  Liquid-crystal networks consist of weakly crosslinked polymers that are
coupled to liquid-crystal molecules. The resultant hybrid system has rich
elastic properties. We develop a phase field model to describe mechanical
properties of a hexagonal liquid-crystal network. The hexagonal liquid-crystal
network is found to have soft shear deformations. The elastic properties are
predicted analytically and confirmed with numerical simulations. In addition
the model incorporates non-linear elasticity and dislocations or disclinations.
