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muSpectre/src/common/voigt_conversion.hh
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/**
* @file voigt_conversion.hh
*
* @author Till Junge <till.junge@epfl.ch>
*
* @date 02 May 2017
*
* @brief utilities to transform vector notation arrays into voigt notation
* arrays and vice-versa
*
* Copyright © 2017 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_COMMON_VOIGT_CONVERSION_HH_
#define SRC_COMMON_VOIGT_CONVERSION_HH_
#include "common/common.hh"
#include <Eigen/Dense>
#include <unsupported/Eigen/CXX11/Tensor>
#include <iostream>
namespace muSpectre {
/**
* implements a bunch of static functions to convert between full
* and Voigt notation of tensors
*/
template <Dim_t dim> class VoigtConversion {
public:
VoigtConversion();
virtual ~VoigtConversion();
//! obtain a fourth order voigt matrix from a tensor
template <class Tens4, class Voigt, bool sym = true>
inline static void fourth_to_voigt(const Tens4 & t, Voigt & v);
//! return a fourth order voigt matrix from a tensor
template <class Tens4, bool sym = true>
inline static Eigen::Matrix<Real, vsize<sym>(dim), vsize<sym>(dim)>
fourth_to_voigt(const Tens4 & t);
//! return a fourth order non-symmetric voigt matrix from a tensor
template <class Tens4>
inline static Eigen::Matrix<Real, vsize<false>(dim), vsize<false>(dim)>
fourth_to_2d(const Tens4 & t) {
return fourth_to_voigt<Tens4, false>(t);
}
//! probably obsolete
template <class Tens2, class Voigt, bool sym = true>
inline static void second_to_voigt(const Tens2 & t, Voigt & v);
//! probably obsolete
template <class Tens2, class Voigt>
inline static void gradient_to_voigt_strain(const Tens2 & F, Voigt & v);
//! probably obsolete
template <class Tens2, class Voigt>
inline static void gradient_to_voigt_GreenLagrange_strain(const Tens2 & F,
Voigt & v);
//! probably obsolete
template <class Tens2, class Voigt, bool sym = true>
inline static void stress_from_voigt(const Voigt & v, Tens2 & sigma);
public:
//! matrix of vector index I as function of tensor indices i,j
static const Eigen::Matrix<Dim_t, dim, dim> mat;
//! matrix of vector index I as function of tensor indices i,j
static const Eigen::Matrix<Dim_t, dim, dim> sym_mat;
//! array of matrix indices ij as function of vector index I
static const Eigen::Matrix<Dim_t, dim * dim, 2> vec;
//! factors to multiply the strain by for voigt notation
static const Eigen::Matrix<Real, vsize(dim), 1> factors;
};
//! voigt vector indices for non-symmetric tensors
template <>
const Eigen::Matrix<Dim_t, 1, 1>
VoigtConversion<1>::mat = (Eigen::Matrix<Dim_t, 1, 1>() << 0).finished();
//! voigt vector indices for non-symmetric tensors
template <>
const Eigen::Matrix<Dim_t, 2, 2> VoigtConversion<2>::mat =
(Eigen::Matrix<Dim_t, 2, 2>() << 0, 2, 3, 1).finished();
//! voigt vector indices for non-symmetric tensors
template <>
const Eigen::Matrix<Dim_t, 3, 3> VoigtConversion<3>::mat =
(Eigen::Matrix<Dim_t, 3, 3>() << 0, 5, 4, 8, 1, 3, 7, 6, 2).finished();
//! voigt vector indices
template <>
const Eigen::Matrix<Dim_t, 1, 1> VoigtConversion<1>::sym_mat =
(Eigen::Matrix<Dim_t, 1, 1>() << 0).finished();
//! voigt vector indices
template <>
const Eigen::Matrix<Dim_t, 2, 2> VoigtConversion<2>::sym_mat =
(Eigen::Matrix<Dim_t, 2, 2>() << 0, 2, 2, 1).finished();
//! voigt vector indices
template <>
const Eigen::Matrix<Dim_t, 3, 3> VoigtConversion<3>::sym_mat =
