diff --git a/src/model/solid_mechanics/materials/material_embedded/material_reinforcement.hh b/src/model/solid_mechanics/materials/material_embedded/material_reinforcement.hh
index a6c3088ff..8ff027c8f 100644
--- a/src/model/solid_mechanics/materials/material_embedded/material_reinforcement.hh
+++ b/src/model/solid_mechanics/materials/material_embedded/material_reinforcement.hh
@@ -1,213 +1,210 @@
/**
* @file material_reinforcement.hh
*
* @author Lucas Frerot <lucas.frerot@epfl.ch>
*
* @date creation: Fri Mar 13 2015
* @date last modification: Tue Nov 24 2015
*
* @brief Reinforcement material
*
* @section LICENSE
*
* Copyright (©) 2015 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"
/* -------------------------------------------------------------------------- */
namespace 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.
*
* Be careful with the dimensions in this class :
* - this->spatial_dimension is always 1
* - the template parameter dim is the dimension of the problem
*/
template <class Mat, UInt dim> class MaterialReinforcement : public Mat {
/* ------------------------------------------------------------------------ */
/* Constructors/Destructors */
/* ------------------------------------------------------------------------ */
public:
/// Constructor
MaterialReinforcement(EmbeddedInterfaceModel & model, const ID & id = "");
/// Destructor
~MaterialReinforcement() override;
protected:
void initialize();
/* ------------------------------------------------------------------------ */
/* Methods */
/* ------------------------------------------------------------------------ */
public:
/// Init the material
void initMaterial() override;
/// Init the filters for background elements
void initFilters();
/// Init the background shape derivatives
void initBackgroundShapeDerivatives();
/// Init the cosine matrices
void initDirectingCosines();
/// Assemble stiffness matrix
void assembleStiffnessMatrix(GhostType ghost_type) override;
/// Compute all the stresses !
void computeAllStresses(GhostType ghost_type) override;
/// Compute energy
Real getEnergy(const std::string & id) override;
/// Assemble the residual of one type of element (typically _segment_2)
void assembleInternalForces(GhostType ghost_type) override;
/* ------------------------------------------------------------------------ */
/* 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);
/// Compute the directing cosines matrix on quadrature points.
inline void computeDirectingCosinesOnQuad(const Matrix<Real> & nodes,
Matrix<Real> & cosines);
/// Add the prestress to the computed stress
void addPrestress(const ElementType & type, GhostType ghost_type);
/// Compute displacement gradient in reinforcement
void computeGradU(const ElementType & interface_type, GhostType ghost_type);
/// Assemble the stiffness matrix for an element type (typically _segment_2)
void assembleStiffnessMatrix(const ElementType & type, GhostType ghost_type);
/// Assemble the stiffness matrix for background & interface types
void assembleStiffnessMatrixInterface(const ElementType & interface_type,
const ElementType & background_type,
GhostType ghost_type);
/// Compute the background shape derivatives for a type
void computeBackgroundShapeDerivatives(const ElementType & type,
GhostType ghost_type);
/// Compute the background shape derivatives for a type pair
void computeBackgroundShapeDerivatives(const ElementType & interface_type,
const ElementType & bg_type,
GhostType ghost_type,
const Array<UInt> & filter);
/// Filter elements crossed by interface of a type
void filterInterfaceBackgroundElements(Array<UInt> & foreground,
Array<UInt> & background,
const ElementType & type,
const ElementType & interface_type,
GhostType ghost_type);
/// Assemble the residual of one type of element (typically _segment_2)
void assembleInternalForces(const ElementType & type, GhostType ghost_type);
/// Assemble the residual for a pair of elements
void assembleInternalForcesInterface(const ElementType & interface_type,
const ElementType & background_type,
GhostType ghost_type);
// 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);
/// Get background filter
Array<UInt> & getBackgroundFilter(const ElementType & fg_type,
const ElementType & bg_type,
GhostType ghost_type) {
return (*background_filter(fg_type, ghost_type))(bg_type, ghost_type);
}
/// Get foreground filter
Array<UInt> & getForegroundFilter(const ElementType & fg_type,
const ElementType & bg_type,
