Quasiconvex envelopes of energies for nematic elastomers in the small strain regime and applications

We provide some explicit formulas for the quasiconvex envelope of energy densities for nematic elastomers in the small strain regime and plane strain conditions. We then demonstrate their use as a powerful tool for the interpretation of mechanical experiments. Analytical formulas characterizing the stressstrain response in pure shear are derived, providing an easily testable benchmark for future numerical and experimental investigations on the mechanics of nematic elastomers.