OOF2: The Manual


IsotropicRank4Tensor — Representations of an isotropic 4th rank tensor.


Subclasses are listed as they appear in the GUI and (in parentheses) as they appear in scripts.


The IsotropicRank4Tensor represents rank 4 tensor properties which are rotationally invariant, such as isotropic elasticity. The isotropic rank 4 tensor has two independent components, as shown in Figure 6.56. Because the elasticity literature uses many different representations of these two components, OOF2 allows you to enter the tensor in a variety of formats.

[Note] Note

The word rank has different meanings in different fields. Here it means the number of indices on a tensor. \(C_{ijkl}\) is a rank 4 tensor.

Figure 6.56. Structure of an Isotropic Fourth Rank Tensor

Isotropic rank 4 tensor diagram

Structure of an isotropic rank 4 tensor. For an explanation of the symbols, see Figure 6.57.

Figure 6.57. Key to the Tensor Diagrams

Key to the Tensor Diagrams

Symbols used in the tensor diagrams. The symmetries of symmetric fourth rank tensors, \(C_{ijkl}\), allow them to be displayed as second rank tensors, \(C_{IK}\), where \(I\) is the Voigt notation for \(ij\) and \(K\) is the Voigt notation for \(kl\). To keep things simple(?), the diagrams use Voigt notation for the columns and \(ij\) notation for the rows.