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material_cohesive_linear_uncoupled.cc
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rAKA akantu
material_cohesive_linear_uncoupled.cc
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/**
* @file material_cohesive_linear_uncoupled.cc
*
* @author Mauro Corrado <mauro.corrado@epfl.ch>
*
* @date creation: Mon Jul 25 2016
* @date last modification: Wed Feb 21 2018
*
* @brief Linear irreversible cohesive law of mixed mode loading with
* random stress definition for extrinsic type
*
*
* Copyright (©) 2016-2018 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 <algorithm>
#include <numeric>
/* -------------------------------------------------------------------------- */
#include "material_cohesive_linear_uncoupled.hh"
#include "solid_mechanics_model_cohesive.hh"
namespace akantu {
/* -------------------------------------------------------------------------- */
template <UInt spatial_dimension>
MaterialCohesiveLinearUncoupled<spatial_dimension>::
MaterialCohesiveLinearUncoupled(SolidMechanicsModel & model, const ID & id)
: MaterialCohesiveLinear<spatial_dimension>(model, id),
delta_n_max("delta_n_max", *this), delta_t_max("delta_t_max", *this),
damage_n("damage_n", *this), damage_t("damage_t", *this) {
AKANTU_DEBUG_IN();
this->registerParam(
"roughness", R, Real(1.), _pat_parsable | _pat_readable,
"Roughness to define coupling between mode II and mode I");
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <UInt spatial_dimension>
void MaterialCohesiveLinearUncoupled<spatial_dimension>::initMaterial() {
AKANTU_DEBUG_IN();
MaterialCohesiveLinear<spatial_dimension>::initMaterial();
delta_n_max.initialize(1);
delta_t_max.initialize(1);
damage_n.initialize(1);
damage_t.initialize(1);
delta_n_max.initializeHistory();
delta_t_max.initializeHistory();
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <UInt spatial_dimension>
void MaterialCohesiveLinearUncoupled<spatial_dimension>::computeTraction(
const Array<Real> & /*unused*/, ElementType el_type, GhostType ghost_type) {
AKANTU_DEBUG_IN();
delta_n_max.resize();
delta_t_max.resize();
damage_n.resize();
damage_t.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 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_n_max_it = delta_n_max(el_type, ghost_type).begin();
auto delta_t_max_it = delta_t_max(el_type, ghost_type).begin();
auto delta_c_it = this->delta_c_eff(el_type, ghost_type).begin();
auto damage_n_it = damage_n(el_type, ghost_type).begin();
auto damage_t_it = damage_t(el_type, ghost_type).begin();
auto insertion_stress_it =
this->insertion_stress(el_type, ghost_type).begin(spatial_dimension);
Vector<Real> normal_opening(spatial_dimension);
Vector<Real> tangential_opening(spatial_dimension);
/// loop on each quadrature point
for (; traction_it != traction_end;
++traction_it, ++opening_it, ++contact_traction_it, ++contact_opening_it,
++normal_it, ++sigma_c_it, ++delta_n_max_it, ++delta_t_max_it,
++delta_c_it, ++damage_n_it, ++damage_t_it, ++insertion_stress_it) {
Real normal_opening_norm;
Real tangential_opening_norm;
bool penetration;
Real delta_c2_R2 = *delta_c_it * (*delta_c_it) / R / R;
/// compute normal and tangential opening vectors
normal_opening_norm = opening_it->dot(*normal_it);
Vector<Real> normal_opening = *normal_it;
normal_opening *= normal_opening_norm;
// std::cout<< "normal_opening_norm = " << normal_opening_norm
// <<std::endl;
Vector<Real> tangential_opening = *opening_it;
tangential_opening -= normal_opening;
tangential_opening_norm = tangential_opening.norm();
/// compute effective opening displacement
Real delta_n =
tangential_opening_norm * tangential_opening_norm * this->beta2_kappa2;
Real delta_t =
tangential_opening_norm * tangential_opening_norm * this->beta2_kappa2;
penetration = normal_opening_norm < 0.0;
if (not this->contact_after_breaking and
Math::are_float_equal(*damage_n_it, 1.)) {
penetration = false;
}
if (penetration) {
/// use penalty coefficient in case of penetration
*contact_traction_it = normal_opening;
*contact_traction_it *= this->penalty;
*contact_opening_it = normal_opening;
/// don't consider penetration contribution for delta
//*opening_it = tangential_opening;
normal_opening.zero();
} else {
delta_n += normal_opening_norm * normal_opening_norm;
