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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 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 VOIGT_CONVERSION_H
#define VOIGT_CONVERSION_H
#include "common/common.hh"
#include <Eigen/Dense>
#include <unsupported/Eigen/CXX11/Tensor>
#include <iostream>
namespace muSpectre {
/**
* compile time computation of voigt vector
*/
template<bool sym=true>
constexpr Dim_t vsize(Dim_t dim) {
if (sym) {
return (dim * (dim - 1) / 2 + dim);
} else {
return dim*dim;
}
}
/**
* 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
const static Eigen::Matrix<Dim_t, dim, dim> mat;
//! matrix of vector index I as function of tensor indices i,j
const static Eigen::Matrix<Dim_t, dim, dim> sym_mat;
//! array of matrix indices ij as function of vector index I
const static Eigen::Matrix<Dim_t, dim*dim, 2>vec;
//! factors to multiply the strain by for voigt notation
const static Eigen::Matrix<Real, vsize(dim), 1> factors;
};
//----------------------------------------------------------------------------//
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);
}
}
} // muSpectre
#endif /* VOIGT_CONVERSION_H */

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