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material_cohesive_linear_inline_impl.hh
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material_cohesive_linear_inline_impl.hh
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/**
* @file material_cohesive_linear_inline_impl.hh
*
* @author Mauro Corrado <mauro.corrado@epfl.ch>
* @author Nicolas Richart <nicolas.richart@epfl.ch>
* @author Marco Vocialta <marco.vocialta@epfl.ch>
*
* @date creation: Wed Apr 22 2015
* @date last modification: Thu Jan 14 2021
*
* @brief Inline functions of the MaterialCohesiveLinear
*
*
* @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.hh"
#include "aka_static_if.hh"
#include "solid_mechanics_model_cohesive.hh"
/* -------------------------------------------------------------------------- */
/* -------------------------------------------------------------------------- */
#ifndef AKANTU_MATERIAL_COHESIVE_LINEAR_INLINE_IMPL_HH_
#define AKANTU_MATERIAL_COHESIVE_LINEAR_INLINE_IMPL_HH_
/* -------------------------------------------------------------------------- */
namespace akantu {
/* -------------------------------------------------------------------------- */
template <Int dim>
template <class D1, class D2, class D3, class D4>
Real MaterialCohesiveLinear<dim>::computeEffectiveNorm(
const Eigen::MatrixBase<D1> & stress, const Eigen::MatrixBase<D2> & normal,
const Eigen::MatrixBase<D3> & tangent,
const Eigen::MatrixBase<D4> & normal_traction_) const {
Eigen::MatrixBase<D4> & normal_traction =
const_cast<Eigen::MatrixBase<D4> &>(normal_traction_);
normal_traction = stress * normal;
Real normal_contrib = normal_traction.dot(normal);
/// in 3D tangential components must be summed
Real tangent_contrib = 0;
if constexpr (dim == 2) {
Real tangent_contrib_tmp = normal_traction.dot(tangent);
tangent_contrib += tangent_contrib_tmp * tangent_contrib_tmp;
} else if constexpr (dim == 3) {
for (auto && tangent_v : tangent) {
Real tangent_contrib_tmp = normal_traction.dot(tangent_v);
tangent_contrib += tangent_contrib_tmp * tangent_contrib_tmp;
}
}
tangent_contrib = std::sqrt(tangent_contrib);
normal_contrib = std::max(Real(0.), normal_contrib);
return std::sqrt(normal_contrib * normal_contrib +
tangent_contrib * tangent_contrib * beta2_inv);
}
/* -------------------------------------------------------------------------- */
template <Int dim>
template <typename Args>
inline void MaterialCohesiveLinear<dim>::computeTractionOnQuad(Args && args) {
auto && delta_c = args["delta_c"_n];
auto && sigma_c = args["sigma_c"_n];
auto && delta_max = args["delta_max"_n];
auto && normal = args["normal"_n];
auto && opening = args["opening"_n];
auto && traction = args["traction"_n];
auto && damage = args["damage"_n];
auto && insertion_stress = args["insertion_stress"_n];
/// compute normal and tangential opening vectors
auto norm = opening.dot(normal);
this->normal_opening_norm = norm;
this->normal_opening = normal * this->normal_opening_norm;
this->tangential_opening = opening - normal_opening;
this->tangential_opening_norm = this->tangential_opening.norm();
/**
* compute effective opening displacement
* @f$ \delta = \sqrt{
* \frac{\beta^2}{\kappa^2} \Delta_t^2 + \Delta_n^2 } @f$
*/
auto delta = this->tangential_opening_norm * this->tangential_opening_norm *
this->beta2_kappa2;
penetration = this->normal_opening_norm / delta_c < -Math::getTolerance();
// penetration = normal_opening_norm < 0.;
if (not this->contact_after_breaking and Math::are_float_equal(damage, 1.)) {
penetration = false;
}
auto && contact_traction = args.get("contact_traction"_n);
auto && contact_opening = args.get("contact_opening"_n);
if (penetration) {
/// use penalty coefficient in case of penetration
contact_traction = this->normal_opening * this->penalty;
