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rAKA/src/fe_engine/shape_cohesive.hh
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/**
* @file shape_cohesive.hh
*
* @author Mohit Pundir <mohit.pundir@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
* @author Marco Vocialta <marco.vocialta@epfl.ch>
*
* @date creation: Tue Feb 15 2011
* @date last modification: Fri May 14 2021
*
* @brief shape functions for cohesive elements description
*
*
* @section LICENSE
*
* Copyright (©) 2010-2021 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_array.hh"
#include "shape_lagrange.hh"
/* -------------------------------------------------------------------------- */
#ifndef AKANTU_SHAPE_COHESIVE_HH_
#define AKANTU_SHAPE_COHESIVE_HH_
namespace akantu {
struct CohesiveReduceFunctionMean {
inline Real operator()(Real u_plus, Real u_minus) {
return .5 * (u_plus + u_minus);
}
};
struct CohesiveReduceFunctionDifference {
inline Real operator()(Real u_plus, Real u_minus) {
return (u_plus - u_minus);
}
};
struct ExtendingOperators {
static Matrix<Real>
getAveragingOperator(const ElementType & type,
const UInt & nb_degree_of_freedom = 1) {
AKANTU_DEBUG_IN();
auto kind = Mesh::getKind(type);
AKANTU_DEBUG_ASSERT(kind == _ek_cohesive,
"Extending operators work only for cohesive elements");
UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
// averaging operator
Matrix<Real> A(nb_degree_of_freedom * nb_nodes_per_element / 2,
nb_degree_of_freedom * nb_nodes_per_element);
for (UInt i = 0; i < nb_degree_of_freedom * nb_nodes_per_element / 2; ++i) {
A(i, i) = 0.5;
A(i, i + nb_degree_of_freedom * nb_nodes_per_element / 2) = 0.5;
}
AKANTU_DEBUG_OUT();
return A;
};
static Matrix<Real>
getDifferencingOperator(const ElementType & type,
const UInt & nb_degree_of_freedom = 1) {
AKANTU_DEBUG_IN();
auto kind = Mesh::getKind(type);
AKANTU_DEBUG_ASSERT(kind == _ek_cohesive,
"Extending operators work only for cohesive elements");
UInt nb_nodes_per_element = Mesh::getNbNodesPerElement(type);
// averaging operator
Matrix<Real> A(nb_degree_of_freedom * nb_nodes_per_element / 2,
nb_degree_of_freedom * nb_nodes_per_element);
for (UInt i = 0; i < nb_degree_of_freedom * nb_nodes_per_element / 2; ++i) {
A(i, i) = 1;
A(i, i + nb_degree_of_freedom * nb_nodes_per_element / 2) = -1;
}
AKANTU_DEBUG_OUT();
return A;
}
};
template <> class ShapeLagrange<_ek_cohesive> : public ShapeLagrangeBase {
/* ------------------------------------------------------------------------
*/
/* Constructors/Destructors */
/* ------------------------------------------------------------------------
*/
public:
ShapeLagrange(const Mesh & mesh, UInt spatial_dimension,
const ID & id = "shape_cohesive");
~ShapeLagrange() override = default;
/* ------------------------------------------------------------------------
*/
/* Methods */
/* ------------------------------------------------------------------------
*/
public:
inline void initShapeFunctions(const Array<Real> & nodes,
const Matrix<Real> & integration_points,
ElementType type, GhostType ghost_type);
/// extract the nodal values and store them per element
template <ElementType type, class ReduceFunction>
void extractNodalToElementField(
const Array<Real> & nodal_f, Array<Real> & elemental_f,
GhostType ghost_type = _not_ghost,
const Array<UInt> & filter_elements = empty_filter) const;
/// computes the shape functions derivatives for given interpolation points
template <ElementType type>
void computeShapeDerivativesOnIntegrationPoints(
const Array<Real> & nodes, const Matrix<Real> & integration_points,
Array<Real> & shape_derivatives, GhostType ghost_type,
const Array<UInt> & filter_elements = empty_filter) const;
void computeShapeDerivativesOnIntegrationPoints(
const Array<Real> & nodes, const Matrix<Real> & integration_points,
Array<Real> & shape_derivative, ElementType type, GhostType ghost_type,
const Array<UInt> & filter_elements) const override;
/// pre compute all shapes on the element integration points from natural
/// coordinates
template <ElementType type>
void precomputeShapesOnIntegrationPoints(const Array<Real> & nodes,
GhostType ghost_type);
/// pre compute all shape derivatives on the element integration points from
/// natural coordinates
template <ElementType type>
void precomputeShapeDerivativesOnIntegrationPoints(const Array<Real> & nodes,
GhostType ghost_type);
