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material_cohesive_linear_friction.cc
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material_cohesive_linear_friction.cc
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/**
* @file material_cohesive_linear_friction.cc
*
* @author Mauro Corrado <mauro.corrado@epfl.ch>
*
* @date creation: Tue Jan 12 2016
* @date last modification: Fri Dec 11 2020
*
* @brief Linear irreversible cohesive law of mixed mode loading with
* random stress definition for extrinsic type
*
*
* @section LICENSE
*
* Copyright (©) 2015-2021 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 "material_cohesive_linear_friction.hh"
#include "solid_mechanics_model_cohesive.hh"
namespace akantu {
/* -------------------------------------------------------------------------- */
template <UInt spatial_dimension>
MaterialCohesiveLinearFriction<spatial_dimension>::
MaterialCohesiveLinearFriction(SolidMechanicsModel & model, const ID & id)
: MaterialParent(model, id), residual_sliding("residual_sliding", *this),
friction_force("friction_force", *this) {
AKANTU_DEBUG_IN();
this->registerParam("mu", mu_max, Real(0.), _pat_parsable | _pat_readable,
"Maximum value of the friction coefficient");
this->registerParam("penalty_for_friction", friction_penalty, Real(0.),
_pat_parsable | _pat_readable,
"Penalty parameter for the friction behavior");
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <UInt spatial_dimension>
void MaterialCohesiveLinearFriction<spatial_dimension>::initMaterial() {
AKANTU_DEBUG_IN();
MaterialParent::initMaterial();
friction_force.initialize(spatial_dimension);
residual_sliding.initialize(1);
residual_sliding.initializeHistory();
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <UInt spatial_dimension>
void MaterialCohesiveLinearFriction<spatial_dimension>::computeTraction(
__attribute__((unused)) const Array<Real> & normal, ElementType el_type,
GhostType ghost_type) {
AKANTU_DEBUG_IN();
residual_sliding.resize();
friction_force.resize();
/// define iterators
auto traction_it =
this->tractions(el_type, ghost_type).begin(spatial_dimension);
auto traction_end =
this->tractions(el_type, ghost_type).end(spatial_dimension);
auto opening_it = this->opening(el_type, ghost_type).begin(spatial_dimension);
auto previous_opening_it =
this->opening.previous(el_type, ghost_type).begin(spatial_dimension);
auto contact_traction_it =
this->contact_tractions(el_type, ghost_type).begin(spatial_dimension);
auto contact_opening_it =
this->contact_opening(el_type, ghost_type).begin(spatial_dimension);
auto normal_it = this->normal.begin(spatial_dimension);
auto sigma_c_it = this->sigma_c_eff(el_type, ghost_type).begin();
auto delta_max_it = this->delta_max(el_type, ghost_type).begin();
auto delta_max_prev_it =
this->delta_max.previous(el_type, ghost_type).begin();
auto delta_c_it = this->delta_c_eff(el_type, ghost_type).begin();
auto damage_it = this->damage(el_type, ghost_type).begin();
auto insertion_stress_it =
this->insertion_stress(el_type, ghost_type).begin(spatial_dimension);
auto res_sliding_it = this->residual_sliding(el_type, ghost_type).begin();
auto res_sliding_prev_it =
this->residual_sliding.previous(el_type, ghost_type).begin();
auto friction_force_it =
this->friction_force(el_type, ghost_type).begin(spatial_dimension);
Vector<Real> normal_opening(spatial_dimension);
Vector<Real> tangential_opening(spatial_dimension);
if (not this->model->isDefaultSolverExplicit()) {
this->delta_max(el_type, ghost_type)
.copy(this->delta_max.previous(el_type, ghost_type));
}
/// loop on each quadrature point
for (; traction_it != traction_end;
++traction_it, ++opening_it, ++normal_it, ++sigma_c_it, ++delta_max_it,
++delta_c_it, ++damage_it, ++contact_traction_it, ++insertion_stress_it,
++contact_opening_it, ++delta_max_prev_it, ++res_sliding_it,
++res_sliding_prev_it, ++friction_force_it, ++previous_opening_it) {
Real normal_opening_norm;
Real tangential_opening_norm;
bool penetration;
this->computeTractionOnQuad(
*traction_it, *opening_it, *normal_it, *delta_max_it, *delta_c_it,
*insertion_stress_it, *sigma_c_it, normal_opening, tangential_opening,
normal_opening_norm, tangential_opening_norm, *damage_it, penetration,
*contact_traction_it, *contact_opening_it);
if (penetration) {
/// the friction coefficient mu increases with the damage. It
/// equals the maximum value when damage = 1.
