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material_linear_elastic4.hh
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/**
* @file material_linear_elastic4.hh
*
* @author Richard Leute <richard.leute@imtek.uni-freiburg.de>
*
* @date 15 March 2018
*
* @brief linear elastic material with distribution of stiffness properties.
* In difference to material_linear_elastic3 two Lame constants are
* stored per pixel instead of the whole elastic matrix C.
* Uses the MaterialMuSpectre facilities to keep it simple.
*
* Copyright © 2018 Till Junge
*
* µSpectre 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, 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 Lesser General Public License
* along with µSpectre; see the file COPYING. If not, write to the
* Free Software Foundation, Inc., 59 Temple Place - Suite 330,
* * Boston, MA 02111-1307, USA.
*
* Additional permission under GNU GPL version 3 section 7
*
* If you modify this Program, or any covered work, by linking or combining it
* with proprietary FFT implementations or numerical libraries, containing parts
* covered by the terms of those libraries' licenses, the licensors of this
* Program grant you additional permission to convey the resulting work.
*/
#ifndef SRC_MATERIALS_MATERIAL_LINEAR_ELASTIC4_HH_
#define SRC_MATERIALS_MATERIAL_LINEAR_ELASTIC4_HH_
#include "materials/material_linear_elastic1.hh"
#include "common/field.hh"
#include "common/tensor_algebra.hh"
#include <Eigen/Dense>
namespace muSpectre {
template <Dim_t DimS, Dim_t DimM>
class MaterialLinearElastic4;
/**
* traits for objective linear elasticity with eigenstrain
*/
template <Dim_t DimS, Dim_t DimM>
struct MaterialMuSpectre_traits<MaterialLinearElastic4<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::GreenLagrange};
//! declare what type of stress measure your law yields as output
constexpr static auto stress_measure{StressMeasure::PK2};
//! local field_collections used for internals
using LFieldColl_t = LocalFieldCollection<DimS>;
//! local Lame constant type
using LLameConstantMap_t = ScalarFieldMap<LFieldColl_t, Real, true>;
//! elasticity without internal variables
using InternalVariables =
std::tuple<LLameConstantMap_t, LLameConstantMap_t>;
};
/**
* implements objective linear elasticity with an eigenstrain per pixel
*/
template <Dim_t DimS, Dim_t DimM>
class MaterialLinearElastic4
: public MaterialMuSpectre<MaterialLinearElastic4<DimS, DimM>, DimS,
DimM> {
public:
//! base class
using Parent = MaterialMuSpectre<MaterialLinearElastic4, DimS, DimM>;
/**
* type used to determine whether the
* `muSpectre::MaterialMuSpectre::iterable_proxy` evaluate only
* stresses or also tangent stiffnesses
*/
using NeedTangent = typename Parent::NeedTangent;
//! global field collection
using Stiffness_t =
Eigen::TensorFixedSize<Real, Eigen::Sizes<DimM, DimM, DimM, DimM>>;
//! traits of this material
using traits = MaterialMuSpectre_traits<MaterialLinearElastic4>;
//! Type of container used for storing eigenstrain
using InternalVariables = typename traits::InternalVariables;
//! Hooke's law implementation
using Hooke =
typename MatTB::Hooke<DimM, typename traits::StrainMap_t::reference,
typename traits::TangentMap_t::reference>;
//! Default constructor
MaterialLinearElastic4() = delete;
//! Construct by name
explicit MaterialLinearElastic4(std::string name);
//! Copy constructor
MaterialLinearElastic4(const MaterialLinearElastic4 & other) = delete;
//! Move constructor
MaterialLinearElastic4(MaterialLinearElastic4 && other) = delete;
//! Destructor
virtual ~MaterialLinearElastic4() = default;
//! Copy assignment operator
MaterialLinearElastic4 &
operator=(const MaterialLinearElastic4 & other) = delete;
//! Move assignment operator
MaterialLinearElastic4 &
operator=(MaterialLinearElastic4 && other) = delete;
/**
* evaluates second Piola-Kirchhoff stress given the Green-Lagrange
* strain (or Cauchy stress if called with a small strain tensor), the first
* Lame constant (lambda) and the second Lame constant (shear modulus/mu).
*/
template <class s_t>
inline decltype(auto) evaluate_stress(s_t && E, const Real & lambda,
const Real & mu);
/**
* evaluates both second Piola-Kirchhoff stress and stiffness given
* the Green-Lagrange strain (or Cauchy stress and stiffness if
* called with a small strain tensor), the first Lame constant (lambda) and
* the second Lame constant (shear modulus/mu).
*/
template <class s_t>
inline decltype(auto) evaluate_stress_tangent(s_t && E, const Real & lambda,
const Real & mu);
/**
* return the empty internals tuple
*/
InternalVariables & get_internals() { return this->internal_variables; }
/**
* overload add_pixel to write into loacal stiffness tensor
*/
void add_pixel(const Ccoord_t<DimS> & pixel) final;
/**
* overload add_pixel to write into local stiffness tensor
*/
void add_pixel(const Ccoord_t<DimS> & pixel,
const Real & Youngs_modulus, const Real & Poisson_ratio);
protected:
//! storage for first Lame constant 'lambda'
//! and second Lame constant(shear modulus) 'mu'
using Field_t = MatrixField<LocalFieldCollection<DimS>, Real, oneD, oneD>;
Field_t & lambda_field;
Field_t & mu_field;
//! tuple for iterable eigen_field
InternalVariables internal_variables;
private:
};
/* ---------------------------------------------------------------------- */
template <Dim_t DimS, Dim_t DimM>
template <class s_t>
auto MaterialLinearElastic4<DimS, DimM>::evaluate_stress(s_t && E,
const Real & lambda,
const Real & mu)
-> decltype(auto) {
auto C = Hooke::compute_C_T4(lambda, mu);
return Matrices::tensmult(C, E);
}
/* ---------------------------------------------------------------------- */
template <Dim_t DimS, Dim_t DimM>
template <class s_t>
auto MaterialLinearElastic4<DimS, DimM>::evaluate_stress_tangent(
s_t && E, const Real & lambda, const Real & mu) -> decltype(auto) {
T4Mat<Real, DimM> C = Hooke::compute_C_T4(lambda, mu);
return std::make_tuple(
this->evaluate_stress(std::forward<s_t>(E), lambda, mu), C);
}
} // namespace muSpectre
#endif // SRC_MATERIALS_MATERIAL_LINEAR_ELASTIC4_HH_

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