Ideally soft nematic elastomers

The paper examines a class of energies W of nematic elastomers that exhibit ideally soft behavior. These are generalizations of the neo-classical energy function proposed by BLADON, TERENTJEV & WARNER [7]. The effective energy (quasiconvexification) of W is calculated for a large subclass of considered energies. Within the subclass, the rank 1 convex, quasiconvex, and polyconvex envelopes coincide and reduce to the largest function below W that satisfies the Baker-Ericksen inequalities. Compressible cases are included. The e ff ective energy displays three regimes: one fluid-like, one partially fluid-like and one hard, as established by DESIMONE & DOLZMANN [20] for the energy function of BLADON, TERENTJEV & WARNER. Ideally soft deformation modes are shown to arise.