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materials_toolbox.hh
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/**
* file materials_toolbox.hh
*
* @author Till Junge <till.junge@epfl.ch>
*
* @date 02 Nov 2017
*
* @brief collection of common continuum mechanics tools
*
* @section LICENCE
*
* Copyright (C) 2017 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 MATERIALS_TOOLBOX_H
#define MATERIALS_TOOLBOX_H
#include <Eigen/Dense>
#include <exception>
#include <sstream>
#include <iostream>
#include <tuple>
#include <type_traits>
#include "common/common.hh"
#include "common/tensor_algebra.hh"
#include "common/eigen_tools.hh"
#include "common/T4_map_proxy.hh"
namespace muSpectre {
namespace MatTB {
class MaterialsToolboxError:public std::runtime_error{
public:
explicit MaterialsToolboxError(const std::string& what)
:std::runtime_error(what){}
explicit MaterialsToolboxError(const char * what)
:std::runtime_error(what){}
};
/* ---------------------------------------------------------------------- */
/**
* Flag used to designate whether the material should compute both stress
* and tangent moduli or only stress
*/
enum class NeedTangent {
yes, // compute both stress and tangent moduli
no}; // compute only stress
/**
* Struct with a single variadic function only used to determine the
* tuple type to store in the various sub-iterators or to return
*/
template <MatTB::NeedTangent NeedTgt>
struct StoredTuple {
template <class ... Args>
decltype(auto) operator()(Args && ... args) {
return std::tie(args ... );
}
};
/**
* struct used to determine the exact type of a tuple of references obtained
* when a bunch of iterators over fiel_maps are dereferenced and their
* results are concatenated into a tuple
*/
template <class... T>
struct ReferenceTuple {
using type = std::tuple<typename T::reference ...>;
};
/**
* specialisation for tuples
*/
template <>
template <class... T>
struct ReferenceTuple<std::tuple<T...>> {
using type = typename ReferenceTuple<T...>::type;
};
/**
* helper type for ReferenceTuple
*/
template <class... T>
using ReferenceTuple_t = typename ReferenceTuple<T...>::type;
/* ---------------------------------------------------------------------- */
/** Structure for functions returning one strain measure as a
function of another
**/
namespace internal {
template <StrainMeasure In, StrainMeasure Out = In>
struct ConvertStrain {
template <class Strain_t>
inline static decltype(auto)
compute(Strain_t&& input) {
// transparent case, in which no conversion is required:
// just a perfect forwarding
static_assert
((In == Out),
"This particular strain conversion is not implemented");
return std::forward<Strain_t>(input);
}
};
/* ---------------------------------------------------------------------- */
/** Specialisation for getting Green-Lagrange strain from the
transformation gradient
**/
template <>
template <class Strain_t>
decltype(auto)
ConvertStrain<StrainMeasure::Gradient, StrainMeasure::GreenLagrange>::
compute(Strain_t && F) {
return (F.transpose()*F - Strain_t::PlainObject::Identity());
}
} // internal
/* ---------------------------------------------------------------------- */
//! set of functions returning one strain measure as a function of
//! another
template <StrainMeasure In, StrainMeasure Out,
class Strain_t>
decltype(auto) convert_strain(Strain_t && strain) {
return internal::ConvertStrain<In, Out>::compute(std::move(strain));
};
/* ---------------------------------------------------------------------- */
/** Structure for functions returning PK1 stress from other stress measures
**/
namespace internal {
template <Dim_t Dim,
StressMeasure StressM,
StrainMeasure StrainM>
struct PK1_stress {
template <class Strain_t, class Stress_t>
