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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 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_LINEAR_ELASTIC_RANDOM_STIFFNESS_2_H
#define MATERIAL_LINEAR_ELASTIC_RANDOM_STIFFNESS_2_H
#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
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) override final;
/**
* overload add_pixel to write into local stiffness tensor
*/
void add_pixel(const Ccoord_t<DimS> & pixel,
const Real & Poisson_ratio, const Real & Youngs_modulus);
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>
decltype(auto)
MaterialLinearElastic4<DimS, DimM>::
evaluate_stress(s_t && E, const Real & lambda, const Real & mu) {
auto C = Hooke::compute_C_T4(lambda, mu);
return Matrices::tensmult(C, E);
}
/* ---------------------------------------------------------------------- */
template <Dim_t DimS, Dim_t DimM>
template <class s_t>
decltype(auto)
MaterialLinearElastic4<DimS, DimM>::
evaluate_stress_tangent(s_t && E, const Real & lambda,
const Real & mu)
{
auto C = Hooke::compute_C_T4(lambda, mu);
return std::make_tuple(Matrices::tensmult(C, E), C);
}
} // muSpectre
#endif /* MATERIAL_LINEAR_ELASTIC_RANDOM_STIFFNESS_2_H */

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