  We consider a class of non-quasiconvex frame indifferent energy densities
which includes Ogden-type energy densities for nematic elastomers. For the
corresponding geometrically linear problem we provide an explicit minimizer of
the energy functional satisfying a nontrivial boundary condition. Other
attainment results, both for the nonlinear and the linearized model, are
obtained by using the theory of convex integration introduced by M\"uller and
Sver\'ak in the context of crystalline solids.
