The totality of soft-states in a neo-classical nematic elastomer

The remarkable ability of nematic elastomers to exist in multiple stable equilibrium configurations in the absence of force and energy cost is known as soft elasticity. Here, we determine all of the soft states that are possible in two particular classes of nematic elastomers: the neo-classical nematic elastomers, which have received considerable recent attention; and a natural theoretical generalization, which we call the Mooney nematic elastomers. For both of these classes, the soft states are minimizers of the free energy. Our starting point is to develop a nonlinear continuum theory for nematic elastomers, the constitutive framework of which includes the special classes noted above. This theory is based on two distinct force balances???one arising from the macroscopic deformation and the other from the nematically-induced distortion of the polymer molecules???and allows for coexistent isotropic, uniaxial, and biaxial phases. These balances are supplemented by a principle of dissipation imbalance, a principle that in conjunction with invariance requirements is used to obtain restrictions on constitutive equations.published or submitted for publicationis peer reviewe