*Relaxation Results for Nematic Elastomers*

**Pierluigi Cesana**

California Institute of Technology

Mechanical Engineering

`cesana@caltech.edu`

**
Abstract**: The relaxation of a free-energy functional which
describes the order-strain interaction in nematic elastomers is obtained
explicitly. We work in the regime of small strains (linearized
kinematics). Adopting the uniaxial order tensor theory (Frank model) to
describe the liquid crystal order, we prove that the minima of the relaxed
functional exhibit an effective biaxial nematic texture, as in the de Gennes
order tensor model. In particular, this implies that, at a sufficiently
macroscopic scale, the response of the material is soft even if the order of
the system is assumed to be fixed at the microscopic scale. The relaxed energy
density satisfies a solenoidal quasiconvexification formula.