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material_cohesive_exponential.cc
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rAKA akantu
material_cohesive_exponential.cc
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/**
* @file material_cohesive_exponential.cc
*
* @author Seyedeh Mohadeseh Taheri Mousavi <mohadeseh.taherimousavi@epfl.ch>
* @author Marco Vocialta <marco.vocialta@epfl.ch>
*
* @date Mon Jul 09 14:13:56 2012
*
* @brief Exponential irreversible cohesive law of mixed mode loading
*
* @section LICENSE
*
* Copyright (©) 2010-2011 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 "material_cohesive_exponential.hh"
#include "solid_mechanics_model.hh"
#include "sparse_matrix.hh"
#include "dof_synchronizer.hh"
__BEGIN_AKANTU__
/* -------------------------------------------------------------------------- */
template<UInt spatial_dimension>
MaterialCohesiveExponential<spatial_dimension>::MaterialCohesiveExponential(SolidMechanicsModel & model, const ID & id) :
MaterialCohesive(model,id) {
AKANTU_DEBUG_IN();
this->registerParam("beta" , beta , 0. , _pat_parsable, "Beta parameter" );
this->registerParam("G_cI" , G_cI , 0. , _pat_parsable, "Mode I fracture energy" );
this->registerParam("G_cII" , G_cII , 0. , _pat_parsable, "Mode II fracture energy");
this->registerParam("kappa" , kappa , 0. , _pat_readable, "Kappa parameter" );
this->registerParam("delta_c", delta_c, 0. , _pat_readable, "Critical displacement" );
// this->initInternalVector(delta_max, 1, _ek_cohesive);
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template<UInt spatial_dimension>
MaterialCohesiveExponential<spatial_dimension>::~MaterialCohesiveExponential() {
AKANTU_DEBUG_IN();
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template<UInt spatial_dimension>
void MaterialCohesiveExponential<spatial_dimension>::initMaterial() {
AKANTU_DEBUG_IN();
MaterialCohesive::initMaterial();
kappa = G_cII / G_cI;
delta_c = 2 * G_cI / sigma_c;
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template<UInt spatial_dimension>
void MaterialCohesiveExponential<spatial_dimension>::resizeCohesiveVectors() {
MaterialCohesive::resizeCohesiveVectors();
//this->resizeInternalVector(delta_max, _ek_cohesive);
}
/* -------------------------------------------------------------------------- */
template<UInt spatial_dimension>
void MaterialCohesiveExponential<spatial_dimension>::computeTraction(const Vector<Real> & normal,
ElementType el_type,
GhostType ghost_type) {
AKANTU_DEBUG_IN();
/// define iterators
Vector<Real>::iterator<types::RVector> traction_it =
tractions(el_type, ghost_type).begin(spatial_dimension);
Vector<Real>::iterator<types::RVector> opening_it =
opening(el_type, ghost_type).begin(spatial_dimension);
Vector<Real>::const_iterator<types::RVector> normal_it =
normal.begin(spatial_dimension);
Vector<Real>::iterator<types::RVector>traction_end =
tractions(el_type, ghost_type).end(spatial_dimension);
Vector<Real>::iterator<Real>delta_max_it =
delta_max(el_type, ghost_type).begin();
/// compute scalars
Real beta2 = beta*beta;
/// loop on each quadrature point
for (; traction_it != traction_end;
++traction_it, ++opening_it, ++normal_it, ++delta_max_it) {
/// compute normal and tangential opening vectors
Real normal_opening_norm = opening_it->dot(*normal_it);
types::Vector<Real> normal_opening(spatial_dimension);
normal_opening = (*normal_it);
normal_opening *= normal_opening_norm;
types::Vector<Real> tangential_opening(spatial_dimension);
tangential_opening = *opening_it;
tangential_opening -= normal_opening;
Real tangential_opening_norm = tangential_opening.norm();
/**
* compute effective opening displacement
* @f$ \delta = \sqrt{
* \frac{\beta^2}{\kappa^2} \Delta_t^2 + \Delta_n^2 } @f$
*/
Real delta = tangential_opening_norm;
delta *= delta * beta2;
delta += normal_opening_norm * normal_opening_norm;