inline static decltype(auto)
compute(Strain_t && /*strain*/, Stress_t && /*stress*/) {
// the following test always fails to generate a compile-time error
static_assert((StressM == StressMeasure::Cauchy) &&
(StressM == StressMeasure::PK1),
"The requested Stress conversion is not implemented. "
"You either made a programming mistake or need to "
"implement it as a specialisation of this function. "
"See PK2stress<PK1,T1, T2> for an example.");
}
template <class Strain_t, class Stress_t, class Tangent_t>
inline static decltype(auto)
compute(Strain_t && /*strain*/, Stress_t && /*stress*/,
Tangent_t && /*stiffness*/) {
// the following test always fails to generate a compile-time error
static_assert((StressM == StressMeasure::Cauchy) &&
(StressM == StressMeasure::PK1),
"The requested Stress conversion is not implemented. "
"You either made a programming mistake or need to "
"implement it as a specialisation of this function. "
"See PK2stress<PK1,T1, T2> for an example.");
}
};
/* ---------------------------------------------------------------------- */
/** Specialisation for the transparent case, where we already
have PK1 stress
**/
template <Dim_t Dim, StrainMeasure StrainM>
struct PK1_stress<Dim, StressMeasure::PK1, StrainM>:
public PK1_stress<Dim, StressMeasure::__nostress__,
StrainMeasure::__nostrain__> {
template <class Strain_t, class Stress_t>
inline static decltype(auto)
compute(Strain_t && /*dummy*/, Stress_t && P) {
return std::forward<Stress_t>(P);
}
};
/* ---------------------------------------------------------------------- */
/** Specialisation for the transparent case, where we already have PK1
stress *and* stiffness is given with respect to the transformation
gradient
**/
template <Dim_t Dim>
struct PK1_stress<Dim, StressMeasure::PK1, StrainMeasure::Gradient>:
public PK1_stress<Dim, StressMeasure::PK1,
StrainMeasure::__nostrain__> {
using Parent = PK1_stress<Dim, StressMeasure::PK1,
StrainMeasure::__nostrain__>;
using Parent::compute;
template <class Strain_t, class Stress_t, class Tangent_t>
decltype(auto)
compute(Strain_t && /*dummy*/, Stress_t && P, Tangent_t && K) {
return std::forward_as_tuple(P, K);
}
};
/* ---------------------------------------------------------------------- */
/**
* Specialisation for the case where we get material stress (PK2)
*/
template <Dim_t Dim, StrainMeasure StrainM>
struct PK1_stress<Dim, StressMeasure::PK2, StrainM>:
public PK1_stress<Dim, StressMeasure::__nostress__,
StrainMeasure::__nostrain__> {
template <class Strain_t, class Stress_t>
inline static decltype(auto)
compute(Strain_t && F, Stress_t && S) {
return F*S;
}
};
/* ---------------------------------------------------------------------- */
/**
* Specialisation for the case where we get material stress (PK2) derived
* with respect to Green-Lagrange strain
*/
template <Dim_t Dim>
struct PK1_stress<Dim, StressMeasure::PK2, StrainMeasure::GreenLagrange>:
public PK1_stress<Dim, StressMeasure::PK2,
StrainMeasure::__nostrain__> {
using Parent = PK1_stress<Dim, StressMeasure::PK2,
StrainMeasure::__nostrain__>;
using Parent::compute;
template <class Strain_t, class Stress_t, class Tangent_t>
inline static decltype(auto)
compute(Strain_t && F, Stress_t && S, Tangent_t && C) {
using T4 = typename Tangent_t::PlainObject;
using Tmap = T4Map<Real, Dim>;
T4 K;
Tmap Kmap{K.data()};
K.setZero();
constexpr int dim{Strain_t::ColsAtCompileTime};
for (int i = 0; i < dim; ++i) {
for (int m = 0; m < dim; ++m) {
for (int n = 0; n < dim; ++n) {
Kmap(i,m,i,n) += S(m,n);
for (int j = 0; j < dim; ++j) {
for (int r = 0; r < dim; ++r) {
for (int s = 0; s < dim; ++s) {
Kmap(i,m,j,n) += F(i,r)*get(C,r,m,n,s)*(F(j,s));
}
}
}
}
}
}
auto && P = compute(std::forward<Strain_t>(F),
std::forward<Stress_t>(S));
