  Classical continuum mechanical theories operate on three-dimensional
Eu-clidian space using scalar, vector, and tensor-valued quantities usually up
to the order of four. For their numerical treatment, it is common practice to
transform the relations into a matrix-vector format. This transformation is
usually performed using the so-called Voigt mapping. This mapping does not
preserve tensor character leaving significant room for error as stress and
strain quantities follow from different mappings and thus have to be treated
differently in certain mathematical operations. Despite its conceptual and
notational difficulties having been pointed out, the Voigt mapping remains the
foundation of most current finite element programmes. An alternative is the
so-called Kelvin mapping which has recently gained recognition in studies of
theoretical mechanics. This article is concerned with benefits of the Kelvin
mapping in numerical modelling tools such as finite element software. The
decisive difference to the Voigt mapping is that Kelvin's method preserves
tensor character, and thus the numerical matrix notation directly corresponds
to the original tensor notation. Further benefits in numerical implementations
are that tensor norms are calculated identically without distinguishing stress
or strain-type quantities and tensor equations can be directly transformed into
matrix equations without additional considerations. The only implementational
changes are related to a scalar factor in certain finite element matrices and
hence, harvesting the mentioned benefits comes at very little cost.
