and we consider an energy density Wmec:M × S2 → [0,∞) defined by

Abstract. We discuss the well-posedness of a new nonlinear model for nematic elastomers. The main novelty in our work is that the Frank energy penalizes spatial variations of the nematic director in the deformed, rather than in the reference configuration, as it is natural in the case of large deformations. In this paper we discuss a new nonlinear model for nematic elastomers, which contains a Frank energy term penalizing spatial variations of the nematic director n in the deformed configuration. Our main result is a theorem on the existence of energy minimizers, which identifies a class of energy densities for which the model is mathematically well-posed. In recent years, considerable attention has been devoted to fully nonlinear mechanical models describing the coupling between elasticity and nematic order (see [16, 1, 2, 6, 7, 10] and references therein). The Frank term, however, has been typically evaluated in the reference configuration while, when large deformations are in order, it is more natural to consider spatial variations in the deformed configuration. Our main result is precisely that of establishing (under reasonable assumptions) existence of minimal energy states when the Frank term is written in the deformed configuration. From the mathematical point of view, the difficulty we face is that our energy functional has two terms, the Frank one defined on the deformed configuration, and the mechanical one defined on the reference configuration. Therefore, we need to push-forward the second one in order to work on the same domain. For this task, it becomes necessary to work with the inverse of the deformation mapping and establishing sufficient regularity properties of this inverse map using only the natural energy bounds is problematic. Let M: = {F ∈ R3×3: detF = 1} and let W: M → [0,∞) be a function such tha