GhostType ghost_type) {
return (*foreground_filter(fg_type, ghost_type))(bg_type, ghost_type);
}
/* ------------------------------------------------------------------------ */
/* Class Members */
/* ------------------------------------------------------------------------ */
protected:
/// Embedded model
EmbeddedInterfaceModel & emodel;
- /// Stress in the reinforcement
- InternalField<Real> stress_embedded;
-
/// Gradu of concrete on reinforcement
InternalField<Real> gradu_embedded;
/// C matrix on quad
InternalField<Real> directing_cosines;
/// Prestress on quad
InternalField<Real> pre_stress;
/// Cross-sectional area
Real area;
template <typename T>
using CrossMap = ElementTypeMap<std::unique_ptr<ElementTypeMapArray<T>>>;
/// Background mesh shape derivatives
CrossMap<Real> shape_derivatives;
/// Foreground mesh filter (contains segment ids)
CrossMap<UInt> foreground_filter;
/// Background element filter (contains bg ids)
CrossMap<UInt> background_filter;
};
} // akantu
#include "material_reinforcement_tmpl.hh"
#endif // __AKANTU_MATERIAL_REINFORCEMENT_HH__
diff --git a/src/model/solid_mechanics/materials/material_embedded/material_reinforcement_tmpl.hh b/src/model/solid_mechanics/materials/material_embedded/material_reinforcement_tmpl.hh
index 17e60356b..09caa4037 100644
--- a/src/model/solid_mechanics/materials/material_embedded/material_reinforcement_tmpl.hh
+++ b/src/model/solid_mechanics/materials/material_embedded/material_reinforcement_tmpl.hh
@@ -1,822 +1,818 @@
/**
* @file material_reinforcement_tmpl.hh
*
* @author Lucas Frerot <lucas.frerot@epfl.ch>
*
* @date creation: Thu Feb 1 2018
*
* @brief Reinforcement material
*
* @section LICENSE
*
* Copyright (©) 2015 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_reinforcement.hh"
namespace akantu {
/* -------------------------------------------------------------------------- */
template <class Mat, UInt dim>
MaterialReinforcement<Mat, dim>::MaterialReinforcement(
EmbeddedInterfaceModel & model, const ID & id)
: Mat(model, 1,
model.getInterfaceMesh(),
model.getFEEngine("EmbeddedInterfaceFEEngine"), id),
emodel(model),
- stress_embedded("stress_embedded", *this, 1,
- model.getFEEngine("EmbeddedInterfaceFEEngine"),
- this->element_filter),
gradu_embedded("gradu_embedded", *this, 1,
model.getFEEngine("EmbeddedInterfaceFEEngine"),
this->element_filter),
directing_cosines("directing_cosines", *this, 1,
model.getFEEngine("EmbeddedInterfaceFEEngine"),
this->element_filter),
pre_stress("pre_stress", *this, 1,
model.getFEEngine("EmbeddedInterfaceFEEngine"),
this->element_filter),
area(1.0), shape_derivatives() {
AKANTU_DEBUG_IN();
this->initialize();
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <class Mat, UInt dim>
void MaterialReinforcement<Mat, dim>::initialize() {
AKANTU_DEBUG_IN();
this->registerParam("area", area, _pat_parsable | _pat_modifiable,
"Reinforcement cross-sectional area");
this->registerParam("pre_stress", pre_stress, _pat_parsable | _pat_modifiable,
"Uniform pre-stress");
// this->unregisterInternal(this->stress);
// Fool the AvgHomogenizingFunctor
// stress.initialize(dim * dim);
// Reallocate the element filter
this->element_filter.initialize(this->emodel.getInterfaceMesh(),
_spatial_dimension = 1);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <class Mat, UInt dim>
MaterialReinforcement<Mat, dim>::~MaterialReinforcement() {
AKANTU_DEBUG_IN();
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <class Mat, UInt dim>
void MaterialReinforcement<Mat, dim>::initMaterial() {
Mat::initMaterial();
- stress_embedded.initialize(dim * dim);
gradu_embedded.initialize(dim * dim);
pre_stress.initialize(1);
/// We initialise the stuff that is not going to change during the simulation
this->initFilters();
this->allocBackgroundShapeDerivatives();
this->initBackgroundShapeDerivatives();
this->initDirectingCosines();
}
/* -------------------------------------------------------------------------- */
namespace detail {
class FilterInitializer : public MeshElementTypeMapArrayInializer {
public:
FilterInitializer(EmbeddedInterfaceModel & emodel,
const GhostType & ghost_type)
: MeshElementTypeMapArrayInializer(emodel.getMesh(),
1, emodel.getSpatialDimension(),
ghost_type, _ek_regular) {}
UInt size(const ElementType & /*bgtype*/) const override { return 0; }
};
}
/* -------------------------------------------------------------------------- */
/// Initialize the filter for background elements
