In this talk we will present some results of attainment of the minimal
energy
when the mechanical response of the system is governed by a certain class
of non-quasiconvex frame indifferent energy densities.
Nonlinear as well as linearised models will be considered, and the relation
between the two,
via a rigorous derivation of the small-strain theory, will be illustrated.
Some models for nematic elastomers represent the main source of inspiration
and the main application of these results.