The present contribution proposes a continuum-mechanical phase-field approach to model the electro-elastic behavior of nematic liquid crystal elastomers. The nemato-electro-elastic model is embedded into the fundamental Landau-de-Gennes theory for isotropic-nematic phase transition and employs a tensorial order parameter as the phase field. Nematic deformations are incorporated through a constitutive ansatz in terms of the order parameter. The phase-field formulation is implemented into the finite element method, so that the microstructure evolution of nematic elastomers under different boundary conditions can be studied. We show that the model is capable to capture characteristic features of nematic elastomers including mechanically and electrically induced microstructure evolution as well as the occurrence of stripe domains.
Nematic liquid crystal elastomers represent a group of materials, which combine elastic properties of rubber with orientational properties of liquid crystals. The present contribution proposes a variational homogenization principle for nematic liquid crystal elastomers. A symmetric and traceless tensorial quantity represents the nematic order parameter, which is used as a phase field. The model is implemented in a finite element framework and the validation is done with two as well as three dimensional nemato-mechanical boundary value problems.
Liquid crystal elastomers bring together the orientational properties of liquid crystals as well as elastic properties of soft rubber. Nematic elastomers are a subclass of these materials which exhibit a phase transition from high-symmetry isotropic state to low-symmetry nematic state, when cooled down below a material specific temperature. We present a phase-field model based on Landau-de-Gennes theory for the modeling of nematic elastomers. The model is implemented within finite element framework and an initial boundary value problem of isotropic-nematic phase transition is solved.
This contribution presents a phase-field model for transversely isotropic barium titanate, which allows for the adjustment of the full set of anisotropic material parameters. It is a direct extension of the work by Schrade et al.[1] who proposed a phasefield model for ferroelectrics in the framework of invariant theory. In the present contribution, the loss of positive definiteness is avoided by formulating energetic terms that provide upper and lower bounds for all material moduli involved. We show the characteristics of the formulation by a set of numerical examples in two and three dimensions.
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