template <class Mat, UInt dim>
void MaterialReinforcement<Mat, dim>::initFilters() {
for (auto gt : ghost_types) {
for (auto && type : emodel.getInterfaceMesh().elementTypes(1, gt)) {
std::string shaped_id = "filter";
if (gt == _ghost)
shaped_id += ":ghost";
auto & background =
background_filter(std::make_unique<ElementTypeMapArray<UInt>>(
"bg_" + shaped_id, this->name),
type, gt);
auto & foreground = foreground_filter(
std::make_unique<ElementTypeMapArray<UInt>>(shaped_id, this->name),
type, gt);
foreground->initialize(detail::FilterInitializer(emodel, gt), 0, true);
background->initialize(detail::FilterInitializer(emodel, gt), 0, true);
// Computing filters
for (auto && bg_type : background->elementTypes(dim, gt)) {
filterInterfaceBackgroundElements(
(*foreground)(bg_type), (*background)(bg_type), bg_type, type, gt);
}
}
}
}
/* -------------------------------------------------------------------------- */
/// Construct a filter for a (interface_type, background_type) pair
template <class Mat, UInt dim>
void MaterialReinforcement<Mat, dim>::filterInterfaceBackgroundElements(
Array<UInt> & foreground, Array<UInt> & background,
const ElementType & type, const ElementType & interface_type,
GhostType ghost_type) {
AKANTU_DEBUG_IN();
foreground.resize(0);
background.resize(0);
Array<Element> & elements =
emodel.getInterfaceAssociatedElements(interface_type, ghost_type);
Array<UInt> & elem_filter = this->element_filter(interface_type, ghost_type);
for (auto & elem_id : elem_filter) {
Element & elem = elements(elem_id);
if (elem.type == type) {
background.push_back(elem.element);
foreground.push_back(elem_id);
}
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
namespace detail {
class BackgroundShapeDInitializer : public ElementTypeMapArrayInializer {
public:
BackgroundShapeDInitializer(UInt spatial_dimension,
FEEngine & engine,
const ElementType & foreground_type,
ElementTypeMapArray<UInt> & filter,
const GhostType & ghost_type)
: ElementTypeMapArrayInializer(spatial_dimension, 0, ghost_type,
_ek_regular) {
auto nb_quad = engine.getNbIntegrationPoints(foreground_type);
// Counting how many background elements are affected by elements of
// interface_type
for (auto type : filter.elementTypes(this->spatial_dimension)) {
// Inserting size
array_size_per_bg_type(filter(type).size() * nb_quad, type,
this->ghost_type);
}
}
auto elementTypes() const -> decltype(auto) {
return array_size_per_bg_type.elementTypes();
}
UInt size(const ElementType & bgtype) const {
return array_size_per_bg_type(bgtype, this->ghost_type);
}
UInt nbComponent(const ElementType & bgtype) const {
return ShapeFunctions::getShapeDerivativesSize(bgtype);
}
protected:
ElementTypeMap<UInt> array_size_per_bg_type;
};
}
/**
* Background shape derivatives need to be stored per background element
* types but also per embedded element type, which is why they are stored
* in an ElementTypeMap<ElementTypeMapArray<Real> *>. The outer ElementTypeMap
* refers to the embedded types, and the inner refers to the background types.
*/
template <class Mat, UInt dim>
void MaterialReinforcement<Mat, dim>::allocBackgroundShapeDerivatives() {
AKANTU_DEBUG_IN();
for (auto gt : ghost_types) {
for (auto && type : emodel.getInterfaceMesh().elementTypes(1, gt)) {
std::string shaped_id = "embedded_shape_derivatives";
if (gt == _ghost)
shaped_id += ":ghost";
auto & shaped_etma = shape_derivatives(
std::make_unique<ElementTypeMapArray<Real>>(shaped_id, this->name),
type, gt);
shaped_etma->initialize(
detail::BackgroundShapeDInitializer(
emodel.getSpatialDimension(),
emodel.getFEEngine("EmbeddedInterfaceFEEngine"), type,
*background_filter(type, gt), gt),
0, true);
}
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <class Mat, UInt dim>
void MaterialReinforcement<Mat, dim>::initBackgroundShapeDerivatives() {
AKANTU_DEBUG_IN();
for (auto interface_type :
this->element_filter.elementTypes(this->spatial_dimension)) {
for (auto type : background_filter(interface_type)->elementTypes(dim)) {
computeBackgroundShapeDerivatives(interface_type, type, _not_ghost,
this->element_filter(interface_type));
}
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <class Mat, UInt dim>
void MaterialReinforcement<Mat, dim>::computeBackgroundShapeDerivatives(
const ElementType & interface_type, const ElementType & bg_type,
GhostType ghost_type, const Array<UInt> & filter) {
auto & interface_engine = emodel.getFEEngine("EmbeddedInterfaceFEEngine");
