Uniaxial nematic elastomers: constitutive framework and a simple application

Abstract

Using a geometrical approach to treat the constraints associated with the continuum description of a uniaxial nematic elastomer—that is, a nematic elastomer whose microstructure can be characterized by a single unit vector field, we develop the general constitutive framework for such a material. We also provide a variational formulation of equilibrium and use that formulation to discuss the inflation of a tubular specimen. The analysis demonstrates the existence of a pair of disconnected solution branches. Of these branches, one is stable at low pressure and the other is stable at high pressure. An intermediate regime within which both branches are stable indicates that during loading the specimen may undergo a discontinuous jump from one solution branch to another and thus suggests the possibility of using nematic elastomers for pressure-sensitive optical switches.