  The purpose of this article is to give a complete and general answer to the
recurrent problem in continuum mechanics of the determination of the number and
the type of symmetry classes of an even-order tensor space. This kind of
investigation was initiated for the space of elasticity tensors. Since then,
different authors solved this problem for other kinds of physics such as
photoelectricity, piezoelectricity, flexoelectricity, and strain-gradient
elasticity. All the aforementioned problems were treated by the same
computational method. Although being effective, this method suffers the
drawback not to provide general results. And, furthermore, its complexity
increases with the tensorial order. In the present contribution, we provide
general theorems that directly give the sought results for any even-order
constitutive tensor. As an illustration of this method, and for the first time,
the symmetry classes of all even-order tensors of Mindlin second
strain-gradient elasticity are provided.
