Modeling and simulation of nematic LCE rods

Abstract

We introduce a nonlinear, one-dimensional bending-twisting model for an inextensible bi-rod that is composed of a nematic liquid crystal elastomer. The model combines an elastic energy that is quadratic in curvature and torsion with a Frank-Oseen energy for the liquid crystal elastomer. Moreover, the model features a nematic-elastic coupling that relates the crystalline orientation with a spontaneous bending-twisting term. We show that the model can be derived as a Γ-limit from three-dimensional nonlinear elasticity. Moreover, we introduce a numerical scheme to compute critical points of the bending-twisting model via a discrete gradient flow. We present various numerical simulations that illustrate the rich mechanical behavior predicted by the model. The numerical experiments reveal good stability and approximation properties of the method.

Liquid Crystal Orientation and Shape Optimization for the Active Response of Liquid Crystal Elastomers

“…Multiple strategies have been proposed to effectively simulate the stimuli response, i.e., motion, of active structures [36][37][38][39]. It is widely recognized that these simulations involve the solution of coupled nonlinear partial differential equations (PDEs), which require specialized strategies to address both numerical and physical instabilities.…”

Reduced Membrane Model for Liquid Crystal Polymer Networks: Asymptotics and Computation

“…Some existing bending models include theory derived via formal asymptotics [25], a von Karman plate model derived in [38] using asymptotics, a rigorous Gamma convergence theory for a model of bilayer materials composed of LCEs and a classical isotropic elastic plate [24], or a plate model where the LC dramatically changes its orientation through the thickness [39]. Moreover, reduced 1D models for LCNs/LCEs have been explored as well; we refer to [40] for a rod model and to [41,42] for ribbon models.…”

“…Computation of LCEs/LCNs have received some attention. Publications include computations of various membrane models [34], a membrane model with regularization [26], a bending model of LCE bilayer structure [24], a relevant 2D model for LCEs [22], 3D models [43,44], and LCE rods [40]. Literature involving numerical analysis is limited, to the best of our knowledge.…”