12 #include <Eigen/Dense>
20 namespace KelvinVector
25 if (displacement_dim == 2)
29 else if (displacement_dim == 3)
34 "Cannot convert displacement dimension {} to kelvin vector dimension.",
45 template <
int DisplacementDim>
53 template <
int DisplacementDim>
61 template <
int KelvinVectorSize>
64 static_assert(KelvinVectorSize == 4 || KelvinVectorSize == 6,
65 "KelvinVector invariants for vectors of size different than "
66 "4 or 6 is not allowed.");
69 static Eigen::Matrix<double, KelvinVectorSize, KelvinVectorSize>
const
73 static Eigen::Matrix<double, KelvinVectorSize, KelvinVectorSize>
const
76 static Eigen::Matrix<double, KelvinVectorSize, 1>
const identity2;
80 Eigen::Matrix<double, KelvinVectorSize, 1>
const& v);
85 Eigen::Matrix<double, KelvinVectorSize, 1>
const& deviatoric_v);
89 Eigen::Matrix<double, KelvinVectorSize, 1>
const& deviatoric_v);
94 Eigen::Matrix<double, KelvinVectorSize, 1>
const& deviatoric_v);
99 Eigen::Matrix<double, KelvinVectorSize, 1>
const& deviatoric_v);
102 static double trace(Eigen::Matrix<double, KelvinVectorSize, 1>
const& v);
107 Eigen::Matrix<double, KelvinVectorSize, 1>
const& v);
116 template <
int KelvinVectorSize>
117 Eigen::Matrix<double, KelvinVectorSize, 1, Eigen::ColMajor, KelvinVectorSize, 1>
127 template <
int KelvinVectorSize>
137 template <
int DisplacementDim>
139 Eigen::Matrix<double, 3, 3>
const& m);
152 template <
int KelvinVectorSize>
153 Eigen::Matrix<double, KelvinVectorSize, 1, Eigen::ColMajor, KelvinVectorSize, 1>
168 template <
typename Derived>
169 Eigen::Matrix<double, Eigen::MatrixBase<Derived>::RowsAtCompileTime, 1>
173 (Eigen::MatrixBase<Derived>::ColsAtCompileTime == 1) ||
174 (Eigen::MatrixBase<Derived>::ColsAtCompileTime == Eigen::Dynamic),
175 "KelvinVector must be a column vector");
179 "KelvinVector must be a column vector, but input has {:d} columns.",
183 Eigen::Matrix<double, Eigen::MatrixBase<Derived>::RowsAtCompileTime, 1>
188 result << v[0], v[1], v[2], v[3] * std::sqrt(2.);
190 else if (v.rows() == 6)
193 result << v[0], v[1], v[2], v[3] * std::sqrt(2.), v[4] * std::sqrt(2.),
194 v[5] * std::sqrt(2.);
199 "Symmetric tensor to Kelvin vector conversion expected an input "
200 "vector of size 4 or 6, but a vector of size {:d} was given.",
210 template <
int DisplacementDim>
212 std::vector<double>
const& values)
214 constexpr
int kelvin_vector_size =
217 if (values.size() != kelvin_vector_size)
220 "Symmetric tensor to Kelvin vector conversion expected an input "
221 "vector of size {:d}, but a vector of size {:d} was given.",
222 kelvin_vector_size, values.size());
227 DisplacementDim>
const>(
235 template <
int DisplacementDim>
237 Eigen::Matrix<
double, DisplacementDim, DisplacementDim, Eigen::ColMajor,
238 DisplacementDim, DisplacementDim>
const& transformation);
Eigen::Matrix< double, 4, 1 > kelvinVectorToSymmetricTensor(Eigen::Matrix< double, 4, 1, Eigen::ColMajor, 4, 1 > const &v)
Eigen::Matrix< double, kelvin_vector_dimensions(DisplacementDim), 1, Eigen::ColMajor > KelvinVectorType
constexpr int kelvin_vector_dimensions(int const displacement_dim)
Kelvin vector dimensions for given displacement dimension.
Eigen::Matrix< double, 3, 3 > kelvinVectorToTensor(Eigen::Matrix< double, 4, 1, Eigen::ColMajor, 4, 1 > const &v)
Eigen::Matrix< double, kelvin_vector_dimensions(DisplacementDim), kelvin_vector_dimensions(DisplacementDim), Eigen::RowMajor > KelvinMatrixType
Eigen::Matrix< double, 4, 1, Eigen::ColMajor, 4, 1 > inverse(Eigen::Matrix< double, 4, 1, Eigen::ColMajor, 4, 1 > const &v)
KelvinVectorType< DisplacementDim > tensorToKelvin(Eigen::Matrix< double, 3, 3 > const &m)
KelvinMatrixType< DisplacementDim > fourthOrderRotationMatrix(Eigen::Matrix< double, DisplacementDim, DisplacementDim, Eigen::ColMajor, DisplacementDim, DisplacementDim > const &transformation)
Eigen::Matrix< double, Eigen::MatrixBase< Derived >::RowsAtCompileTime, 1 > symmetricTensorToKelvinVector(Eigen::MatrixBase< Derived > const &v)
static double FrobeniusNorm(Eigen::Matrix< double, KelvinVectorSize, 1 > const &deviatoric_v)
Get the norm of the deviatoric stress.
static Eigen::Matrix< double, KelvinVectorSize, 1 > const identity2
Kelvin mapping of 2nd order identity tensor.
static Eigen::Vector3d diagonal(Eigen::Matrix< double, KelvinVectorSize, 1 > const &v)
static double trace(Eigen::Matrix< double, KelvinVectorSize, 1 > const &v)
Trace of the corresponding tensor.
static Eigen::Matrix< double, KelvinVectorSize, KelvinVectorSize > const spherical_projection
static double J2(Eigen::Matrix< double, KelvinVectorSize, 1 > const &deviatoric_v)
static Eigen::Matrix< double, KelvinVectorSize, KelvinVectorSize > const deviatoric_projection
static double determinant(Eigen::Matrix< double, KelvinVectorSize, 1 > const &v)
Determinant of a matrix in Kelvin vector representation.
static double equivalentStress(Eigen::Matrix< double, KelvinVectorSize, 1 > const &deviatoric_v)
static double J3(Eigen::Matrix< double, KelvinVectorSize, 1 > const &deviatoric_v)