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muSpectre/src/materials/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 <exception>
#include <sstream>
#include <iostream>
#include <tuple>
#include "common/common.hh"
#include "common/tensor_algebra.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){}
};
/* ---------------------------------------------------------------------- */
//! Material laws can declare which type of stress measure they provide,
//! and µSpectre will handle conversions
enum class StressMeasure {
Cauchy, PK1, PK2, Kirchhoff, Biot, Mandel, __nostress__};
std::ostream & operator<<(std::ostream & os, StressMeasure s) {
switch (s) {
case StressMeasure::Cauchy: {os << "Cauchy"; break;}
case StressMeasure::PK1: {os << "PK1"; break;}
case StressMeasure::PK2: {os << "PK2"; break;}
case StressMeasure::Kirchhoff: {os << "Kirchhoff"; break;}
case StressMeasure::Biot: {os << "Biot"; break;}
case StressMeasure::Mandel: {os << "Mandel"; break;}
default:
throw MaterialsToolboxError
("a stress measure must be missing");
break;
}
return os;
}
/* ---------------------------------------------------------------------- */
//! Material laws can declare which type of strain measure they require and
//! µSpectre will provide it
enum class StrainMeasure {
Gradient, Infinitesimal, GreenLagrange, Biot, Log, Almansi,
RCauchyGreen, LCauchyGreen, __nostrain__};
std::ostream & operator<<(std::ostream & os, StrainMeasure s) {
switch (s) {
case StrainMeasure::Gradient: {os << "Gradient"; break;}
case StrainMeasure::Infinitesimal: {os << "Infinitesimal"; break;}
case StrainMeasure::GreenLagrange: {os << "Green-Lagrange"; break;}
case StrainMeasure::Biot: {os << "Biot"; break;}
case StrainMeasure::Log: {os << "Logarithmic"; break;}
case StrainMeasure::Almansi: {os << "Almansi"; break;}
case StrainMeasure::RCauchyGreen: {os << "Right Cauchy-Green"; break;}
case StrainMeasure::LCauchyGreen: {os << "Left Cauchy-Green"; break;}
default:
throw MaterialsToolboxError
("a strain measure must be missing");
break;
}
return os;
}
/* ---------------------------------------------------------------------- */
/** Structure for functions returning PK1 stress from other stress measures
**/
namespace internal {
template <StressMeasure StressM,
StrainMeasure StrainM = StrainMeasure::__nostrain__>
struct PK1_stress {
template <class Stress_t, class Strain_t>
inline static decltype(auto)
compute(Stress_t && /*stress*/, Strain_t && /*strain*/) {
// 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 Stress_t, class Strain_t, class Stiffness_t>
inline static decltype(auto)
compute(Stress_t && /*stress*/, Stiffness_t && /*stiffness*/,
Strain_t && /*strain*/) {
// 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 <StrainMeasure StrainM>
struct PK1_stress<StressMeasure::PK1, StrainM>:
public PK1_stress<StressMeasure::__nostress__,
StrainMeasure::__nostrain__> {
template <class Stress_t, class Strain_t>
inline static decltype(auto)
compute(Stress_t && P, Strain_t && /*dummy*/) {
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 <>
struct PK1_stress<StressMeasure::PK1, StrainMeasure::Gradient>:
public PK1_stress<StressMeasure::PK1,
StrainMeasure::__nostrain__> {
template <class Stress_t, class Strain_t, class Stiffness_t>
decltype(auto)
compute(Stress_t && P, Stiffness_t && K, Strain_t && /*dummy*/) {
return std::forward_as_tuple(P, K);
}
};
/* ---------------------------------------------------------------------- */
/**
* Specialisation for the case where we get material stress (PK2)
*/
template <StrainMeasure StrainM>
struct PK1_stress<StressMeasure::PK2, StrainM>:
public PK1_stress<StressMeasure::__nostress__,
StrainMeasure::__nostrain__> {
template <class Stress_t, class Strain_t>
inline static decltype(auto)
compute(Stress_t && S, Strain_t && F) {
return F*S;
}
};
/* ---------------------------------------------------------------------- */
/**
* Specialisation for the case where we get material stress (PK2) derived
* with respect to Green-Lagrange strain
*/
template <>
struct PK1_stress<StressMeasure::PK2, StrainMeasure::GreenLagrange>:
public PK1_stress<StressMeasure::PK2,
StrainMeasure::__nostrain__> {
template <class Stress_t, class Strain_t, class Stiffness_t>
inline static decltype(auto)
compute(Stress_t && S, Stiffness_t && C, Strain_t && F) {
using T4 = typename Stiffness_t::PlainObject;
T4 K;
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) {
K(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) {
K(i,m,j,n) += F(i,r)*C(r,m,n,s)*(F(j,s));
}
}
}
}
}
}
return 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(Stress_t && stress,
Strain_t && strain) {
return internal::PK1_stress<StressM>::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 Stiffness_t>
decltype(auto) PK1_stress(Stress_t && stress,
Strain_t && strain,
Stiffness_t && stiffness) {
return internal::PK1_stress<StressM>::compute(std::move(stress),
std::move(strain),
std::move(stiffness));
};
/* ---------------------------------------------------------------------- */
/** 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>());
};
/* ---------------------------------------------------------------------- */
//! function returning expressions for PK2 stress and stiffness
template <class Tens1, class Tens2,
StressMeasure StressM, StrainMeasure StrainM>
decltype(auto) PK2_stress_stiffness(Tens1 && stress, Tens2 && F) {
}
} // MatTB
} // muSpectre
#endif /* MATERIALS_TOOLBOX_H */
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