hookeai.simulators.fetorch.material.models.standard.drucker_prager.get_id_operators

get_id_operators(n_dim, device=None)

Set common second- and fourth-order identity operators.

Parameters:

• n_dim (int) – Number of dimensions.

• device (torch.device, default=None) – Device on which torch.Tensor is allocated.

Returns:

• soid (torch.Tensor(2d)) – Second-order identity tensor:

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

• foid (torch.Tensor(4d)) – Fourth-order identity tensor:

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

• fotransp (torch.Tensor(4d)) – Fourth-order transposition tensor:

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

• fosym (torch.Tensor(4d)) – Fourth-order symmetric projection tensor:

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

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

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

• fodevproj (torch.Tensor(4d)) – Fourth-order deviatoric projection tensor:

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

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

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