return std::forward_as_tuple(std::move(P), K);
}
};
} // internal
/* ---------------------------------------------------------------------- */
//! set of functions returning an expression for PK2 stress based on
template <StressMeasure StressM, StrainMeasure StrainM,
class Stress_t, class Strain_t>
decltype(auto) PK1_stress(Strain_t && strain, Stress_t && stress) {
constexpr Dim_t dim{EigenCheck::TensorDim(strain)};
static_assert((dim == EigenCheck::TensorDim(stress)),
"Stress and strain tensors have differing dimensions");
return internal::PK1_stress<dim, StressM, StrainM>::compute
(std::move(stress), std::move(strain));
};
/* ---------------------------------------------------------------------- */
//! set of functions returning an expression for PK2 stress based on
template <StressMeasure StressM, StrainMeasure StrainM,
class Stress_t, class Strain_t, class Tangent_t>
decltype(auto) PK1_stress(Strain_t && strain,
Stress_t && stress,
Tangent_t && tangent) {
constexpr Dim_t dim{EigenCheck::TensorDim(strain)};
static_assert((dim == EigenCheck::TensorDim(stress)),
"Stress and strain tensors have differing dimensions");
static_assert((dim*dim == EigenCheck::TensorDim(tangent)),
"Stress and tangent tensors have differing dimensions");
return internal::PK1_stress<dim, StressM, StrainM>::compute
(std::move(stress), std::move(strain), std::move(tangent));
};
/* ---------------------------------------------------------------------- */
/** Structure for functions returning ∂strain/∂F (where F is the transformation
* gradient. (e.g. for a material law expressed as PK2 stress S as
* function of Green-Lagrange strain E, this would return F^T ⊗̲ I) (⊗_
* refers to Curnier's notation) WARNING: this function assumes that your
* stress measure has the two minor symmetries due to stress equilibrium
* and the major symmetry due to the existance of an elastic potential
* W(E). Do not rely on this function if you are using exotic stress
* measures
**/
namespace internal {
template<StrainMeasure StrainM>
struct StrainDerivative
{
template <class Grad_t>
inline static decltype(auto)
compute (Grad_t && grad) {
// the following test always fails to generate a compile-time error
static_assert((StrainM == StrainMeasure::Almansi) &&
(StrainM == StrainMeasure::Biot),
"The requested StrainDerivative calculation is not "
"implemented. You either made a programming mistake or "
"need to implement it as a specialisation of this "
"function. See "
"StrainDerivative<StrainMeasure::GreenLagrange> for an "
"example.");
}
};
template <>
template <class Grad_t>
decltype(auto) StrainDerivative<StrainMeasure::GreenLagrange>::
compute(Grad_t && grad) {
}
} // internal
/* ---------------------------------------------------------------------- */
//! set of functions returning ∂strain/∂F
template<StrainMeasure StrainM>
auto StrainDerivative = [](auto && F) decltype(auto) {
// the following test always fails to generate a compile-time error
static_assert((StrainM == StrainMeasure::Almansi) &&
(StrainM == StrainMeasure::Biot),
"The requested StrainDerivative calculation is not "
"implemented. You either made a programming mistake or "
"need to implement it as a specialisation of this "
"function. See "
"StrainDerivative<StrainMeasure::GreenLagrange> for an "
"example.");
};
/* ---------------------------------------------------------------------- */
template<>
auto StrainDerivative<StrainMeasure::GreenLagrange> =
[] (auto && F) -> decltype(auto) {
constexpr size_t order{2};
constexpr Dim_t dim{F.Dimensions[0]};
return Tensors::outer_under<dim>
(F.shuffle(std::array<Dim_t, order>{1,0}), Tensors::I2<dim>());
};
} // MatTB
} // muSpectre
#endif /* MATERIALS_TOOLBOX_H */

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