Reference documentation for deal.II version GIT b6bf1e606d 2022-08-11 15:25:02+00:00
Physics::Notation Namespace Reference

## Namespaces

Kelvin
A namespace with functions that assist in the conversion of vectors and tensors to and from a compressed format using Kelvin notation and weighting.

## Detailed Description

Notations that reduce the order of tensors, effectively storing them in some sort of consistent compressed storage pattern. An example is storing the 6 independent components of $$3\times 3$$ symmetric tensors of rank 2 as a vector with 6 components, and then representing the 36 independent elements of symmetric $$3\times 3 \times 3\times 3$$ tensors of rank 4 (which when applied to a symmetric rank-2 tensor yields another symmetric rank-2 tensor) as a $$6 \times 6$$ matrix.

Although this method of representing tensors is most regularly associated with the efficient storage of the fourth-order elasticity tensor, with its generalization it has wider applicability. This representation is also common in the physics, material science and FEM literature.

There are several variations of tensor notation, each a slightly different structure. The primary difference between the various forms of tensor notation is the weighting prescribed to the various elements of the compressed tensors. This wikipedia article has some further general insights on this topic.