contact_opening = this->normal_opening;
/// don't consider penetration contribution for delta
opening = tangential_opening;
this->normal_opening.zero();
} else {
delta += this->normal_opening_norm * this->normal_opening_norm;
contact_traction.zero();
contact_opening.zero();
}
delta = std::sqrt(delta);
/// update maximum displacement and damage
delta_max = std::max(delta_max, delta);
damage = std::min(delta_max / delta_c, Real(1.));
/**
* Compute traction @f$ \mathbf{T} = \left(
* \frac{\beta^2}{\kappa} \Delta_t \mathbf{t} + \Delta_n
* \mathbf{n} \right) \frac{\sigma_c}{\delta} \left( 1-
* \frac{\delta}{\delta_c} \right)@f$
*/
if (Math::are_float_equal(damage, 1.)) {
traction.zero();
} else if (Math::are_float_equal(damage, 0.)) {
if (penetration) {
traction.zero();
} else {
traction = insertion_stress;
}
} else {
AKANTU_DEBUG_ASSERT(delta_max != 0.,
"Division by zero, tolerance might be too low");
traction =
(this->tangential_opening * this->beta2_kappa + this->normal_opening) *
sigma_c / delta_max * (1. - damage);
}
}
/* -------------------------------------------------------------------------- */
template <Int dim>
template <class Derived, class Args>
inline void MaterialCohesiveLinear<dim>::computeTangentTractionOnQuad(
Eigen::MatrixBase<Derived> & tangent, Args && args) {
/**
* 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.
*/
auto && delta_c = args["delta_c"_n];
auto && delta_max = args["delta_max"_n];
auto && normal = args["normal"_n];
auto && opening = args["opening"_n];
auto && contact_opening = args["contact_opening"_n];
auto && damage = args["damage"_n];
opening += contact_opening;
/// compute normal and tangential opening vectors
this->normal_opening_norm = opening.dot(normal);
this->normal_opening = normal * normal_opening_norm;
this->tangential_opening = opening - normal_opening;
this->tangential_opening_norm = tangential_opening.norm();
auto delta = this->tangential_opening_norm * this->tangential_opening_norm *
this->beta2_kappa2;
penetration = normal_opening_norm < 0.0;
if (not this->contact_after_breaking and Math::are_float_equal(damage, 1.)) {
penetration = false;
}
Real derivative = 0; // derivative = d(t/delta)/ddelta
Real t = 0;
auto && n_outer_n = normal * normal.transpose();
if (penetration) {
/// stiffness in compression given by the penalty parameter
tangent = penalty * (tangent + n_outer_n);
opening = tangential_opening;
normal_opening_norm = opening.dot(normal);
normal_opening = normal * normal_opening_norm;
} else {
delta += normal_opening_norm * normal_opening_norm;
}
delta = std::sqrt(delta);
/**
* 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 < Math::getTolerance()) {
delta = delta_c / 1000.;
}
if (delta >= delta_max) {
if (delta <= delta_c) {
derivative = -sigma_c / (delta * delta);
t = sigma_c * (1 - delta / delta_c);
} else {
derivative = 0.;
t = 0.;
}
} else if (delta < delta_max) {
Real tmax = sigma_c * (1 - delta_max / delta_c);
t = tmax / delta_max * delta;
}
/// computation of the derivative of the constitutive law (dT/ddelta)
auto && I = Eigen::Matrix<Real, dim, dim>::Identity() * this->beta2_kappa;
auto && nn = (n_outer_n * (1. - this->beta2_kappa) + I) * t / delta;
auto && mm = opening * this->beta2_kappa2;
auto && t_tilde = normal_opening * (1. - this->beta2_kappa2) + mm;
auto && t_hat = normal_opening + this->beta2_kappa * tangential_opening;
auto && prov = t_hat * t_tilde.transpose() * derivative / delta + nn;
tangent += prov.transpose();
}
/* -------------------------------------------------------------------------- */
} // namespace akantu
/* -------------------------------------------------------------------------- */
#endif // AKANTU_MATERIAL_COHESIVE_LINEAR_INLINE_IMPL_HH_

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