transfer.hpp

Overview 

Functions for transferring quantities between Voigt notation (6-vectors) and full tensor form (3x3 matrices), as well as fourth-order tensor conversions.

API Reference 

arma::mat v2t_strain(const arma::vec &v)

Provides the matrix (3x3 arma::mat) version of a strain tensor initially written with Voigt notation (arma::vec size=6)

Example:

vec v = randu(6);
mat m = v2t_strain(v);

Parameters:: v – (arma::vec size=6) the strain tensor written in with Voigt notation
Returns:: (3x3 arma::mat) the strain tensor written as a 3x3 matrix

arma::vec t2v_strain(const arma::mat &m)

Provides the Voigt notation (arma::vec size=6) version of a strain tensor initially written using a matrix format (3x3 arma::mat)

Example:

mat m = randu(3,3);
vec v = t2v_strain(m);

Parameters:: m – (3x3 arma::mat) the strain tensor written as a 3x3 matrix
Returns:: (arma::vec size=6) the strain tensor written in with Voigt notation

arma::mat v2t_stress(const arma::vec &v)

Provides the matrix (3x3 arma::mat) version of a stress tensor initially written with Voigt notation (arma::vec size=6)

Example:

vec v = randu(6);
mat m = v2t_stress(v);

Parameters:: v – (arma::vec size=6) the stress tensor written in with Voigt notation
Returns:: (3x3 arma::mat) the stress tensor written as a 3x3 matrix

arma::vec t2v_stress(const arma::mat &m)

Provides the Voigt notation (arma::vec size=6) version of a stress tensor initially written using a matrix format (3x3 arma::mat)

Example:

mat m = randu(3,3);
vec v = t2v_stress(m);

Parameters:: m – (3x3 arma::mat) the stress tensor written as a 3x3 matrix
Returns:: (arma::vec size=6) the stress tensor written in with Voigt notation

arma::vec t2v_sym(const arma::mat &m)

Provides the Voigt notation (arma::vec size=6) version of a symmetric tensor initially written using a matrix format (3x3 arma::mat)

Note that the 6 components are organized as the following (it is a column vector) : \( \mathbf{v} \equiv \left( m_{11},m_{22},m_{33},m_{12},m_{13},m_{23} right) \)

Example:

mat m = randu(3,3);
vec v = t2v_sym(m);

Parameters:: m – (3x3 arma::mat) the symmetric tensor written as a 3x3 matrix
Returns:: (arma::vec size=6) the symmetric tensor written in with Voigt notation

arma::mat v2t_sym(const arma::vec &v)

Provides the matrix (3x3 arma::mat) version of a symmetric tensor initially written with Voigt notation (arma::vec size=6)

Note that the 6 components are organized as the following (it is a column vector) : \( \mathbf{v} \equiv \left( m_{11},m_{22},m_{33},m_{12},m_{13},m_{23} right) \)

Example:

vec v = randu(6);
mat m = v2t_sym(v);

Parameters:: v – (arma::vec size=6) the symmetric tensor written in with Voigt notation
Returns:: (3x3 arma::mat) the symmetric tensor written as a 3x3 matrix

arma::mat v2t_skewsym(const arma::vec &v)

Provides the matrix (3x3 arma::mat) version of a skew-symmetric tensor initially written with Voigt notation (arma::vec size=6)

Note that the 6 components are organized as the following (it is a column vector) : \( \mathbf{v} \equiv \left( m_{11},m_{22},m_{33},m_{12},m_{13},m_{23} right) \)

so that the components \( m_{21} = -m_{12}, \quad m_{31} = -m_{13}, \quad m_{32} = -m_{23} \) so that:

\[\begin{split} m = \left( \begin{array}{ccc} v_1 & v_4 & v_5 \\ -v_4 & v_2 & v_6 \\ v_5 & -v_6 & v_3 \end{array} \right) \end{split}\]

Example:

vec v = randu(6);
mat m = v2t_skewsym(v);

Parameters:: v – (arma::vec size=6) the skew-symmetric tensor written in with Voigt notation
Returns:: (3x3 arma::mat) the skew-symmetric tensor written as a 3x3 matrix

arma::mat v2t(const arma::vec &v)

Provides the matrix (3x3 arma::mat) version of a tensor initially written with Voigt notation (arma::vec size=9)

Note that the 9 components are organized as the following (it is a column vector) : \( \mathbf{v} \equiv \left( m_{11},m_{12},m_{13},m_{21},m_{22},m_{23},m_{31},m_{32},m_{33} right) \) So that this operation is the opposite of a flatten (.as_col() for armadillo matrix to column vectors)

Example:

vec v = randu(9);
mat m = v2t(v);

Parameters:: v – (arma::vec size=9) the flatten tensor written in with Voigt notation
Returns:: (3x3 arma::mat) the tensor written as a 3x3 matrix

FTensor::Tensor1<double, 3> vec_FTensor1(const arma::vec &v)

Provides the FTensor vector (Tensor1<double,3>) of a dimension 3 colvec (arma::vec size=3)

Example:

vec v = randu(3);
FTensor::Tensor1<double,3> F1 = vec_FTensor1(v);

Parameters:: v – (arma::vec size=3) the column tensor
Returns:: (Tensor1<double,3>) the Ftensor of dimension 1, size=3

FTensor::Tensor2<double, 3, 3> mat_FTensor2(const arma::mat &m)

Provides the FTensor matrix (Tensor2<double,3,3>) of a 3x3 armadillo matrix (arma::mat 3x3)

Example:

mat m = randu(3,3);
FTensor::Tensor2<double,3,3> FT2 = mat_FTensor2(m);