auto & engine = emodel.getFEEngine();
auto & interface_mesh = emodel.getInterfaceMesh();
const auto nb_nodes_elem_bg = Mesh::getNbNodesPerElement(bg_type);
// const auto nb_strss = VoigtHelper<dim>::size;
const auto nb_quads_per_elem =
interface_engine.getNbIntegrationPoints(interface_type);
Array<Real> quad_pos(0, dim, "interface_quad_pos");
interface_engine.interpolateOnIntegrationPoints(interface_mesh.getNodes(),
quad_pos, dim, interface_type,
ghost_type, filter);
auto & background_shapesd =
(*shape_derivatives(interface_type, ghost_type))(bg_type, ghost_type);
auto & background_elements =
(*background_filter(interface_type, ghost_type))(bg_type, ghost_type);
auto & foreground_elements =
(*foreground_filter(interface_type, ghost_type))(bg_type, ghost_type);
auto shapesd_begin =
background_shapesd.begin(dim, nb_nodes_elem_bg, nb_quads_per_elem);
auto quad_begin = quad_pos.begin(dim, nb_quads_per_elem);
for (auto && tuple : zip(background_elements, foreground_elements)) {
UInt bg = std::get<0>(tuple), fg = std::get<1>(tuple);
for (UInt i = 0; i < nb_quads_per_elem; ++i) {
Matrix<Real> shapesd = Tensor3<Real>(shapesd_begin[fg])(i);
Vector<Real> quads = Matrix<Real>(quad_begin[fg])(i);
engine.computeShapeDerivatives(quads, bg, bg_type, shapesd,
ghost_type);
}
}
}
/* -------------------------------------------------------------------------- */
template <class Mat, UInt dim>
void MaterialReinforcement<Mat, dim>::initDirectingCosines() {
AKANTU_DEBUG_IN();
Mesh & mesh = emodel.getInterfaceMesh();
Mesh::type_iterator type_it = mesh.firstType(1, _not_ghost);
Mesh::type_iterator type_end = mesh.lastType(1, _not_ghost);
const UInt voigt_size = VoigtHelper<dim>::size;
directing_cosines.initialize(voigt_size);
for (; type_it != type_end; ++type_it) {
computeDirectingCosines(*type_it, _not_ghost);
// computeDirectingCosines(*type_it, _ghost);
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <class Mat, UInt dim>
void MaterialReinforcement<Mat, dim>::assembleStiffnessMatrix(
GhostType ghost_type) {
AKANTU_DEBUG_IN();
Mesh & interface_mesh = emodel.getInterfaceMesh();
Mesh::type_iterator type_it = interface_mesh.firstType(1, _not_ghost);
Mesh::type_iterator type_end = interface_mesh.lastType(1, _not_ghost);
for (; type_it != type_end; ++type_it) {
assembleStiffnessMatrix(*type_it, ghost_type);
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <class Mat, UInt dim>
void MaterialReinforcement<Mat, dim>::assembleInternalForces(
GhostType ghost_type) {
AKANTU_DEBUG_IN();
Mesh & interface_mesh = emodel.getInterfaceMesh();
Mesh::type_iterator type_it = interface_mesh.firstType(1, _not_ghost);
Mesh::type_iterator type_end = interface_mesh.lastType(1, _not_ghost);
for (; type_it != type_end; ++type_it) {
this->assembleInternalForces(*type_it, ghost_type);
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <class Mat, UInt dim>
void MaterialReinforcement<Mat, dim>::computeAllStresses(GhostType ghost_type) {
AKANTU_DEBUG_IN();
Mesh::type_iterator it = emodel.getInterfaceMesh().firstType();
Mesh::type_iterator last_type = emodel.getInterfaceMesh().lastType();
for (; it != last_type; ++it) {
computeGradU(*it, ghost_type);
this->computeStress(*it, ghost_type);
addPrestress(*it, ghost_type);
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <class Mat, UInt dim>
void MaterialReinforcement<Mat, dim>::addPrestress(const ElementType & type,
GhostType ghost_type) {
auto & stress = this->stress(type, ghost_type);
auto & sigma_p = this->pre_stress(type, ghost_type);
for (auto && tuple : zip(stress, sigma_p)) {
std::get<0>(tuple) += std::get<1>(tuple);
}
}
/* -------------------------------------------------------------------------- */
template <class Mat, UInt dim>
void MaterialReinforcement<Mat, dim>::assembleInternalForces(
const ElementType & type, GhostType ghost_type) {
AKANTU_DEBUG_IN();
Mesh & mesh = emodel.getMesh();
Mesh::type_iterator type_it = mesh.firstType(dim, ghost_type);
Mesh::type_iterator type_end = mesh.lastType(dim, ghost_type);
for (; type_it != type_end; ++type_it) {
assembleInternalForcesInterface(type, *type_it, ghost_type);
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
/**
* 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]
*/
template <class Mat, UInt dim>
void MaterialReinforcement<Mat, dim>::assembleInternalForcesInterface(
const ElementType & interface_type, const ElementType & background_type,
GhostType ghost_type) {
AKANTU_DEBUG_IN();
