Material instabilities in nematic elastomers

Soft deformation paths and domain patterns in nematic elastomers are analyzed through the minimization of a nonconvex free-energy recently proposed in the literature. The free-energy density has multiple wells, and is not restricted to small deformations. The problems of calculating the quasiconvex hull of the energy wells and the quasiconvex envelope of the free-energy density are formulated and solved (the latter only in two spatial dimensions). This leads to a complete characterization of the set of soft deformations paths available to a given material, and of its effective macroscopic energy.