### Voigt Notation for Symmetric Tensors

Voigt notation is a way to represent a symmetric tensor by reducing its order. This is very useful when implementing finite element programs in Fortran. For example, the stress tensor in matrix representation is often given as

In Voigt notation, it is simplified to a vector:

For 2D problems, the stress tensor in matrix representation is simply

In Voigt notation, it becomes:

Note that the Voigt notation used in Abaqus software is slightly different. We will cover that later.