The VOIGT notation is used to exploit the symmetry of condensed matter to transform second-order tensors (cf. e.g. stress tensor) to vectors and kinetic forth-order tensors to square matrices (cf. e.g. elasticity tensor) . This notation is often used in continuum mechanics.
A symmetric tensor, for instance the stress tensor
in three dimensions, can be written as
This simplification can be often applied if only tensile or compressive stress in the direction of one main axis of an orthotropic material is considered.
For the strain tensor
the transformation is very similar. Due to
historical conventions, the resulting VOIGT-transform of the strain tensor
is the engineering strain