(Eigen::Matrix<Dim_t, 3, 3>() << 0, 5, 4, 5, 1, 3, 4, 3, 2).finished();
//! matrix indices from voigt vectors
template <>
const Eigen::Matrix<Dim_t, 1 * 1, 2> VoigtConversion<1>::vec =
(Eigen::Matrix<Dim_t, 1 * 1, 2>() << 0, 0).finished();
//! matrix indices from voigt vectors
template <>
const Eigen::Matrix<Dim_t, 2 * 2, 2> VoigtConversion<2>::vec =
(Eigen::Matrix<Dim_t, 2 * 2, 2>() << 0, 0, 1, 1, 0, 1, 1, 0).finished();
//! matrix indices from voigt vectors
template <>
const Eigen::Matrix<Dim_t, 3 * 3, 2>
VoigtConversion<3>::vec = (Eigen::Matrix<Dim_t, 3 * 3, 2>() << 0, 0, 1, 1,
2, 2, 1, 2, 0, 2, 0, 1, 2, 1, 2, 0, 1, 0)
.finished();
//! factors for shear components in voigt notation
template <>
const Eigen::Matrix<Real, vsize(1), 1> VoigtConversion<1>::factors =
(Eigen::Matrix<Real, vsize(1), 1>() << 1).finished();
//! factors for shear components in voigt notation
template <>
const Eigen::Matrix<Real, vsize(2), 1> VoigtConversion<2>::factors =
(Eigen::Matrix<Real, vsize(2), 1>() << 1, 1, 2).finished();
//! factors for shear components in voigt notation
template <>
const Eigen::Matrix<Real, vsize(3), 1> VoigtConversion<3>::factors =
(Eigen::Matrix<Real, vsize(3), 1>() << 1, 1, 1, 2, 2, 2).finished();
//----------------------------------------------------------------------------//
template <Dim_t dim>
template <class Tens4, class Voigt, bool sym>
inline void VoigtConversion<dim>::fourth_to_voigt(const Tens4 & t,
Voigt & v) {
// upper case indices for Voigt notation, lower case for standard tensorial
for (Dim_t I = 0; I < vsize<sym>(dim); ++I) {
auto && i = vec(I, 0);
auto && j = vec(I, 1);
for (Dim_t J = 0; J < vsize<sym>(dim); ++J) {
auto && k = vec(J, 0);
auto && l = vec(J, 1);
v(I, J) = t(i, j, k, l);
}
}
}
//----------------------------------------------------------------------------//
template <Dim_t dim>
template <class Tens4, bool sym>
inline Eigen::Matrix<Real, vsize<sym>(dim), vsize<sym>(dim)>
VoigtConversion<dim>::fourth_to_voigt(const Tens4 & t) {
using V_t = Eigen::Matrix<Real, vsize<sym>(dim), vsize<sym>(dim)>;
V_t temp;
fourth_to_voigt<decltype(t), V_t, sym>(t, temp);
return temp;
}
//----------------------------------------------------------------------------//
template <Dim_t dim>
template <class Tens2, class Voigt, bool sym>
inline void VoigtConversion<dim>::second_to_voigt(const Tens2 & F,
Voigt & v) {
for (Dim_t I = 0; I < vsize(dim); ++I) {
auto && i = vec(I, 0);
auto && j = vec(I, 1);
v(I) = F(i, j);
}
}
//----------------------------------------------------------------------------//
template <Dim_t dim>
template <class Tens2, class Voigt>
inline void VoigtConversion<dim>::gradient_to_voigt_strain(const Tens2 & F,
Voigt & v) {
for (Dim_t I = 0; I < vsize(dim); ++I) {
auto && i = vec(I, 0);
auto && j = vec(I, 1);
v(I) = (F(i, j) + F(j, i)) / 2 * factors(I);
}
}
//----------------------------------------------------------------------------//
template <Dim_t dim>
template <class Tens2, class Voigt>
inline void
VoigtConversion<dim>::gradient_to_voigt_GreenLagrange_strain(const Tens2 & F,
Voigt & v) {
using mat = Eigen::Matrix<Real, dim, dim>;
mat E = 0.5 * (F.transpose() * F - mat::Identity());
for (Dim_t I = 0; I < vsize(dim); ++I) {
auto && i = vec(I, 0);
auto && j = vec(I, 1);
v(I) = E(i, j) * factors(I);
}
}
} // namespace muSpectre
#endif // SRC_COMMON_VOIGT_CONVERSION_HH_
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