stress.rst

The Transfer Library

.. default-domain:: cpp

.. function:: mat v2t_strain(const vec &v)

    Converts a second order strain tensor written as a vector v in the 'simcoon' formalism into a second order strain tensor written as a matrix m.

    .. code-block:: cpp

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

.. function:: vec t2v_strain (const mat &strain)

    Converts a second order strain tensor written as a matrix m in the 'simcoon' formalism into a second order strain tensor written as a vector v.

    .. code-block:: cpp

        mat m = randu(6,6);
        vec v = t2v_strain(m);

.. function:: mat v2t_stress(const vec &v)

    Converts a second order stress tensor written as a vector v in the 'simcoon' formalism into a second order stress tensor written as a matrix m.

    .. code-block:: cpp

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

.. function:: vec t2v_stress (const mat &stress)

    Converts a second order stress tensor written as a matrix m in the 'simcoon' formalism into a second order stress tensor written as a vector v.

    .. code-block:: cpp

        mat m = randu(6,6);
        vec v = t2v_stress(m);

.. function:: mat v2t_stress(const vec &v)

    Converts a second order stress tensor written as a vector v in the 'simcoon' formalism into a second order stress tensor written as a matrix m.

    .. code-block:: cpp

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

.. function:: vec t2v_sym(const mat &m)

    Converts a 3x3 symmetric matrix into a 6 component vector {11,22,33,12,13,23}

    .. code-block:: cpp

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

.. function:: mat v2t_sym(const vec &v)

    Converts a 6 component vector {11,22,33,12,13,23} into a 3x3 symmetric matrix

    .. code-block:: cpp

        vec v = randu(6);
        mat m = t2v_sym(m);

.. function:: mat v2t_skewsym(const vec &v)

    Converts a 6 component vector {11,22,33,12,13,23} into a 3x3 antisymmetric matrix, while keeping the diagonal components

    .. math::

        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)

    .. code-block:: cpp

        vec v = randu(6);
        mat m = t2v_sym(m);

.. function:: mat v2t(const vec &v)

    Converts a 9 component vector {11,12,13,21,22,23,31,32,33} into a 3x3 symmetric matrix

vec v = randu(9);
mat m = t2v(m);

.. function:: Tensor1<double,3> vec_FTensor1(const vec &v)

    Converts an armadillo colvec of size 3 to a FTensor Tensor of the 1st rank

    .. code-block:: cpp

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

.. function:: Tensor1<double,3> vec_FTensor1(const vec &v)

    Converts an armadillo colvec of size 3 to a FTensor Tensor of the 1st rank

    .. code-block:: cpp

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

.. function:: Tensor2<double,3,3> mat_FTensor2(const mat &m)

Converts an armadillo 3x3 matrix to a FTensor Tensor of the 2nd rank

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

.. function:: Tensor2<double,3,3> v_FTensor2_strain(const vec &v)

Converts an armadillo column vector (6) that correspond to a strain vector in Voigt notation to a FTensor Tensor of the 2nd rank

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

.. function:: Tensor2<double,3,3> v_FTensor2_stress(const vec &v)

    Converts an armadillo column vector (6) that correspond to a stress vector in Voigt notation to a FTensor Tensor of the 2nd rank

    .. code-block:: cpp

        mat m = randu(3,3);
        vec v = t2v_stress(m);
        FTensor::Tensor2<double,3,3> = v_FTensor2_stress(v);

.. function:: mat FTensor4_mat(const Tensor4<double,3,3,3,3> &C)

    Converts a FTensor 4th order tensor with minor symmetries into an armadillo 6x6 matrix

    .. code-block:: cpp

        Tensor4<double,3,3,3,3> C;
        ... fill L_tilde to obtain a stiffness 4th order tensor
        mat L = FTensor4_mat(C);

.. function:: Tensor4<double,3,3,3,3> mat_FTensor4(const mat &L)

    Converts a FTensor 4th order tensor with minor symmetries into an armadillo 6x6 matrix

    .. code-block:: cpp

    mat L = L_iso(70000,0.3,'Enu');
    Tensor4<double,3,3,3,3> C = mat_FTensor4(L);

.. function:: mat B_klmn(const vec &b_i, const vec &b_j)