Liquid crystals (LCs) exhibit a state between crystalline solids and liquids and can deform
under the influence of an external electric or magnetic field. Also, the birefringent response of
the LCs to the light is being primarily studied and utilized in many applications, such as LCDs,
actuators, sensors, etc. Liquid crystal elastomers (LCEs) are elastomers with liquid crystalline
molecules (mesogens) as part of the polymer chains. They can change their shape whenever the
orientation of these mesogens undergoes changes due to external stimuli like electric, magnetic
field, or temperature.
For liquid crystalline elastomers, that is elastic liquid crystalline polymers, Bladon, Ter-
entjev, and Warner developed a non-linear theory for nematic elastomers by extending the
classical Gaussian network theory of rubber elasticity to allow for anisotropic distributions of
the end-to-end vector between two crosslinks, also known as neo-classical theory. However, in
this theory, they assumed the molecules to be 'rigid rods' which is not the case for polymeric
liquid crystals. The theory also assumes 'affine deformation' for the end-to-end distance vector
of the polymer chain. As a result of these limitations, this theory fails to agree with some signif-
icant experimental results. This motivates us to go for the generalized microstretch continuum
theory by E.C.Eringen.
In the microstretch continuum, a material point has macro-deformation given by three trans-
lations, and micro-deformation given by three microrotations and one microstretch of the three
deformable directors. To start with, we extend the existing model for a special neo-Hookean
type elastic energy with mixed invariants of macro and micro deformation gradients. We aim
to develop a theoretical model for the static behavior of liquid crystalline elastomers to derive
the stress responses following the thermodynamic laws. We calibrate the model parameters for
the proposed free energy function using the experiments reported in the literature and verify
the model with the widely accepted neo-classical theory for liquid crystalline elastomers in the
cases of uniaxial stretching and simple shear.