OOF2: The Manual

`IsotropicRank4Tensor`
	6.5.1. Base RegisteredClasses

Name

IsotropicRank4Tensor — Representations of an isotropic 4th rank tensor.

Subclasses

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

Cij (IsotropicRank4TensorCij) -- Explicit representation in terms of tensor components.
Lame (IsotropicRank4TensorLame) -- Isotropic rank 4 tensor in terms of Lame coefficients.
E and nu (IsotropicRank4TensorEnu) -- Isotropic rank 4 tensor in terms of Young's modulus and Poisson's ratio.
Bulk and Shear (IsotropicRank4TensorBulkShear) -- Isotropic rank 4 tensor in terms of bulk and shear moduli.

Description

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
	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

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

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.


`Invariant`		`IterationManager`