•The strain and stress concentration behaviors of a monodomain LCE sheet with an elliptical hole subjected to uniaxial stretches are studied using finite element methods.•Liquid crystal elastomers ...exhibit severer stress and strain concentration than neoHookean, and such concentration is further aggravated with the sharpening of the elliptical hole.•The location of maximal strain deviates slightly from that of maximal stress when the applied stretches are small. The two locations merge together as the elliptical holes become sharper or the applied stretches become larger.•Director reorientations and resulting spontaneous strains around the hole edge are the main causes of these unusual stress and strain concentration behaviors.
Liquid crystal elastomers (LCEs) are a kind of soft materials which couple the high elastic deformability with the unique properties of liquid crystals. Such combination endows notched LCEs unusual stress and strain concentration behaviors, which is preliminary discussed by us in the case of a large sheet with a centralized circular hole. Here we extend our study from circular holes to more generalized, elliptical holes. We investigate the stress and strain fields around a centralized elliptical hole in a LCE sheet subjected to uniaxial stretches by finite element methods. The effects of the shape factor, defined as the ratio of the minor-to-major axis of the ellipse, are mainly concerned. Compared with common elastomers like neoHookean, LCEs get higher stress and strain concentration factors (SCFs), and the location of maximal strain deviates slightly from that of maximal stress. With the decrease of the shape factor (a sharper ellipse) the SCFs of LCEs rise much severer than those of neoHookean, and the deviation is diminishing. In addition, as the stretch increases, the region near the root is getting close to an approximately uniaxial stress state, and the high strain region will extend non-monotonously along the hole edge, which differs from a monotonous extension of the high stress region. All the unusual behaviors of LCEs above are attributed to the spontaneous strain induced by director rotation. Attempts to correlate stress and strain concentration behaviors to the spontaneous strain are made in this article.
•Liquid crystal elastomers exhibit much severe concentrations of stress and strain.•The locations of the strain concentration may not coincide with that of the stress concentration.•Director ...rotations and resulting spontaneous strains around the hole edge are the main causes of usual concentration behavior.•Samples with larger spontaneous strains have severer stress and strain concentrations.
Liquid crystal elastomers combine the hyperelasticity of elastomers with the multi-functionality of liquid crystals and have emerged as an important class of soft active materials. Monodomain liquid crystal elastomers under loading exhibit the soft elastic behavior due to the stress induced director rotation and the resulting spontaneous strain. Here, we numerically study their stress and strain concentration behavior by considering the classical example, a large sheet with a small circular hole in the middle under uniaxial loading. The concentration behavior is found to be very different from regular elastomers. Firstly, the concentration factors are much bigger at both small and large strains. Secondly, the locations of the strain concentration may not coincide with that of the stress concentration. Detailed analysis of the director rotation and the resulting spontaneous strain around the free edge of the hole are shown to be the main causes for the unusual concentration behavior. Moreover, under a given strain, the stress level of the LCE sample, and therefore the free energy, is slightly lower than that of the neo-Hookean material, while the local free energy density on the hole edge is much bigger due to the severer concentrations. By considering material parameters obtained from various samples of polysiloxane and polyacrylate side-chain nematic elastomers, we find that their stress and strain concentration behaviors are qualitatively similar but quantitatively quite different. As a result, at a prescribed strain, the samples with a larger maximal spontaneous strain has severer stress and strain concentrations. The stress concentration factor difference scaled by a coupling constant that combines the effect of the two material parameters, r and a, increases as the semi-soft coefficient a decreases. Similar results are found for the scaled maximal spontaneous strains and the scaled strain concentration factor difference at small strains.
•Nonlinear electro-opto-mechanical coupling in dielectric nematic elastomers is simulated.•Governing and constitutive equations are derived based on the variational approach.•A modification of the ...semi-soft elastic energy of nematic elastomers is proposed.•The subcritical character of the solid Fréedericksz transition is changed to supercritical.•Analytical and finite element solutions for the solid Fréedericksz transition are obtained.
Based on the variational principle, we derive the balance equation for momentum, Maxwell equation, and the equation of director fields for nonlinear electro-opto-mechanical coupling in dielectric liquid crystal elastomers (LCEs). Further, we establish a simple constitutive model to study the electric-field-induced director reorientation with the deformation of monodomain nematic LCEs, which is called the solid Fréedericksz transition (SFT). Semi-analytical method is utilized to obtain the solutions of stress-free homogeneous SFT. The results indicate that the semi-soft elasticity of LCEs is insufficient to simulate the supercritical SFT of samples, as observed in earlier reported experiments. A modification of the semi-soft elastic energy of LCEs is proposed to change the subcritical character of the SFT to supercritical. In addition to the semi-analytical methods, finite element method is employed to simulate the experiments in which samples are immersed in dielectric liquids. The simulation results show good agreement with the experimental data from literature.
Liquid crystal elastomers present features not found in ordinary elastic materials, such as semi-soft elasticity and the related stripe domain phenomenon. In this paper, the two-dimensional ...Bladon–Terentjev–Warner model and the one-constant Oseen–Frank energy expression are combined to study the liquid crystal elastomer. We also impose two material constraints, the incompressibility of the elastomer and the unit director norm of the liquid crystal. We prove existence of minimiser of the energy for the proposed model. Next we formulate the discrete model, and also prove that it possesses a minimiser of the energy. The inf-sup values of the discrete linearised system are then related to the smallest singular values of certain matrices. Next the existence and uniqueness of the Lagrange multipliers associated with the two material constraints are proved under the assumption that the inf-sup conditions hold. Finally numerical simulations of the clamped-pulling experiment are presented for elastomer samples with aspect ratio 1 or 3. The semi-soft elasticity is successfully recovered in both cases. The stripe domain phenomenon, however, is not observed, which might be due to the relative coarse mesh employed in the numerical experiment. Possible improvements are discussed that might lead to the recovery of the stripe domain phenomenon.
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