UInt voigt_size = VoigtHelper<dim>::size;
FEEngine & interface_engine = emodel.getFEEngine("EmbeddedInterfaceFEEngine");
Array<UInt> & elem_filter = this->element_filter(interface_type, ghost_type);
UInt nodes_per_background_e = Mesh::getNbNodesPerElement(background_type);
UInt nb_quadrature_points =
interface_engine.getNbIntegrationPoints(interface_type, ghost_type);
UInt nb_element = elem_filter.size();
UInt back_dof = dim * nodes_per_background_e;
Array<Real> & shapesd = (*shape_derivatives(interface_type, ghost_type))(
background_type, ghost_type);
Array<Real> integrant(nb_quadrature_points * nb_element, back_dof,
"integrant");
Array<Real>::vector_iterator integrant_it = integrant.begin(back_dof);
Array<Real>::vector_iterator integrant_end = integrant.end(back_dof);
Array<Real>::matrix_iterator B_it =
shapesd.begin(dim, nodes_per_background_e);
Array<Real>::vector_iterator C_it =
directing_cosines(interface_type, ghost_type).begin(voigt_size);
auto sigma_it = this->stress(interface_type, ghost_type).begin();
Matrix<Real> Bvoigt(voigt_size, back_dof);
for (; integrant_it != integrant_end;
++integrant_it, ++B_it, ++C_it, ++sigma_it) {
VoigtHelper<dim>::transferBMatrixToSymVoigtBMatrix(*B_it, Bvoigt,
nodes_per_background_e);
Vector<Real> & C = *C_it;
Vector<Real> & BtCt_sigma = *integrant_it;
BtCt_sigma.mul<true>(Bvoigt, C);
BtCt_sigma *= *sigma_it * area;
}
Array<Real> residual_interface(nb_element, back_dof, "residual_interface");
interface_engine.integrate(integrant, residual_interface, back_dof,
interface_type, ghost_type, elem_filter);
integrant.resize(0);
Array<UInt> background_filter(nb_element, 1, "background_filter");
auto & filter =
getBackgroundFilter(interface_type, background_type, ghost_type);
emodel.getDOFManager().assembleElementalArrayLocalArray(
residual_interface, emodel.getInternalForce(), background_type,
ghost_type, -1., filter);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <class Mat, UInt dim>
void MaterialReinforcement<Mat, dim>::computeDirectingCosines(
const ElementType & type, GhostType ghost_type) {
AKANTU_DEBUG_IN();
Mesh & interface_mesh = emodel.getInterfaceMesh();
const UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
const UInt steel_dof = dim * nb_nodes_per_element;
const UInt voigt_size = VoigtHelper<dim>::size;
const UInt nb_quad_points = emodel.getFEEngine("EmbeddedInterfaceFEEngine")
.getNbIntegrationPoints(type, ghost_type);
Array<Real> node_coordinates(this->element_filter(type, ghost_type).size(),
steel_dof);
this->emodel.getFEEngine().template extractNodalToElementField<Real>(
interface_mesh, interface_mesh.getNodes(), node_coordinates, type,
ghost_type, this->element_filter(type, ghost_type));
Array<Real>::matrix_iterator directing_cosines_it =
directing_cosines(type, ghost_type).begin(1, voigt_size);
Array<Real>::matrix_iterator node_coordinates_it =
node_coordinates.begin(dim, nb_nodes_per_element);
Array<Real>::matrix_iterator node_coordinates_end =
node_coordinates.end(dim, nb_nodes_per_element);
for (; node_coordinates_it != node_coordinates_end; ++node_coordinates_it) {
for (UInt i = 0; i < nb_quad_points; i++, ++directing_cosines_it) {
Matrix<Real> & nodes = *node_coordinates_it;
Matrix<Real> & cosines = *directing_cosines_it;
computeDirectingCosinesOnQuad(nodes, cosines);
}
}
// Mauro: the directing_cosines internal is defined on the quadrature points
// of each element
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <class Mat, UInt dim>
void MaterialReinforcement<Mat, dim>::assembleStiffnessMatrix(
const ElementType & type, GhostType ghost_type) {
AKANTU_DEBUG_IN();
Mesh & mesh = emodel.getMesh();
Mesh::type_iterator type_it = mesh.firstType(dim, ghost_type);
Mesh::type_iterator type_end = mesh.lastType(dim, ghost_type);
for (; type_it != type_end; ++type_it) {
assembleStiffnessMatrixInterface(type, *type_it, ghost_type);
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
/**
* 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]
*/
template <class Mat, UInt dim>
void MaterialReinforcement<Mat, dim>::assembleStiffnessMatrixInterface(
const ElementType & interface_type, const ElementType & background_type,
GhostType ghost_type) {
AKANTU_DEBUG_IN();
UInt voigt_size = VoigtHelper<dim>::size;
FEEngine & interface_engine = emodel.getFEEngine("EmbeddedInterfaceFEEngine");
Array<UInt> & elem_filter = this->element_filter(interface_type, ghost_type);
Array<Real> & grad_u = gradu_embedded(interface_type, ghost_type);