// Real damage = std::min(*delta_max_prev_it / *delta_c_it,
// Real(1.));
Real mu = mu_max; // * damage;
/// the definition of tau_max refers to the opening
/// (penetration) of the previous incremental step
Real tau_max = mu * this->penalty * (std::abs(normal_opening_norm));
Real delta_sliding_norm =
std::abs(tangential_opening_norm - *res_sliding_prev_it);
/// tau is the norm of the friction force, acting tangentially to the
/// surface
Real tau = std::min(friction_penalty * delta_sliding_norm, tau_max);
if ((tangential_opening_norm - *res_sliding_prev_it) < 0.0) {
tau = -tau;
}
/// from tau get the x and y components of friction, to be added in the
/// force vector
Vector<Real> tangent_unit_vector(spatial_dimension);
tangent_unit_vector = tangential_opening / tangential_opening_norm;
*friction_force_it = tau * tangent_unit_vector;
/// update residual_sliding
if (friction_penalty == 0.) {
*res_sliding_it = tangential_opening_norm;
} else {
*res_sliding_it =
tangential_opening_norm - (std::abs(tau) / friction_penalty);
}
} else {
friction_force_it->zero();
}
*traction_it += *friction_force_it;
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <UInt spatial_dimension>
void MaterialCohesiveLinearFriction<spatial_dimension>::computeTangentTraction(
ElementType el_type, Array<Real> & tangent_matrix,
__attribute__((unused)) const Array<Real> & normal, GhostType ghost_type) {
AKANTU_DEBUG_IN();
/// define iterators
auto tangent_it = tangent_matrix.begin(spatial_dimension, spatial_dimension);
auto tangent_end = tangent_matrix.end(spatial_dimension, spatial_dimension);
auto normal_it = this->normal.begin(spatial_dimension);
auto opening_it = this->opening(el_type, ghost_type).begin(spatial_dimension);
auto previous_opening_it =
this->opening.previous(el_type, ghost_type).begin(spatial_dimension);
/**
* NB: delta_max_it points on delta_max_previous, i.e. the
* delta_max related to the solution of the previous incremental
* step
*/
auto delta_max_it = this->delta_max.previous(el_type, ghost_type).begin();
auto sigma_c_it = this->sigma_c_eff(el_type, ghost_type).begin();
auto delta_c_it = this->delta_c_eff(el_type, ghost_type).begin();
auto damage_it = this->damage(el_type, ghost_type).begin();
auto contact_opening_it =
this->contact_opening(el_type, ghost_type).begin(spatial_dimension);
auto res_sliding_prev_it =
this->residual_sliding.previous(el_type, ghost_type).begin();
Vector<Real> normal_opening(spatial_dimension);
Vector<Real> tangential_opening(spatial_dimension);
for (; tangent_it != tangent_end;
++tangent_it, ++normal_it, ++opening_it, ++previous_opening_it,
++delta_max_it, ++sigma_c_it, ++delta_c_it, ++damage_it,
++contact_opening_it, ++res_sliding_prev_it) {
Real normal_opening_norm;
Real tangential_opening_norm;
bool penetration;
this->computeTangentTractionOnQuad(
*tangent_it, *delta_max_it, *delta_c_it, *sigma_c_it, *opening_it,
*normal_it, normal_opening, tangential_opening, normal_opening_norm,
tangential_opening_norm, *damage_it, penetration, *contact_opening_it);
if (penetration) {
// Real damage = std::min(*delta_max_it / *delta_c_it, Real(1.));
Real mu = mu_max; // * damage;
Real normal_opening_prev_norm =
std::min(previous_opening_it->dot(*normal_it), Real(0.));
// Vector<Real> normal_opening_prev = (*normal_it);
// normal_opening_prev *= normal_opening_prev_norm;
Real tau_max = mu * this->penalty * (std::abs(normal_opening_prev_norm));
Real delta_sliding_norm =
std::abs(tangential_opening_norm - *res_sliding_prev_it);
// tau is the norm of the friction force, acting tangentially to the
// surface
Real tau = std::min(friction_penalty * delta_sliding_norm, tau_max);
if (tau < tau_max && tau_max > Math::getTolerance()) {
Matrix<Real> I(spatial_dimension, spatial_dimension);
I.eye(1.);
Matrix<Real> n_outer_n(spatial_dimension, spatial_dimension);
n_outer_n.outerProduct(*normal_it, *normal_it);
Matrix<Real> nn(n_outer_n);
I -= nn;
*tangent_it += I * friction_penalty;
}
}
// check if the tangential stiffness matrix is symmetric
// for (UInt h = 0; h < spatial_dimension; ++h){
// for (UInt l = h; l < spatial_dimension; ++l){
// if (l > h){
// Real k_ls = (*tangent_it)[spatial_dimension*h+l];
// Real k_us = (*tangent_it)[spatial_dimension*l+h];
// // std::cout << "k_ls = " << k_ls << std::endl;
// // std::cout << "k_us = " << k_us << std::endl;
// if (std::abs(k_ls) > 1e-13 && std::abs(k_us) > 1e-13){
// Real error = std::abs((k_ls - k_us) / k_us);
// if (error > 1e-10){
// std::cout << "non symmetric cohesive matrix" << std::endl;
// // std::cout << "error " << error << std::endl;
// }
// }
// }
// }
// }
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
INSTANTIATE_MATERIAL(cohesive_linear_friction, MaterialCohesiveLinearFriction);
} // namespace akantu

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