Nematic elastomers possess an internal structure characterized by cross-linked polymer chains incorporating rod-like mesogens as pendant side groups or spacer elements of the main chain. The orientation of the mesogens is described by an order parameter called the director field. Changes in the director orientation can be captured by governing equations similar to those familiar from the theory of nematic fluids. Usually, the macroscopic deformation of the network is assumed to be isochoric, reflecting the incompressibility of the material, and the mesogens are treated as rigid and, thus, inextensible. Anderson et al. [1] and Chen and Fried [2] propose a framework in which the isochoricity and inextensibility conditions are viewed as internal constraints, to be enforced by means of the Lagrange multiplier technique. Moreover, they include the gradient of the director field in the list of the constitutive independent variables, so as to account for the understanding that, although uniform distributions for the director are sometimes energetically favored, higher-energy states with nonzero director gradients can arise. As a consequence, the vanishing of the gradient of the inextensibility constraint is also taken as an independent constraint, and is interpreted as an “orthogonality” condition. In this presentation, we show that the Lagrange multipliers associated with the inextensibility and orthogonality constraints are not uniquely determined by the governing equations and boundary conditions. Our approach [3] tackles this issue by following two equivalent strategies: one is based on appropriate gauge conditions; the other one is based on the introduction of two “effective”, uniquely defined, multipliers and “effective” reaction forces to the inextensibility constraint. Finally, we explore some physical implications of both formulations. REFERENCES [1] D.R. Anderson, D.E. Carlson and E. Fried, A continuum-mechanical theory of nematic elastomers. J. Elast. (1999) 56: 33–58. [2] Y. Chen and E. Fried, Uniaxial nematic elastomers: constitutive framework and a simple application. Proc. R. Soc. A (2006) 462, 1295–1314. [3] A. Pastore, A. Grillo and E. Fried, Internal constraints and gauge relations in the theory of uniaxial nematic elastomers. Submitted to J. Elast.