delta_t += normal_opening_norm * normal_opening_norm * delta_c2_R2;
contact_traction_it->zero();
contact_opening_it->zero();
}
delta_n = std::sqrt(delta_n);
delta_t = std::sqrt(delta_t);
/// update maximum displacement and damage
*delta_n_max_it = std::max(*delta_n_max_it, delta_n);
*damage_n_it = std::min(*delta_n_max_it / *delta_c_it, Real(1.));
*delta_t_max_it = std::max(*delta_t_max_it, delta_t);
*damage_t_it = std::min(*delta_t_max_it / *delta_c_it, Real(1.));
Vector<Real> normal_traction(spatial_dimension);
Vector<Real> shear_traction(spatial_dimension);
/// NORMAL TRACTIONS
if (Math::are_float_equal(*damage_n_it, 1.)) {
normal_traction.zero();
} else if (Math::are_float_equal(*damage_n_it, 0.)) {
if (penetration) {
normal_traction.zero();
} else {
normal_traction = *insertion_stress_it;
}
} else {
// the following formulation holds both in loading and in
// unloading-reloading
normal_traction = normal_opening;
AKANTU_DEBUG_ASSERT(*delta_n_max_it != 0.,
"Division by zero, tolerance might be too low");
normal_traction *= *sigma_c_it / (*delta_n_max_it) * (1. - *damage_n_it);
}
/// SHEAR TRACTIONS
if (Math::are_float_equal(*damage_t_it, 1.) or
Math::are_float_equal(*damage_t_it, 0.)) {
shear_traction.zero();
} else {
shear_traction = tangential_opening;
AKANTU_DEBUG_ASSERT(*delta_t_max_it != 0.,
"Division by zero, tolerance might be too low");
shear_traction *= this->beta2_kappa;
shear_traction *= *sigma_c_it / (*delta_t_max_it) * (1. - *damage_t_it);
}
*traction_it = normal_traction;
*traction_it += shear_traction;
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
template <UInt spatial_dimension>
void MaterialCohesiveLinearUncoupled<spatial_dimension>::computeTangentTraction(
ElementType el_type, Array<Real> & tangent_matrix,
const Array<Real> & /*unused*/, 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);
/// 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_n_max_it = delta_n_max.previous(el_type, ghost_type).begin();
auto delta_t_max_it = delta_t_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_n_it = damage_n(el_type, ghost_type).begin();
auto contact_opening_it =
this->contact_opening(el_type, ghost_type).begin(spatial_dimension);
Vector<Real> normal_opening(spatial_dimension);
Vector<Real> tangential_opening(spatial_dimension);
for (; tangent_it != tangent_end; ++tangent_it, ++normal_it, ++opening_it,
++sigma_c_it, ++delta_c_it,
++delta_n_max_it, ++delta_t_max_it,
++damage_n_it, ++contact_opening_it) {
Real normal_opening_norm;
Real tangential_opening_norm;
bool penetration;
Real delta_c2_R2 = *delta_c_it * (*delta_c_it) / R / R;
/**
* During the update of the residual the interpenetrations are
* stored in the array "contact_opening", therefore, in the case
* of penetration, in the array "opening" there are only the
* tangential components.
*/
*opening_it += *contact_opening_it;
/// compute normal and tangential opening vectors
normal_opening_norm = opening_it->dot(*normal_it);
Vector<Real> normal_opening = *normal_it;
normal_opening *= normal_opening_norm;
Vector<Real> tangential_opening = *opening_it;
tangential_opening -= normal_opening;
tangential_opening_norm = tangential_opening.norm();
Real delta_n =
tangential_opening_norm * tangential_opening_norm * this->beta2_kappa2;
Real delta_t =
tangential_opening_norm * tangential_opening_norm * this->beta2_kappa2;
penetration = normal_opening_norm < 0.0;
if (not this->contact_after_breaking and
Math::are_float_equal(*damage_n_it, 1.)) {
penetration = false;
}
Real derivative = 0; // derivative = d(t/delta)/ddelta
Real T = 0;
/// TANGENT STIFFNESS FOR NORMAL TRACTIONS
Matrix<Real> n_outer_n(spatial_dimension, spatial_dimension);
n_outer_n.outerProduct(*normal_it, *normal_it);
if (penetration) {
/// stiffness in compression given by the penalty parameter
*tangent_it = n_outer_n;
*tangent_it *= this->penalty;
//*opening_it = tangential_opening;
normal_opening.zero();
} else {
delta_n += normal_opening_norm * normal_opening_norm;
delta_n = std::sqrt(delta_n);
delta_t += normal_opening_norm * normal_opening_norm * delta_c2_R2;
/**
* Delta has to be different from 0 to have finite values of
* tangential stiffness. At the element insertion, delta =
* 0. Therefore, a fictictious value is defined, for the
* evaluation of the first value of K.