UInt nb_element = elem_filter.size();
UInt nodes_per_background_e = Mesh::getNbNodesPerElement(background_type);
UInt nb_quadrature_points =
interface_engine.getNbIntegrationPoints(interface_type, ghost_type);
UInt back_dof = dim * nodes_per_background_e;
UInt integrant_size = back_dof;
grad_u.resize(nb_quadrature_points * nb_element);
Array<Real> tangent_moduli(nb_element * nb_quadrature_points, 1,
"interface_tangent_moduli");
this->computeTangentModuli(interface_type, tangent_moduli, ghost_type);
Array<Real> & shapesd = (*shape_derivatives(interface_type, ghost_type))(
background_type, ghost_type);
Array<Real> integrant(nb_element * nb_quadrature_points,
integrant_size * integrant_size, "B^t*C^t*D*C*B");
/// Temporary matrices for integrant product
Matrix<Real> Bvoigt(voigt_size, back_dof);
Matrix<Real> DCB(1, back_dof);
Matrix<Real> CtDCB(voigt_size, back_dof);
Array<Real>::scalar_iterator D_it = tangent_moduli.begin();
Array<Real>::scalar_iterator D_end = tangent_moduli.end();
Array<Real>::matrix_iterator C_it =
directing_cosines(interface_type, ghost_type).begin(1, voigt_size);
Array<Real>::matrix_iterator B_it =
shapesd.begin(dim, nodes_per_background_e);
Array<Real>::matrix_iterator integrant_it =
integrant.begin(integrant_size, integrant_size);
for (; D_it != D_end; ++D_it, ++C_it, ++B_it, ++integrant_it) {
Real & D = *D_it;
Matrix<Real> & C = *C_it;
Matrix<Real> & B = *B_it;
Matrix<Real> & BtCtDCB = *integrant_it;
VoigtHelper<dim>::transferBMatrixToSymVoigtBMatrix(B, Bvoigt,
nodes_per_background_e);
DCB.mul<false, false>(C, Bvoigt);
DCB *= D * area;
CtDCB.mul<true, false>(C, DCB);
BtCtDCB.mul<true, false>(Bvoigt, CtDCB);
}
tangent_moduli.resize(0);
Array<Real> K_interface(nb_element, integrant_size * integrant_size,
"K_interface");
interface_engine.integrate(integrant, K_interface,
integrant_size * integrant_size, interface_type,
ghost_type, elem_filter);
integrant.resize(0);
// Mauro: Here K_interface contains the local stiffness matrices,
// directing_cosines contains the information about the orientation
// of the reinforcements, any rotation of the local stiffness matrix
// can be done here
auto & filter =
getBackgroundFilter(interface_type, background_type, ghost_type);
emodel.getDOFManager().assembleElementalMatricesToMatrix(
"K", "displacement", K_interface, background_type, ghost_type, _symmetric,
filter);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <class Mat, UInt dim>
Real MaterialReinforcement<Mat, dim>::getEnergy(const std::string & id) {
AKANTU_DEBUG_IN();
if (id == "potential") {
Real epot = 0.;
this->computePotentialEnergyByElements();
Mesh::type_iterator it = this->element_filter.firstType(
this->spatial_dimension),
end = this->element_filter.lastType(
this->spatial_dimension);
for (; it != end; ++it) {
FEEngine & interface_engine =
emodel.getFEEngine("EmbeddedInterfaceFEEngine");
epot += interface_engine.integrate(
this->potential_energy(*it, _not_ghost), *it, _not_ghost,
this->element_filter(*it, _not_ghost));
epot *= area;
}
return epot;
}
AKANTU_DEBUG_OUT();
return 0;
}
/* -------------------------------------------------------------------------- */
template <class Mat, UInt dim>
void MaterialReinforcement<Mat, dim>::computeGradU(
const ElementType & interface_type, GhostType ghost_type) {
// Looping over background types
for (auto && bg_type :
background_filter(interface_type, ghost_type)->elementTypes(dim)) {
const UInt nodes_per_background_e = Mesh::getNbNodesPerElement(bg_type);
const UInt voigt_size = VoigtHelper<dim>::size;
auto & bg_shapesd =
(*shape_derivatives(interface_type, ghost_type))(bg_type, ghost_type);
auto & filter = getBackgroundFilter(interface_type, bg_type, ghost_type);
Array<Real> disp_per_element(0, dim * nodes_per_background_e, "disp_elem");
FEEngine::extractNodalToElementField(
emodel.getMesh(), emodel.getDisplacement(), disp_per_element, bg_type,
ghost_type, filter);
Matrix<Real> concrete_du(dim, dim);
Matrix<Real> epsilon(dim, dim);
Vector<Real> evoigt(voigt_size);
for (auto && tuple :
zip(make_view(disp_per_element, dim, nodes_per_background_e),
make_view(bg_shapesd, dim, nodes_per_background_e),
this->gradu(interface_type, ghost_type),
make_view(this->directing_cosines(interface_type, ghost_type),
voigt_size))) {
auto & u = std::get<0>(tuple);
auto & B = std::get<1>(tuple);
auto & du = std::get<2>(tuple);
auto & C = std::get<3>(tuple);
concrete_du.mul<false, true>(u, B);
