A new approach to modeling liquid crystal elastomers using phase field methods

A phase field modeling framework is developed to quantify domain structure evolution in nematic phase liquid crystal elastomers. A hyperelastic energy function is combined with liquid crystal energy relations to formulate a constitutive model for liquid crystal elastomers that undergo thermo-mechanical loads and finite deformation. A set of balance laws and constitutive relations are defined which lead to coupling behavior when finite deformation is introduced within the energy description. The theoretical framework is implemented numerically using a non-linear finite element phase field modeling approach which couples deformation of the elastomer network with microscopic liquid crystal domain structure evolution. A comparison of monodomain and polydomain behavior is analyzed to illustrate spontaneous deformation and polydomain evolution during heating and mechanical stretching. Many of the essential constitutive relations governing these materials are obtained without the use of explicit phenomenological coupling between the liquid crystals and the host elastomer.