Internal Constraints and Gauge Relations in the Theory of Uniaxial Nematic Elastomers

We apply the formalism of analytical mechanics for constrained systems to reformulate the equilibrium theory of uniaxial nematic elastomers, allowing for constitutive dependence on the gradient of the director . In this setting, inextensibility is enforced by requiring that and that . Starting from these constraints, and using the principle of virtual work within a thermomechanically consistent framework, we derive boundary-value problems for determining equilibrium configurations. We show that the original formulation yields an underdetermined system for the Lagrange multiplier fields unless ancillary gauge conditions are imposed. To resolve this indeterminacy, we introduce two effective Lagrange multiplier fields: one defined in the interior of the referential region and the other on that portion of the boundary where the director traction is prescribed.