An extended neo-classical model for nematic elastomers with transversely isotropic semisoft elasticity

Nematic elastomers exhibit transversely isotropic semisoft elasticity due to the coupling of the liquid crystal mesogen and polymer network. Existing constitutive models are unable to simultaneously capture both the elastic anisotropy at small deformations and the semisoft stress plateau under large orthogonal loadings. Based on the decompositions of the strain energy and the deformation gradient, we propose an extended neo-classical model for nematic elastomers, which consists of a transversely isotropic soft elastic energy plus a semisoft penalty for the free rotation of the liquid crystal director. The proposed model contains four temperature-dependent material parameters that can be determined through experiments. The determination of the material parameters by thermal-mechanical experiments is illustrated. Also, the temperature dependences of the material parameters are summarized into empirical formulae based on experimental and theoretical studies. Analytical and numerical examples are given to demonstrate that the proposed model can capture both the transversely isotropic elasticity at the small deformations and the stress-induced director rotations with large shear deformations at larger deformations.