cratepy.tensor.tensoroperations.get_id_operators

get_id_operators(n_dim)

Set common second- and fourth-order identity operators.

Parameters:

n_dim (int) – Number of dimensions.

Returns:

• soid (numpy.ndarray (2d)) – Second-order identity tensor:

  \[I_{ij} = \delta_{ij}\]

• foid (numpy.ndarray (4d)) – Fourth-order identity tensor:

  \[I_{ijkl} = \delta_{ik}\delta_{jl}\]

• fotransp (numpy.ndarray (4d)) – Fourth-order transposition tensor:

  \[I_{ijkl} = \delta_{il}\delta_{jk}\]

• fosym (numpy.ndarray (4d)) – Fourth-order symmetric projection tensor:

  \[I_{ij} = 0.5(\delta_{ik}\delta_{jl} + \delta_{il}\delta_{jk})\]

• fodiagtrace (numpy.ndarray (4d)) – Fourth-order ‘diagonal trace’ tensor:

  \[I_{ijkl} = \delta_{ij}\delta_{kl}\]

• fodevproj (numpy.ndarray (4d)) – Fourth-order deviatoric projection tensor:

  \[I_{ijkl} = \delta_{ik}\delta_{jl} - \dfrac{1}{3} \delta_{ij}\delta_{kl}\]

• fodevprojsym (numpy.ndarray (4d)) – Fourth-order deviatoric projection tensor (second-order symmetric tensors):

  \[I_{ijkl} = 0.5(\delta_{ik}\delta_{jl} + \delta_{il}\delta_{jk}) - \dfrac{1}{3} \delta_{ij}\delta_{kl}\]