Incompressible Biaxial Nematic Liquid Crystal Elastomers for Artificial Muscles

Assuming only incompressibility, in the simplest complete theory for monodomain liquid crystalline elastomers as rectangular parallelepipeds, we find two biaxial nematic phases, $N_{2+}$ and $N_{2-}$ with a first order $N_{2+}-N_{2-}$ transition exhibiting spontaneous shape change. We identify $N_{2+}$ as icosahedral ($Y_{h}$) and $N_{2-}$, as simple orthorhombic ($D_{2h}$) nematics. Using standard orientational mechanics, we derive the stress-strain behavior before swelling to pin-point the recently discovered elastic strain limits for swelling with $5CB$.