformation() const { return finite_deformation; }
bool isInelasticDeformation() const { return inelastic_deformation; }
template <typename T> inline void setParam(const ID & param, T value);
inline const Parameter & getParam(const ID & param) const;
template <typename T>
void flattenInternal(const std::string & field_id,
ElementTypeMapArray<T> & internal_flat,
const GhostType ghost_type = _not_ghost,
ElementKind element_kind = _ek_not_defined) const;
/// apply a constant eigengrad_u everywhere in the material
virtual void applyEigenGradU(const Matrix<Real> & prescribed_eigen_grad_u,
const GhostType = _not_ghost);
bool hasMatrixChanged(const ID & id) {
if (id == "K") {
return hasStiffnessMatrixChanged() or finite_deformation;
}
return true;
}
MatrixType getMatrixType(const ID & id) {
if (id == "K") {
return getTangentType();
} else if (id == "M") {
return _symmetric;
}
return _mt_not_defined;
}
/// specify if the matrix need to be recomputed for this material
virtual bool hasStiffnessMatrixChanged() { return true; }
/// specify the type of matrix, if not overloaded the material is not valid
/// for static or implicit computations
virtual MatrixType getTangentType() { return _mt_not_defined; }
/// static method to reteive the material factory
static MaterialFactory & getFactory();
protected:
bool isInit() const { return is_init; }
/* ------------------------------------------------------------------------ */
/* Class Members */
/* ------------------------------------------------------------------------ */
protected:
/// boolean to know if the material has been initialized
bool is_init;
std::map<ID, InternalField<Real> *> internal_vectors_real;
std::map<ID, InternalField<UInt> *> internal_vectors_uint;
std::map<ID, InternalField<bool> *> internal_vectors_bool;
protected:
/// Link to the fem object in the model
FEEngine & fem;
/// Finite deformation
bool finite_deformation;
/// Finite deformation
bool inelastic_deformation;
/// material name
std::string name;
/// The model to witch the material belong
SolidMechanicsModel & model;
/// density : rho
Real rho;
/// spatial dimension
UInt spatial_dimension;
/// list of element handled by the material
ElementTypeMapArray<UInt> element_filter;
/// stresses arrays ordered by element types
InternalField<Real> stress;
/// eigengrad_u arrays ordered by element types
InternalField<Real> eigengradu;
/// grad_u arrays ordered by element types
InternalField<Real> gradu;
/// Green Lagrange strain (Finite deformation)
InternalField<Real> green_strain;
/// Second Piola-Kirchhoff stress tensor arrays ordered by element types
/// (Finite deformation)
InternalField<Real> piola_kirchhoff_2;
/// potential energy by element
InternalField<Real> potential_energy;
/// tell if using in non local mode or not
bool is_non_local;
/// tell if the material need the previous stress state
bool use_previous_stress;
/// tell if the material need the previous strain state
bool use_previous_gradu;
/// elemental field interpolation coordinates
InternalField<Real> interpolation_inverse_coordinates;
/// elemental field interpolation points
InternalField<Real> interpolation_points_matrices;
/// vector that contains the names of all the internals that need to
/// be transferred when material interfaces move
std::vector<ID> internals_to_transfer;
};
/// standard output stream operator
inline std::ostream & operator<<(std::ostream & stream,
const Material & _this) {
_this.printself(stream);
return stream;
}
} // namespace akantu
#include "material_inline_impl.hh"
#include "internal_field_tmpl.hh"
#include "random_internal_field_tmpl.hh"
/* -------------------------------------------------------------------------- */
/* Auto loop */
/* -------------------------------------------------------------------------- */
/// This can be used to automatically write the loop on quadrature points in
/// functions such as computeStress. This macro in addition to write the loop
/// provides two tensors (matrices) sigma and grad_u
#define MATERIAL_STRESS_QUADRATURE_POINT_LOOP_BEGIN(el_type, ghost_type) \
auto && grad_u_view = \
make_view(this->gradu(el_type, ghost_type), this->spatial_dimension, \
this->spatial_dimension); \
\
auto stress_view = \
make_view(this->stress(el_type, ghost_type), this->spatial_dimension, \
this->spatial_dimension); \
\
if (this->isFiniteDeformation()) { \
stress_view = make_view(this->piola_kirchhoff_2(el_type, ghost_type), \
this->spatial_dimension, this->spatial_dimension); \
} \
\
for (auto && data : zip(grad_u_view, stress_view)) { \
[[gnu::unused]] Matrix<Real> & grad_u = std::get<0>(data); \
[[gnu::unused]] Matrix<Real> & sigma = std::get<1>(data)
#define MATERIAL_STRESS_QUADRATURE_POINT_LOOP_END }
/// This can be used to automatically write the loop on quadrature points in
/// functions such as computeTangentModuli. This macro in addition to write the
/// loop provides two tensors (matrices) sigma_tensor, grad_u, and a matrix
/// where the elemental tangent moduli should be stored in Voigt Notation
#define MATERIAL_TANGENT_QUADRATURE_POINT_LOOP_BEGIN(tangent_mat) \
auto && grad_u_view = \
make_view(this->gradu(el_type, ghost_type), this->spatial_dimension, \
this->spatial_dimension); \
\
auto && stress_view = \
make_view(this->stress(el_type, ghost_type), this->spatial_dimension, \
this->spatial_dimension); \
\
auto tangent_size = \
this->getTangentStiffnessVoigtSize(this->spatial_dimension); \
\
auto && tangent_view = make_view(tangent_mat, tangent_size, tangent_size); \
\
for (auto && data : zip(grad_u_view, stress_view, tangent_view)) { \
[[gnu::unused]] Matrix<Real> & grad_u = std::get<0>(data); \
[[gnu::unused]] Matrix<Real> & sigma = std::get<1>(data); \
Matrix<Real> & tangent = std::get<2>(data);
#define MATERIAL_TANGENT_QUADRATURE_POINT_LOOP_END }
/* -------------------------------------------------------------------------- */
#define INSTANTIATE_MATERIAL_ONLY(mat_name) \
template class mat_name<1>; \
template class mat_name<2>; \
template class mat_name<3>
#define MATERIAL_DEFAULT_PER_DIM_ALLOCATOR(id, mat_name) \
[](UInt dim, const ID &, SolidMechanicsModel & model, \
const ID & id) -> std::unique_ptr<Material> { \
switch (dim) { \
case 1: \
return std::make_unique<mat_name<1>>(model, id); \
case 2: \
return std::make_unique<mat_name<2>>(model, id); \
case 3: \
return std::make_unique<mat_name<3>>(model, id); \
default: \
AKANTU_EXCEPTION("The dimension " \
<< dim << "is not a valid dimension for the material " \
<< #id); \
} \
}
#define INSTANTIATE_MATERIAL(id, mat_name) \
INSTANTIATE_MATERIAL_ONLY(mat_name); \
static bool material_is_alocated_##id [[gnu::unused]] = \
MaterialFactory::getInstance().registerAllocator( \
#id, MATERIAL_DEFAULT_PER_DIM_ALLOCATOR(id, mat_name))
#endif /* __AKANTU_MATERIAL_HH__ */
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