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material_reinforcement_tmpl.hh
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/**
* @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, model.getInterfaceMesh().getSpatialDimension(),
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("EmbeddedInterfaceFEEEngine"),
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() {
Material::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->initBackgroundFilter();
this->allocBackgroundShapeDerivatives();
this->initBackgroundShapeDerivatives();
this->initDirectingCosines();
}
/* -------------------------------------------------------------------------- */
namespace detail {
class BackgroundFilterInitializer : public MeshElementTypeMapArrayInializer {
public:
BackgroundFilterInitializer(EmbeddedInterfaceModel & emodel,
const GhostType & ghost_type)
: MeshElementTypeMapArrayInializer(
emodel.getMesh(), emodel.getSpatialDimension(), 2, // pairs
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>::initBackgroundFilter() {
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 filter =
std::make_unique<ElementTypeMapArray<UInt>>(shaped_id, this->name);
background_filter(std::move(filter), type, gt);
filter->initialize(
detail::BackgroundFilterInitializer(emodel, gt), 0, true);
// Computing filters
for (auto && bg_type : filter->elementTypes(dim, gt)) {
filterInterfaceBackgroundElements((*filter)(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> & filter, const ElementType & type,
const ElementType & interface_type, GhostType ghost_type) {
AKANTU_DEBUG_IN();
filter.resize(0);
AKANTU_DEBUG_ASSERT(filter.getNbComponent() == 2,
"background filter should have 2 components");
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)
filter.push_back(Vector<UInt>({elem_id, elem.element}));
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
namespace detail {
class BackgroundShapeDInitializer : public ElementTypeMapArrayInializer {
public:
BackgroundShapeDInitializer(UInt spatial_dimension,
ElementTypeMapArray<UInt> & filter,
const GhostType & ghost_type)
: ElementTypeMapArrayInializer(spatial_dimension, 0, ghost_type,
_ek_regular) {
// Conting 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(), 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 =
std::make_unique<ElementTypeMapArray<Real>>(shaped_id, this->name);
shape_derivatives(std::move(shaped_etma), type, gt);
shaped_etma->initialize(
detail::BackgroundShapeDInitializer(emodel.getSpatialDimension(),
*background_filter(type), 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 ndof = dim * Mesh::getNbNodesPerElement(bg_type);
const auto nb_stress =
ShapeFunctions::getShapeDerivativesSize(bg_type) / ndof;
// 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 shapesd_begin =
background_shapesd.begin(nb_stress, ndof, nb_quads_per_elem);
auto quad_begin = quad_pos.begin(dim, Mesh::getNbNodesPerElement(bg_type));
for (const auto & elem : make_view(background_elements, 2)) {
for (UInt i = 0; i < nb_quads_per_elem; ++i) {
Matrix<Real> shapesd = Tensor3<Real>(shapesd_begin[elem(0)])(i);
Vector<Real> quads = Matrix<Real>(quad_begin[elem(0)])(i);
engine.computeShapeDerivatives(quads, elem(1), 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 * 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>::computeGradU(const ElementType & type,
GhostType ghost_type) {
AKANTU_DEBUG_IN();
Array<UInt> & elem_filter = this->element_filter(type, ghost_type);
UInt nb_element = elem_filter.size();
UInt nb_quad_points = emodel.getFEEngine("EmbeddedInterfaceFEEngine")
.getNbIntegrationPoints(type);
Array<Real> & gradu_vec = gradu_embedded(type, ghost_type);
Mesh::type_iterator back_it = emodel.getMesh().firstType(dim, ghost_type);
Mesh::type_iterator back_end = emodel.getMesh().lastType(dim, ghost_type);
for (; back_it != back_end; ++back_it) {
UInt nodes_per_background_e = Mesh::getNbNodesPerElement(*back_it);
Array<Real> & shapesd =
shape_derivatives(type, ghost_type)->operator()(*back_it, ghost_type);
Array<UInt> * background_filter =
new Array<UInt>(nb_element, 1, "background_filter");
filterInterfaceBackgroundElements(*background_filter, *back_it, type,
ghost_type);
Array<Real> * disp_per_element =
new Array<Real>(0, dim * nodes_per_background_e, "disp_elem");
FEEngine::extractNodalToElementField(
emodel.getMesh(), emodel.getDisplacement(), *disp_per_element, *back_it,
ghost_type, *background_filter);
Array<Real>::matrix_iterator disp_it =
disp_per_element->begin(dim, nodes_per_background_e);
Array<Real>::matrix_iterator disp_end =
disp_per_element->end(dim, nodes_per_background_e);
Array<Real>::matrix_iterator shapes_it =
shapesd.begin(dim, nodes_per_background_e);
Array<Real>::matrix_iterator grad_u_it = gradu_vec.begin(dim, dim);
for (; disp_it != disp_end; ++disp_it) {
for (UInt i = 0; i < nb_quad_points; i++, ++shapes_it, ++grad_u_it) {
Matrix<Real> & B = *shapes_it;
Matrix<Real> & du = *grad_u_it;
Matrix<Real> & u = *disp_it;
du.mul<false, true>(u, B);
}
}
delete background_filter;
delete disp_per_element;
}
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);
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
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>::matrix_iterator C_it =
directing_cosines(interface_type, ghost_type)
.begin(voigt_size, voigt_size);
Array<Real>::matrix_iterator sigma_it =
stress_embedded(interface_type, ghost_type).begin(dim, dim);
Vector<Real> sigma(voigt_size);
Matrix<Real> Bvoigt(voigt_size, back_dof);
Vector<Real> Ct_sigma(voigt_size);
for (; integrant_it != integrant_end;
++integrant_it, ++B_it, ++C_it, ++sigma_it) {
VoigtHelper<dim>::transferBMatrixToSymVoigtBMatrix(*B_it, Bvoigt,
nodes_per_background_e);
Matrix<Real> & C = *C_it;
Vector<Real> & BtCt_sigma = *integrant_it;
stressTensorToVoigtVector(*sigma_it, sigma);
Ct_sigma.mul<true>(C, sigma);
BtCt_sigma.mul<true>(Bvoigt, Ct_sigma);
BtCt_sigma *= 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");
filterInterfaceBackgroundElements(background_filter, background_type,
interface_type, ghost_type);
emodel.getDOFManager().assembleElementalArrayLocalArray(
residual_interface, emodel.getInternalForce(), background_type,
ghost_type, -1., background_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(voigt_size, 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> DC(voigt_size, voigt_size);
Matrix<Real> DCB(voigt_size, 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(voigt_size, 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);
DC.clear();
DC(0, 0) = D * area;
DC *= C;
DCB.mul<false, false>(DC, Bvoigt);
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
Array<UInt> background_filter(nb_element, 1, "background_filter");
filterInterfaceBackgroundElements(background_filter, background_type,
interface_type, ghost_type);
emodel.getDOFManager().assembleElementalMatricesToMatrix(
"K", "displacement", K_interface, background_type, ghost_type, _symmetric,
background_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;
}
/* -------------------------------------------------------------------------- */
/**
* 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;
cosines.clear();
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
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