delta = sqrt(delta);
/// full damage case
if (std::abs(delta) < Math::getTolerance()) {
/// set traction to zero
traction_it->clear();
} else { /// element not fully damaged
/**
* Compute traction loading @f$ \mathbf{T} =
* e \sigma_c \frac{\delta}{\delta_c} e^{-\delta/ \delta_c}@f$
*/
/**
* Compute traction unloading @f$ \mathbf{T} =
* \frac{t_{max}}{\delta_{max}} \delta @f$
*/
*traction_it = tangential_opening;
*traction_it *= beta2;
*traction_it += normal_opening;
/// crack opening case
if (delta > *delta_max_it) {
Real k = exp(1)*sigma_c*exp(- delta / delta_c)/delta_c;
*traction_it *= k;
/// update maximum displacement
*delta_max_it = delta;
} else { /// unloading-reloading case
Real k = exp(1)*sigma_c*exp(- *delta_max_it / delta_c)/delta_c;
*traction_it *= k;
}
}
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template<UInt spatial_dimension>
void MaterialCohesiveExponential<spatial_dimension>::computeTangentTraction(const ElementType & el_type,
Vector<Real> & tangent_matrix,
const Vector<Real> & normal,
GhostType ghost_type) {
AKANTU_DEBUG_IN();
Vector<Real>::iterator<types::RMatrix> tangent_it = tangent_matrix.begin(spatial_dimension, spatial_dimension);
Vector<Real>::iterator<types::RMatrix> tangent_end = tangent_matrix.end(spatial_dimension, spatial_dimension);
Vector<Real>::const_iterator<types::RVector> normal_it = normal.begin(spatial_dimension);
Vector<Real>::iterator<types::RVector> opening_it = opening(el_type, ghost_type).begin(spatial_dimension);
Vector<Real>::iterator<types::RVector> traction_it = tractions(el_type, ghost_type).begin(spatial_dimension);
Vector<Real>::iterator<Real>delta_max_it = delta_max(el_type, ghost_type).begin();
Real beta2 = beta*beta;
/**
* compute tangent matrix @f$ \frac{\partial \mathbf{t}}
* {\partial \delta} = \hat{\mathbf{t}} \otimes
* \frac{\partial (t/\delta)}{\partial \delta}
* \frac{\hat{\mathbf{t}}}{\delta}+ \frac{t}{\delta} [ \beta^2 \mathbf{I} +
* (1-\beta^2) (\mathbf{n} \otimes \mathbf{n})] @f$
**/
/**
* In which @f$
* \frac{\partial(t/ \delta)}{\partial \delta} =
* \left\{\begin{array} {l l}
* -e \frac{\sigma_c}{\delta_c^2 }e^{-\delta / \delta_c} & \quad if
* \delta \geq \delta_{max} \\
* 0 & \quad if \delta < \delta_{max}, \delta_n > 0
* \end{array}\right. @f$
**/
for (; tangent_it != tangent_end; ++tangent_it, ++normal_it, ++opening_it, ++traction_it) {
Real normal_opening_norm = opening_it->dot(*normal_it);
types::Vector<Real> normal_opening(spatial_dimension);
normal_opening = (*normal_it);
normal_opening *= normal_opening_norm;
types::Vector<Real> tangential_opening(spatial_dimension);
tangential_opening = *opening_it;
tangential_opening -= normal_opening;
Real tangential_opening_norm = tangential_opening.norm();
Real delta = tangential_opening_norm;
delta *= delta * beta2;
delta += normal_opening_norm * normal_opening_norm;
delta = sqrt(delta);
types::RVector t_hat(tangential_opening);
t_hat *= beta2;
t_hat += normal_opening;
types::RMatrix nn(spatial_dimension, spatial_dimension);
nn.outerProduct(*normal_it, *normal_it);
types::RMatrix I(spatial_dimension, spatial_dimension);
I.eye(beta2);
nn *= (1-beta2);
I += nn;
if(std::abs(delta) < Math::getTolerance()){
*tangent_it += I;
*tangent_it *= exp(1)* sigma_c/delta_c;
} else {
Real traction_norm = traction_it->norm();
I *= traction_norm / delta;
types::RVector t_hat_tmp (t_hat);
Real temp_var = 0;
if ((delta > *delta_max_it) || (std::abs(delta - *delta_max_it) < 1e-12)) {
temp_var = -exp(1- delta/delta_c) * sigma_c/(delta_c * delta_c);
}
temp_var /= delta;
t_hat_tmp *= temp_var;
types::RMatrix t_var_t(spatial_dimension, spatial_dimension);
t_var_t.outerProduct(t_hat, t_hat_tmp);
*tangent_it += I;
*tangent_it += t_var_t;
}
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
INSTANSIATE_MATERIAL(MaterialCohesiveExponential);
__END_AKANTU__
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