Parameters:: m – (arma::mat 3x3) the armadillo matrix
Returns:: (Tensor2<double,3,3>) the Ftensor of dimension 2, size=3x3

FTensor::Tensor2<double, 3, 3> v_FTensor2_strain(const arma::vec &v)

Provides the FTensor matrix (Tensor2<double,3,3>) of armadillo column vector that correspond to a strain vector in Voigt notation (arma::vec size=6)

Example:

mat m = randu(3,3);
vec v = t2v_strain(m);
FTensor::Tensor2<double,3,3> FT2_strain = v_FTensor2_strain(v);

Parameters:: v – (arma::vec size=6) the strain tensor written in with Voigt notation
Returns:: (Tensor2<double,3,3>) the Ftensor of dimension 2, size=3x3

FTensor::Tensor2<double, 3, 3> v_FTensor2_stress(const arma::vec &v)

Provides the FTensor matrix (Tensor2<double,3,3>) of armadillo column vector that correspond to a stress vector in Voigt notation (arma::vec size=6)

Example:

mat m = randu(3,3);
vec v = t2v_strain(m);
FTensor::Tensor2<double,3,3> FT2_strain = v_FTensor2_strain(v);

Parameters:: v – (arma::vec size=6) the strain tensor written in with Voigt notation
Returns:: (Tensor2<double,3,3>) the Ftensor of dimension 2, size=3x3

arma::vec FTensor1_vec(const FTensor::Tensor1<double, 3> &FT1)

Provides an armadillo vector (arma::vec size=3) from a FTensor Tensor of the 1st rank (Tensor1<double,3>)

Example:

FTensor::Tensor1<double,3> FT1 {0,1,2};
arma::vec v = FTensor1_vec(FT1);

Parameters:: FT1 – (FTensor::Tensor1<double,3>) the FTensor of rank 1, and dimension 3
Returns:: (arma::vec size=3) the corresponding armadillo vector

arma::mat FTensor2_mat(const FTensor::Tensor2<double, 3, 3> &FT2)

Provides an armadillo matrix (arma::mat 3x3) to a FTensor Tensor of the 2nd rank (Tensor2<double,3,3>)

Example:

FTensor::Tensor2<double,3,3> FT2 {00, 01, 02
                                  10, 11, 12
                                  20, 21, 22};
arma::mat m = FTensor2_mat(FT2);

Parameters:: FT2 – (Tensor2<double,3,3>) the Ftensor of dimension 2, size=3x3
Returns:: (arma::mat 3x3) the corresponding armadillo matrix

arma::vec FTensor2_v_strain(const FTensor::Tensor2<double, 3, 3> &FT2)

Provides an armadillo vec in Voigt notation (arma::vec size=6) from a strain tensor expressed as a FTensor Tensor of the 2nd rank (Tensor2<double,3,3>)

Example:

FTensor::Tensor2<double,3,3> FT2 {00, 01, 02
                                  10, 11, 12
                                  20, 21, 22};
arma::vec E = FTensor2_v_strain(FT2);

Parameters:: FT2 – (Tensor2<double,3,3>) the Ftensor of dimension 2, size=3x3
Returns:: (arma::vec size=6) the corresponding armadillo strain vector in Voigt notation

arma::vec FTensor2_v_stress(const FTensor::Tensor2<double, 3, 3> &FT2)

Provides an armadillo vec in Voigt notation (arma::vec size=6) from a stress tensor expressed as a FTensor Tensor of the 2nd rank (Tensor2<double,3,3>)

Example:

FTensor::Tensor2<double,3,3> FT2 {00, 01, 02
                                  10, 11, 12
                                  20, 21, 22};
arma::vec sigma = FTensor2_v_stress(FT2);

Parameters:: FT2 – (Tensor2<double,3,3>) the Ftensor of dimension 2, size=3x3
Returns:: (arma::vec size=6) the corresponding armadillo strain vector in Voigt notation

arma::mat FTensor4_mat(const FTensor::Tensor4<double, 3, 3, 3, 3> &FT4)

Provides an armadillo (stiffness) mat in Voigt notation (arma::mat 6x6) from a 4th order tensor expressed as a FTensor (Tensor2<double,3,3,3,3>)

Example:

Tensor2<double,3,3> A_ = mat_FTensor2(A);
Tensor4<double,3,3,3,3> C_;

Index<'i', 3> i;
Index<'j', 3> j;
Index<'k', 3> k;
Index<'l', 3> l;
       
C_(i,j,k,l) = A_(i,j)*A_(k,l);
return FTensor4_mat(C_);

Parameters:: FT4 – (Tensor4<double,3,3,3,3>) the (stifness) tensor Ftensor of dimension 4, size=3x3x3x3
Returns:: (arma::mat 6x6) the corresponding armadillo (stiffness) matrix in Voigt notation

FTensor::Tensor4<double, 3, 3, 3, 3> mat_FTensor4(const arma::mat &L)

Provides a 4th order (stiffness) tensor expressed as a FTensor (Tensor2<double,3,3,3,3>) from an armadillo (stiffness) mat in Voigt notation (arma::mat 6x6)

Example:

mat L = randu(6,6);
   Tensor4<double,3,3,3,3> C;  
C = mat_FTensor4(L);

Parameters:: L – (arma::mat 6x6) the corresponding armadillo (stiffness) matrix in Voigt notation
Returns:: (Tensor4<double,3,3,3,3>) the (stifness) tensor Ftensor of dimension 4, size=3x3x3x3

transfer.hpp

Overview

API Reference

Overview 

API Reference 