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material_hyper_elasto_plastic1.hh
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/**
* @file material_hyper_elasto_plastic1.hh
*
* @author Till Junge <till.junge@epfl.ch>
*
* @date 20 Feb 2018
*
* @brief Material for logarithmic hyperelasto-plasticity, as defined in de
* Geus 2017 (https://doi.org/10.1016/j.cma.2016.12.032) and further
* explained in Geers 2003 (https://doi.org/10.1016/j.cma.2003.07.014)
*
* Copyright © 2018 Till Junge
*
* µSpectre is free software; you can redistribute it and/or
* modify it under the terms of the GNU General Public License as
* published by the Free Software Foundation, either version 3, or (at
* your option) any later version.
*
* µSpectre 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
* General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with GNU Emacs; see the file COPYING. If not, write to the
* Free Software Foundation, Inc., 59 Temple Place - Suite 330,
* Boston, MA 02111-1307, USA.
*/
#ifndef MATERIAL_HYPER_ELASTO_PLASTIC1_H
#define MATERIAL_HYPER_ELASTO_PLASTIC1_H
#include "materials/material_muSpectre_base.hh"
#include "materials/materials_toolbox.hh"
#include "common/eigen_tools.hh"
#include <algorithm>
namespace muSpectre {
template <Dim_t DimS, Dim_t DimM>
class MaterialHyperElastoPlastic1;
/**
* traits for hyper-elastoplastic material
*/
template <Dim_t DimS, Dim_t DimM>
struct MaterialMuSpectre_traits<MaterialHyperElastoPlastic1<DimS, DimM>> {
//! global field collection
using GFieldCollection_t = typename
MaterialBase<DimS, DimM>::GFieldCollection_t;
//! expected map type for strain fields
using StrainMap_t =
MatrixFieldMap<GFieldCollection_t, Real, DimM, DimM, true>;
//! expected map type for stress fields
using StressMap_t = MatrixFieldMap<GFieldCollection_t, Real, DimM, DimM>;
//! expected map type for tangent stiffness fields
using TangentMap_t = T4MatrixFieldMap<GFieldCollection_t, Real, DimM>;
//! declare what type of strain measure your law takes as input
constexpr static auto strain_measure{StrainMeasure::Gradient};
//! declare what type of stress measure your law yields as output
constexpr static auto stress_measure{StressMeasure::Kirchhoff};
//! local field collection used for internals
using LFieldColl_t = LocalFieldCollection<DimS, DimM>;
//! storage type for plastic flow measure (εₚ in the papers)
using ScalarMap_t = ScalarFieldMap<LFieldColl_t, Real>;
/**
* storage type for for previous gradient Fᵗ and elastic left
* Cauchy-Green deformation tensor bₑᵗ
*/
using LStrainMap_t = MatrixFieldMap<LFieldColl_t, Real, DimM, DimM, false>;
/**
* format in which to receive internals (previous gradient Fᵗ,
* previous elastic lef Cauchy-Green deformation tensor bₑᵗ, and
* the plastic flow measure εₚ
*/
using InternalVariables = std::tuple<LStrainMap_t, LStrainMap_t,
ScalarMap_t>;
};
/**
* Material implementation for hyper-elastoplastic constitutive law
*/
template <Dim_t DimS, Dim_t DimM=DimS>
class MaterialHyperElastoPlastic1: public
MaterialMuSpectre<MaterialHyperElastoPlastic1<DimS, DimM>, DimS, DimM>
{
public:
//! base class
using Parent = MaterialMuSpectre
<MaterialHyperElastoPlastic1<DimS, DimM>, DimS, DimM>;
/**
* type used to determine whether the
* `muSpectre::MaterialMuSpectre::iterable_proxy` evaluate only
* stresses or also tangent stiffnesses
*/
using NeedTangent = typename Parent::NeedTangent;
//! shortcut to traits
using traits = MaterialMuSpectre_traits<MaterialHyperElastoPlastic1>;
//! Hooke's law implementation
using Hooke = typename
MatTB::Hooke<DimM,
typename traits::StrainMap_t::reference,
typename traits::TangentMap_t::reference>;
//! type in which the previous strain is referenced
using StrainRef_t = typename traits::LStrainMap_t::reference;
//! Default constructor
MaterialHyperElastoPlastic1() = delete;
//! Constructor with name and material properties
MaterialHyperElastoPlastic1(std::string name, Real young, Real poisson,
Real tau_y0, Real H);
//! Copy constructor
MaterialHyperElastoPlastic1(const MaterialHyperElastoPlastic1 &other) = delete;
//! Move constructor
MaterialHyperElastoPlastic1(MaterialHyperElastoPlastic1 &&other) = delete;
//! Destructor
virtual ~MaterialHyperElastoPlastic1() = default;
//! Copy assignment operator
MaterialHyperElastoPlastic1& operator=(const MaterialHyperElastoPlastic1 &other) = delete;
//! Move assignment operator
MaterialHyperElastoPlastic1& operator=(MaterialHyperElastoPlastic1 &&other) = delete;
/**
* evaluates Kirchhoff stress given the current placement gradient
* Fₜ, the previous Gradient Fₜ₋₁ and the cumulated plastic flow
* εₚ
*/
template <class grad_t>
inline decltype(auto) evaluate_stress(grad_t && F, StrainRef_t F_prev,
StrainRef_t be_prev,
Real & plast_flow);
/**
