Applications
The notation is named after physicist Woldemar Voigt. It is useful, for example, in calculations involving constitutive models to simulate materials, such as the generalized Hooke's law, as well as finite element analysis.
Hooke's law has a symmetric fourth-order stiffness tensor with 81 components (3×3×3×3). Voigt notation enables this to be simplified to a 6×6 matrix. However, Voigt's form does not preserve the sum of the squares, which in the case of Hooke's law has geometric significance. This explains why weights are introduced (to make the mapping an isometry).
A discussion of invariance of Voigt's notation and Mandel's notation be found in Helnwein (2001).
Read more about this topic: Voigt Notation