auto epsilon = 0.5 * (concrete_du + concrete_du.transpose());
strainTensorToVoigtVector(epsilon, evoigt);
du = C.dot(evoigt);
}
}
}
/* -------------------------------------------------------------------------- */
/**
* The structure of the directing cosines matrix is :
* \f{eqnarray*}{
* C_{1,\cdot} & = & (l^2, m^2, n^2, mn, ln, lm) \\
* 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]
*/
template <class Mat, UInt dim>
inline void MaterialReinforcement<Mat, dim>::computeDirectingCosinesOnQuad(
const Matrix<Real> & nodes, Matrix<Real> & cosines) {
AKANTU_DEBUG_IN();
AKANTU_DEBUG_ASSERT(nodes.cols() == 2,
"Higher order reinforcement elements not implemented");
const Vector<Real> a = nodes(0), b = nodes(1);
Vector<Real> delta = b - a;
Real sq_length = 0.;
for (UInt i = 0; i < dim; i++) {
sq_length += delta(i) * delta(i);
}
if (dim == 2) {
cosines(0, 0) = delta(0) * delta(0); // l^2
cosines(0, 1) = delta(1) * delta(1); // m^2
cosines(0, 2) = delta(0) * delta(1); // lm
} else if (dim == 3) {
cosines(0, 0) = delta(0) * delta(0); // l^2
cosines(0, 1) = delta(1) * delta(1); // m^2
cosines(0, 2) = delta(2) * delta(2); // n^2
cosines(0, 3) = delta(1) * delta(2); // mn
cosines(0, 4) = delta(0) * delta(2); // ln
cosines(0, 5) = delta(0) * delta(1); // lm
}
cosines /= sq_length;
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <class Mat, UInt dim>
inline void MaterialReinforcement<Mat, dim>::stressTensorToVoigtVector(
const Matrix<Real> & tensor, Vector<Real> & vector) {
AKANTU_DEBUG_IN();
for (UInt i = 0; i < dim; i++) {
vector(i) = tensor(i, i);
}
if (dim == 2) {
vector(2) = tensor(0, 1);
} else if (dim == 3) {
vector(3) = tensor(1, 2);
vector(4) = tensor(0, 2);
vector(5) = tensor(0, 1);
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <class Mat, UInt dim>
inline void MaterialReinforcement<Mat, dim>::strainTensorToVoigtVector(
const Matrix<Real> & tensor, Vector<Real> & vector) {
AKANTU_DEBUG_IN();
for (UInt i = 0; i < dim; i++) {
vector(i) = tensor(i, i);
}
if (dim == 2) {
vector(2) = 2 * tensor(0, 1);
} else if (dim == 3) {
vector(3) = 2 * tensor(1, 2);
vector(4) = 2 * tensor(0, 2);
vector(5) = 2 * tensor(0, 1);
}
AKANTU_DEBUG_OUT();
}
} // akantu
diff --git a/test/test_model/test_solid_mechanics_model/test_embedded_interface/test_embedded_interface_model_prestress.cc b/test/test_model/test_solid_mechanics_model/test_embedded_interface/test_embedded_interface_model_prestress.cc
index 6ed24517d..116108dc1 100644
--- a/test/test_model/test_solid_mechanics_model/test_embedded_interface/test_embedded_interface_model_prestress.cc
+++ b/test/test_model/test_solid_mechanics_model/test_embedded_interface/test_embedded_interface_model_prestress.cc
@@ -1,225 +1,224 @@
/**
* @file test_embedded_interface_model_prestress.cc
*
* @author Lucas Frerot <lucas.frerot@epfl.ch>
*
* @date creation: Tue Apr 28 2015
* @date last modification: Thu Oct 15 2015
*
* @brief Embedded model test for prestressing (bases on stress norm)
*
* @section LICENSE
*
* Copyright (©) 2015 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 "embedded_interface_model.hh"
/* -------------------------------------------------------------------------- */
using namespace akantu;
#define YG 0.483644859
#define I_eq 0.012488874
#define A_eq (1e-2 + 1. / 7. * 1.)
/* -------------------------------------------------------------------------- */
struct StressSolution : public BC::Neumann::FromHigherDim {
Real M;
Real I;
Real yg;
Real pre_stress;
StressSolution(UInt dim, Real M, Real I, Real yg = 0, Real pre_stress = 0) :
BC::Neumann::FromHigherDim(Matrix<Real>(dim, dim)),
M(M), I(I), yg(yg), pre_stress(pre_stress)
{}
virtual ~StressSolution() {}
void operator()(const IntegrationPoint & /*quad_point*/, Vector<Real> & dual,
const Vector<Real> & coord,
const Vector<Real> & normals) const {
UInt dim = coord.size();
if (dim < 2) AKANTU_DEBUG_ERROR("Solution not valid for 1D");
Matrix<Real> stress(dim, dim); stress.clear();
stress(0, 0) = this->stress(coord(1));
dual.mul<false>(stress, normals);
}
inline Real stress(Real height) const {
return -M / I * (height - yg) + pre_stress;
}
inline Real neutral_axis() const {
return -I * pre_stress / M + yg;
}
};
/* -------------------------------------------------------------------------- */
int main (int argc, char * argv[]) {
initialize("prestress.dat", argc, argv);
debug::setDebugLevel(dblError);
Math::setTolerance(1e-6);
const UInt dim = 2;
/* -------------------------------------------------------------------------- */