template <ElementType type>
void computeShapeDerivativesOnIntegrationPointsLowerDimension(
const Array<Real> & nodes, const Matrix<Real> & integration_points,
Array<Real> & shape_derivatives, const GhostType & ghost_type,
const Array<UInt> & filter_elements = empty_filter) const;
/// interpolate nodal values on the integration points
template <ElementType type, class ReduceFunction>
void interpolateOnIntegrationPoints(
const Array<Real> & u, Array<Real> & uq, UInt nb_degree_of_freedom,
GhostType ghost_type = _not_ghost,
const Array<UInt> & filter_elements = empty_filter) const;
template <ElementType type>
void interpolateOnIntegrationPoints(
const Array<Real> & u, Array<Real> & uq, UInt nb_degree_of_freedom,
GhostType ghost_type = _not_ghost,
const Array<UInt> & filter_elements = empty_filter) const {
interpolateOnIntegrationPoints<type, CohesiveReduceFunctionMean>(
u, uq, nb_degree_of_freedom, ghost_type, filter_elements);
}
/// compute the gradient of u on the integration points in the natural
/// coordinates
template <ElementType type>
void gradientOnIntegrationPoints(
const Array<Real> & u, Array<Real> & nablauq, UInt nb_degree_of_freedom,
GhostType ghost_type = _not_ghost,
const Array<UInt> & filter_elements = empty_filter) const {
gradientOnIntegrationPoints<type, CohesiveReduceFunctionMean>(
u, nablauq, nb_degree_of_freedom, ghost_type, filter_elements);
}
/// compute gradient on the facet element placed in the base of dim - 1
template <ElementType type, class ReduceFunction>
void gradientOnIntegrationPoints(
const Array<Real> & u, Array<Real> & nablauq, UInt nb_degree_of_freedom,
GhostType ghost_type = _not_ghost,
const Array<UInt> & filter_elements = empty_filter) const;
/* ------------------------------------------------------------------------
*/
template <ElementType type>
void computeBtD(const Array<Real> & Ds, Array<Real> & BtDs,
GhostType ghost_type = _not_ghost,
const Array<UInt> & filter_elements = empty_filter) const;
template <ElementType type>
void
computeExtendedBtD(const Array<Real> & Ds, Array<Real> & AtBtDs,
GhostType ghost_type = _not_ghost,
const Array<UInt> & filter_elements = empty_filter) const;
template <ElementType type>
void computeBtDB(const Array<Real> & Ds, Array<Real> & BtDBs, UInt order_d,
GhostType ghost_type,
const Array<UInt> & filter_elements) const {
AKANTU_TO_IMPLEMENT();
};
/// multiply a field by shape functions
template <ElementType type>
void computeNtb(const Array<Real> & bs, Array<Real> & Ntbs,
GhostType ghost_type = _not_ghost,
const Array<UInt> & filter_elements = empty_filter) const;
/// extend shape functions to the number of nodes in cohesive element
template <ElementType type>
void
computeExtendedNtb(const Array<Real> & bs, Array<Real> & Ntbs,
GhostType ghost_type = _not_ghost,
const Array<UInt> & filter_elements = empty_filter) const;
template <ElementType type>
void computeNtbN(const Array<Real> & /*bs*/, Array<Real> & /*NtbNs*/,
GhostType /*ghost_type*/,
const Array<UInt> & /*filter_elements*/) const {
AKANTU_TO_IMPLEMENT();
}
/* ------------------------------------------------------------------------
*/
/// compute the gradient of u on the integration points
template <ElementType type, class ReduceFunction>
void variationOnIntegrationPoints(
const Array<Real> & u, Array<Real> & nablauq, UInt nb_degree_of_freedom,
GhostType ghost_type = _not_ghost,
const Array<UInt> & filter_elements = empty_filter) const;
/// compute the normals to the field u on integration points
template <ElementType type, class ReduceFunction>
void computeNormalsOnIntegrationPoints(
const Array<Real> & u, Array<Real> & normals_u,
GhostType ghost_type = _not_ghost,
const Array<UInt> & filter_elements = empty_filter) const;
/// computes bases alligned with cohesive elements
template <ElementType type, class ReduceFunction>
void computeAllignedBasisOnIntegrationPoints(
const Array<Real> & u, Array<Real> & basis_u, GhostType ghost_type,
const Array<UInt> & filter_elements = empty_filter) const;
};
/// standard output stream operator
template <class ShapeFunction>
inline std::ostream & operator<<(std::ostream & stream,
const ShapeCohesive<ShapeFunction> & _this) {
_this.printself(stream);
return stream;
}
} // namespace akantu
#include "shape_cohesive_inline_impl.hh"
#endif /* AKANTU_SHAPE_COHESIVE_HH_ */
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