26 if (displacement_dim == 2)
30 else if (displacement_dim == 3)
35 "Cannot convert displacement dimension {} to kelvin vector dimension.",
46template <
int DisplacementDim>
54template <
int DisplacementDim>
62template <
int KelvinVectorSize>
65 static_assert(KelvinVectorSize == 4 || KelvinVectorSize == 6,
66 "KelvinVector invariants for vectors of size different than "
67 "4 or 6 is not allowed.");
70 static Eigen::Matrix<double, KelvinVectorSize, KelvinVectorSize>
const
74 static Eigen::Matrix<double, KelvinVectorSize, KelvinVectorSize>
const
77 static Eigen::Matrix<double, KelvinVectorSize, 1>
const identity2;
81 Eigen::Matrix<double, KelvinVectorSize, 1>
const&
v);
86 Eigen::Matrix<double, KelvinVectorSize, 1>
const& deviatoric_v);
90 Eigen::Matrix<double, KelvinVectorSize, 1>
const& deviatoric_v);
95 Eigen::Matrix<double, KelvinVectorSize, 1>
const& deviatoric_v);
100 Eigen::Matrix<double, KelvinVectorSize, 1>
const& deviatoric_v);
103 static double trace(Eigen::Matrix<double, KelvinVectorSize, 1>
const&
v);
108 Eigen::Matrix<double, KelvinVectorSize, 1>
const&
v);
117template <
int KelvinVectorSize>
118Eigen::Matrix<double, KelvinVectorSize, 1, Eigen::ColMajor, KelvinVectorSize, 1>
128template <
int KelvinVectorSize>
138template <
int DisplacementDim>
140 Eigen::Matrix<double, 3, 3>
const& m);
153template <
int KelvinVectorSize>
154Eigen::Matrix<double, KelvinVectorSize, 1, Eigen::ColMajor, KelvinVectorSize, 1>
169template <
typename Derived>
170Eigen::Matrix<double, Eigen::MatrixBase<Derived>::RowsAtCompileTime, 1>
174 (Eigen::MatrixBase<Derived>::ColsAtCompileTime == 1) ||
175 (Eigen::MatrixBase<Derived>::ColsAtCompileTime == Eigen::Dynamic),
176 "KelvinVector must be a column vector");
180 "KelvinVector must be a column vector, but input has {:d} columns.",
184 Eigen::Matrix<double, Eigen::MatrixBase<Derived>::RowsAtCompileTime, 1>
189 result <<
v[0],
v[1],
v[2],
v[3] * std::sqrt(2.);
191 else if (
v.rows() == 6)
194 result <<
v[0],
v[1],
v[2],
v[3] * std::sqrt(2.),
v[4] * std::sqrt(2.),
195 v[5] * std::sqrt(2.);
200 "Symmetric tensor to Kelvin vector conversion expected an input "
201 "vector of size 4 or 6, but a vector of size {:d} was given.",
211template <
int DisplacementDim>
213 std::vector<double>
const& values)
215 constexpr int kelvin_vector_size =
218 if (values.size() != kelvin_vector_size)
221 "Symmetric tensor to Kelvin vector conversion expected an input "
222 "vector of size {:d}, but a vector of size {:d} was given.",
223 kelvin_vector_size, values.size());
228 DisplacementDim>
const>(
235template <
int DisplacementDim>
236Eigen::Matrix<double, DisplacementDim,
242template <
int DisplacementDim>
244 Eigen::Matrix<
double, DisplacementDim,
251template <
int DisplacementDim>
253 Eigen::Matrix<
double, DisplacementDim, DisplacementDim, Eigen::ColMajor,
254 DisplacementDim, DisplacementDim>
const& transformation);
Eigen::Matrix< double, kelvin_vector_dimensions(DisplacementDim), 1, Eigen::ColMajor > KelvinVectorType
Eigen::Matrix< double, DisplacementDim, 1 > reduceKelvinToVector(Eigen::Matrix< double, DisplacementDim, kelvin_vector_dimensions(DisplacementDim)> const &m)
KelvinMatrixType< DisplacementDim > fourthOrderRotationMatrix(Eigen::Matrix< double, DisplacementDim, DisplacementDim, Eigen::ColMajor, DisplacementDim, DisplacementDim > const &transformation)
Eigen::Matrix< double, 4, 1 > kelvinVectorToSymmetricTensor(Eigen::Matrix< double, 4, 1, Eigen::ColMajor, 4, 1 > const &v)
constexpr int kelvin_vector_dimensions(int const displacement_dim)
Kelvin vector dimensions for given displacement dimension.
Eigen::Matrix< double, Eigen::MatrixBase< Derived >::RowsAtCompileTime, 1 > symmetricTensorToKelvinVector(Eigen::MatrixBase< Derived > const &v)
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, DisplacementDim, kelvin_vector_dimensions(DisplacementDim)> liftVectorToKelvin(Eigen::Matrix< double, DisplacementDim, 1 > const &v)
KelvinVectorType< DisplacementDim > tensorToKelvin(Eigen::Matrix< double, 3, 3 > const &m)
Eigen::Matrix< double, 4, 1, Eigen::ColMajor, 4, 1 > inverse(Eigen::Matrix< double, 4, 1, Eigen::ColMajor, 4, 1 > 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)