Mesh mesh(dim);
mesh.read("embedded_mesh_prestress.msh");
// mesh.createGroupsFromMeshData<std::string>("physical_names");
Mesh reinforcement_mesh(dim, "reinforcement_mesh");
try {
reinforcement_mesh.read("embedded_mesh_prestress_reinforcement.msh");
} catch(debug::Exception & e) {}
// reinforcement_mesh.createGroupsFromMeshData<std::string>("physical_names");
EmbeddedInterfaceModel model(mesh, reinforcement_mesh, dim);
model.initFull(EmbeddedInterfaceModelOptions(_static));
/* -------------------------------------------------------------------------- */
/* Computation of analytical residual */
/* -------------------------------------------------------------------------- */
/*
* q = 1000 N/m
* L = 20 m
* a = 1 m
*/
- Real steel_area =
- model.getMaterial("reinforcement").get("area");
- Real pre_stress = 1e6;
+ Real steel_area = model.getMaterial("reinforcement").get("area");
+ Real pre_stress = model.getMaterial("reinforcement").get("pre_stress");
Real stress_norm = 0.;
StressSolution * concrete_stress = nullptr, * steel_stress = nullptr;
Real pre_force = pre_stress * steel_area;
Real pre_moment = -pre_force * (YG - 0.25);
Real neutral_axis = YG - I_eq / A_eq * pre_force / pre_moment;
concrete_stress = new StressSolution(dim, pre_moment, 7. * I_eq, YG, -pre_force / (7. * A_eq));
steel_stress = new StressSolution(dim, pre_moment, I_eq, YG, pre_stress - pre_force / A_eq);
stress_norm = std::abs(concrete_stress->stress(1)) * (1 - neutral_axis) * 0.5
+ std::abs(concrete_stress->stress(0)) * neutral_axis * 0.5
+ std::abs(steel_stress->stress(0.25)) * steel_area;
model.applyBC(*concrete_stress, "XBlocked");
auto end_node = *mesh.getElementGroup("EndNode").getNodeGroup().begin();
Vector<Real> end_node_force = model.getForce().begin(dim)[end_node];
end_node_force(0) += steel_stress->stress(0.25) * steel_area;
Array<Real> analytical_residual(mesh.getNbNodes(), dim, "analytical_residual");
analytical_residual.copy(model.getForce());
model.getForce().clear();
delete concrete_stress;
delete steel_stress;
/* -------------------------------------------------------------------------- */
model.applyBC(BC::Dirichlet::FixedValue(0.0, _x), "XBlocked");
model.applyBC(BC::Dirichlet::FixedValue(0.0, _y), "YBlocked");
try {
model.solveStep();
} catch (debug::Exception e) {
std::cerr << e.what() << std::endl;
return EXIT_FAILURE;
}
/* -------------------------------------------------------------------------- */
/* Computation of FEM residual norm */
/* -------------------------------------------------------------------------- */
ElementGroup & xblocked = mesh.getElementGroup("XBlocked");
NodeGroup & boundary_nodes = xblocked.getNodeGroup();
NodeGroup::const_node_iterator
nodes_it = boundary_nodes.begin(),
nodes_end = boundary_nodes.end();
model.assembleInternalForces();
Array<Real> residual(mesh.getNbNodes(), dim, "my_residual");
residual.copy(model.getInternalForce());
residual -= model.getForce();
Array<Real>::vector_iterator com_res = residual.begin(dim);
Array<Real>::vector_iterator position = mesh.getNodes().begin(dim);
Real res_sum = 0.;
UInt lower_node = -1;
UInt upper_node = -1;
Real lower_dist = 1;
Real upper_dist = 1;
for (; nodes_it != nodes_end ; ++nodes_it) {
UInt node_number = *nodes_it;
const Vector<Real> res = com_res[node_number];
const Vector<Real> pos = position[node_number];
if (!Math::are_float_equal(pos(1), 0.25)) {
if ((std::abs(pos(1) - 0.25) < lower_dist) && (pos(1) < 0.25)) {
lower_dist = std::abs(pos(1) - 0.25);
lower_node = node_number;
}
if ((std::abs(pos(1) - 0.25) < upper_dist) && (pos(1) > 0.25)) {
upper_dist = std::abs(pos(1) - 0.25);
upper_node = node_number;
}
}
for (UInt i = 0 ; i < dim ; i++) {
if (!Math::are_float_equal(pos(1), 0.25)) {
res_sum += std::abs(res(i));
}
}
}
const Vector<Real> upper_res = com_res[upper_node], lower_res = com_res[lower_node];
const Vector<Real> end_node_res = com_res[end_node];
Vector<Real> delta = upper_res - lower_res;
delta *= lower_dist / (upper_dist + lower_dist);
Vector<Real> concrete_residual = lower_res + delta;
Vector<Real> steel_residual = end_node_res - concrete_residual;
for (UInt i = 0 ; i < dim ; i++) {
res_sum += std::abs(concrete_residual(i));
res_sum += std::abs(steel_residual(i));
}
Real relative_error = std::abs(res_sum - stress_norm) / stress_norm;
if (relative_error > 1e-3) {
std::cerr << "Relative error = " << relative_error << std::endl;
return EXIT_FAILURE;
}
finalize();
return 0;
}