*/
if (delta_n < Math::getTolerance()) {
delta_n = *delta_c_it / 1000.;
}
// loading
if (delta_n >= *delta_n_max_it) {
if (delta_n <= *delta_c_it) {
derivative = -(*sigma_c_it) / (delta_n * delta_n);
T = *sigma_c_it * (1 - delta_n / *delta_c_it);
} else {
derivative = 0.;
T = 0.;
}
// unloading-reloading
} else if (delta_n < *delta_n_max_it) {
Real T_max = *sigma_c_it * (1 - *delta_n_max_it / *delta_c_it);
derivative = 0.;
T = T_max / *delta_n_max_it * delta_n;
}
/// computation of the derivative of the constitutive law (dT/ddelta)
Matrix<Real> nn(n_outer_n);
nn *= T / delta_n;
Vector<Real> Delta_tilde(normal_opening);
Delta_tilde *= (1. - this->beta2_kappa2);
Vector<Real> mm(*opening_it);
mm *= this->beta2_kappa2;
Delta_tilde += mm;
const Vector<Real> & Delta_hat(normal_opening);
Matrix<Real> prov(spatial_dimension, spatial_dimension);
prov.outerProduct(Delta_hat, Delta_tilde);
prov *= derivative / delta_n;
prov += nn;
Matrix<Real> prov_t = prov.transpose();
*tangent_it = prov_t;
}
derivative = 0.;
T = 0.;
/// TANGENT STIFFNESS FOR SHEAR TRACTIONS
delta_t = std::sqrt(delta_t);
/**
* Delta has to be different from 0 to have finite values of
* tangential stiffness. At the element insertion, delta =
* 0. Therefore, a fictictious value is defined, for the
* evaluation of the first value of K.
*/
if (delta_t < Math::getTolerance()) {
delta_t = *delta_c_it / 1000.;
}
// loading
if (delta_t >= *delta_t_max_it) {
if (delta_t <= *delta_c_it) {
derivative = -(*sigma_c_it) / (delta_t * delta_t);
T = *sigma_c_it * (1 - delta_t / *delta_c_it);
} else {
derivative = 0.;
T = 0.;
}
// unloading-reloading
} else if (delta_t < *delta_t_max_it) {
Real T_max = *sigma_c_it * (1 - *delta_t_max_it / *delta_c_it);
derivative = 0.;
T = T_max / *delta_t_max_it * delta_t;
}
/// computation of the derivative of the constitutive law (dT/ddelta)
Matrix<Real> I(spatial_dimension, spatial_dimension);
I.eye();
Matrix<Real> nn(n_outer_n);
I -= nn;
I *= T / delta_t;
Vector<Real> Delta_tilde(normal_opening);
Delta_tilde *= (delta_c2_R2 - this->beta2_kappa2);
Vector<Real> mm(*opening_it);
mm *= this->beta2_kappa2;
Delta_tilde += mm;
Vector<Real> Delta_hat(tangential_opening);
Delta_hat *= this->beta2_kappa;
Matrix<Real> prov(spatial_dimension, spatial_dimension);
prov.outerProduct(Delta_hat, Delta_tilde);
prov *= derivative / delta_t;
prov += I;
Matrix<Real> prov_t = prov.transpose();
*tangent_it += prov_t;
}
AKANTU_DEBUG_OUT();
}
/* -------------------------------------------------------------------------- */
INSTANTIATE_MATERIAL(cohesive_linear_uncoupled,
MaterialCohesiveLinearUncoupled);
} // namespace akantu
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