Liquid Crystal Elastomers: modeling analysis, and simulation

Liquid crystal elastomers (LCEs) are rubbery solids exhibiting many of the partially ordered mesophases (mematc, smectic A, smectic C) of liquid crystals.
The resulting phase transitions are at the root of their many interesting material properties, such as soft elasticity and shape memory effects.

In recent years, the application of modern tools in the calculus of variations (in particular, relaxation of nonconvex energy functionals) has contributed significantly to the understanding of the material properties of LCEs.
I will review some of the recent results justifying this claim.