* evaluates Kirchhoff stress and stiffness given the current placement gradient
* Fₜ, the previous Gradient Fₜ₋₁ and the cumulated plastic flow
* εₚ
*/
template <class grad_t>
inline decltype(auto) evaluate_stress_tangent(grad_t && F, StrainRef_t F_prev,
StrainRef_t be_prev,
Real & plast_flow);
/**
* return the internals tuple
*/
typename traits::InternalVariables & get_internals() {
return this->internal_variables;};
protected:
/**
* worker function computing stresses and internal variables
*/
template <class grad_t>
inline decltype(auto) stress_n_internals_worker(grad_t && F, StrainRef_t F_prev,
StrainRef_t be_prev,
Real & plast_flow);
using LColl_t = LocalFieldCollection<DimS, DimM>;
//! storage for cumulated plastic flow εₚ
ScalarField<LColl_t, Real> & plast_flow_field;
//! storage for previous gradient Fᵗ
TensorField<LColl_t, Real, secondOrder, DimM> & F_prev_field;
//! storage for elastic left Cauchy-Green deformation tensor bₑᵗ
TensorField<LColl_t, Real, secondOrder, DimM> & be_prev_field;
// material properties
const Real young; //!< Young's modulus
const Real poisson; //!< Poisson's ratio
const Real lambda; //!< first Lamé constant
const Real mu; //!< second Lamé constant (shear modulus)
const Real K; //!< Bulk modulus
const Real tau_y0; //!< initial yield stress
const Real H; //!< hardening modulus
const T4Mat<Real, DimM> C; //!< stiffness tensor
typename traits::InternalVariables internal_variables;
private:
};
//----------------------------------------------------------------------------//
template <Dim_t DimS, Dim_t DimM>
template <class grad_t>
decltype(auto)
MaterialHyperElastoPlastic1<DimS, DimM>::
stress_n_internals_worker(grad_t && F, StrainRef_t F_prev,
StrainRef_t be_prev, Real & eps_p) {
// the notation in this function follows Geers 2003
// (https://doi.org/10.1016/j.cma.2003.07.014).
// computation of trial state
auto && f{F*F_prev.inverse()};
log_comp::Mat_t<DimM> be_star{f*be_prev*f.transpose()};
auto && ln_be_star{logm(be_star)};
auto && tau_star{.5*Hooke::evaluate_stress(this->lambda, this->mu, ln_be_star)};
// deviatoric part of Kirchhoff stress
// TODO: There seems to be disagreement regarding whether the deviator in 2D also needs to have 3 times the trace subtracted or just 2 times. Have an eye on this!
auto && tau_d_star{tau_star - tau_star.trace()/3*tau_star.Identity()};
auto && tau_eq_star{std::sqrt(3*.5*(tau_d_star.array()*
tau_d_star.transpose().array()).sum())};
auto && N_star{3*.5*tau_d_star/tau_eq_star};
// this is eq (27), and the std::min enforces the Kuhn-Tucker relation (16)
auto && phi_star{std::min(tau_eq_star - this->tau_y0 - this->H * eps_p, 0.)};
// return mapping
auto && Del_gamma{phi_star/(this->H + 3 * this->mu)};
auto && tau{tau_star - 2*Del_gamma*this->mu*N_star};
//auto && tau_eq{tau_eq_star - 3*this->mu*Del_gamma};
// update the previous values to the new ones
F_prev = F;
be_prev = expm(log_comp::Mat_t<DimM>(ln_be_star-2*Del_gamma*N_star));
eps_p += Del_gamma;
// transmit info whether this is a plastic step or not
auto && is_plastic{phi_star >= 0};
return std::make_tuple(std::move(tau), std::move(tau_eq_star),
std::move(Del_gamma), std::move(N_star),
std::move(is_plastic));
}
//----------------------------------------------------------------------------//
template <Dim_t DimS, Dim_t DimM>
template <class grad_t>
decltype(auto)
MaterialHyperElastoPlastic1<DimS, DimM>::
evaluate_stress(grad_t && F, StrainRef_t F_prev, StrainRef_t be_prev,
Real & eps_p) {
return std::get<0>(this->stress_n_internals_worker
(std::forward<grad_t>(F), F_prev, be_prev, eps_p));
}
//----------------------------------------------------------------------------//
template <Dim_t DimS, Dim_t DimM>
template <class grad_t>
decltype(auto)
MaterialHyperElastoPlastic1<DimS, DimM>::
evaluate_stress_tangent(grad_t && F, StrainRef_t F_prev, StrainRef_t be_prev,
Real & eps_p) {
//! after the stress computation, all internals are up to date
auto && vals{this->stress_n_internals_worker
(std::forward<grad_t>(F), F_prev, be_prev, eps_p)};
auto && tau {std::get<0>(vals)};
auto && tau_eq_star{std::get<1>(vals)};
auto && Del_gamma {std::get<2>(vals)};
auto && N_star {std::get<3>(vals)};
auto && is_plastic {std::get<4>(vals)};
if (is_plastic) {
auto && a0 = Del_gamma*this->mu/tau_eq_star;
auto && a1 = this->mu/(this->H + 3*this->mu);
return std::make_tuple(std::move(tau), T4Mat<Real, DimM>{
((this->K/2. - this->mu/3 + a0*this->mu)*Matrices::Itrac<DimM>() +
(1 - 3*a0) * this->mu*Matrices::Isymm<DimM>() +
2*this->mu * (a0 - a1)*Matrices::outer(N_star, N_star))});
} else {
return std::make_tuple(std::move(tau), T4Mat<Real, DimM>{this->C});
}
}
} // muSpectre
#endif /* MATERIAL_HYPER_ELASTO_PLASTIC1_H */

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