An electro‐elastic phase‐field model for nematic liquid crystal elastomers based on Landau‐de‐Gennes theory

Abstract

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.

Numerical Methods in Studies of Liquid Crystal Elastomers

“…More recently, Keip and Nadgir [ 128 ] proposed a continuum mechanics, phase-field method for modeling the electro-elastic behavior of nematic LCEs. The nemato-electro-elastic model is coupled with the Landau–de-Gennes theory and the phase field is described by using a tensorial order parameter.…”

“…This model contrasts with its predecessors [ 129 , 130 ] in that, it considers the full Landau–de-Gennes order parameter as phase field; therefore, allowing the new model to overcome the numerical challenges inherent in other director models [ 131 , 132 ]. A complete derivation of the mathematical framework used by the authors [ 128 ] can be found in the original manuscript. The authors’ results demonstrate that the proposed model was able to characterize how the nematic microstructures evolved to a good degree.…”

“…(1) exploring the dynamical behavior of LCEs [111,112] (2) model thermal-order-mechanical coupling behaviors in LCEs [36] (3) modeling the mechanical procedure by which biological cells exchange information [120] (4) studying the mechanical behavior of Smectic-A LCEs, in response to electromechanical stimuli [124] (5) modeling the electro-elastic behavior of nematic LCEs [128] (6) studying the thermos-mechanical behavior of a soft robot [133] (7) developing a general frame work for studying the interactions between LCs and polymer backbones that constitute a LCE [134] Table 2. Categorization of the reviewed numerical methods.…”

“…After deriving equations for mechanical and phase equilibrium, total free energy was considered to be a hybrid of the entropy-induced elastic energy and the Landau-de-Gennes nematic energy [36] (3) soft matter cell model based on Lagrange-type mesh-free Galerkin formulation was developed [120] (4) A free energy density function was obtained by summing contributions from (a) elastic free energy, (b) change in the layer thickness (c) variation in chirality, or equivalently the tilt (or rotation) of the director, (d) energetic contribution of the electrical sources to the total energy and (e) external mechanical loading [124] (5) a continuum-mechanical phase-field approach was adopted. A nemato-electro-elastic model is coupled with the fundamental Landau-de-Gennes theory for isotropic-nematic phase transition [128] (6) transient analytical solution consisting of a one dimensional heat transfer equation (solved using Green's function) coupled with a bilayer beam model [133] (7) A continuum mechanics model was developed that in addition to taking into account the director or order tensors, along with their respective time derivatives, the deformation gradient and its derivative with respect to time was also considered [134] The tabularized findings in Tables 1 and 2 have been summarized, in order to provide a concise set of recommendations, to act as reference for researchers:…”

Computational homogenization of nematic liquid crystal elastomers based on Landau‐de‐Gennes theory

“…In the current contribution, we discuss a rate-type variational homogenization framework for nemato-elastic solids. We refer to [4] for the employed phase-field model of nematic elastomers.…”