Yongzhong Huo

Strongly anisotropic elastic moduli of nematic elastomers: Analytical expressions and nonlinear temperature dependence

Abstract.Exact formulae for the elastic moduli of the nematic elastomers are obtained by the implicit function method based on somewhat general energy functions. The formulae indicate that both the moduli parallel and perpendicular to the director of the nematic elastomers are smaller than the modulus of the classical elastomers because of the mechanical-nematic coupling. Moreover, the moduli are generally anisotropic due to the biaxiality induced by stretching the nematic elastomers perpendicular to the director. Then we get the explicit analytical expressions of the parallel and perpendicular moduli by making use of the Landau-de Gennes free energy and the neo-classical elastic energy. Very different from the classical elastomers, they are both strongly nonlinear functions of the temperature in the nematic phase. Furthermore, their ratio, the degree of anisotropy, changes with the temperature as well. The results agree qualitatively with some experiments. Better quantitative agreement is obtained by some modifications of the constitutive relation of the elastic energy.

Light-Induced Bending and Buckling of Large-Deflected Liquid Crystalline Polymer Plates

Cross-linked liquid crystalline polymers (LCPs) are smart materials for large light-activated variation or bend to transfer luminous energy into mechanical energy. We study the light-induced behavior of homeotropic nematic network polymer plates. The perturbation method is applied to find approximate solutions under uniform illumination and compared with finite element simulations. Moreover, situations of nonuniform laser illumination are investigated. Unlike single solution obtained from small displacement assumption, multiple solutions within Foppl–von Karman nonlinear geometry framework are found in the post-buckling regime and the effect of various boundary conditions is discussed. The nonuniform bending moment generated by the inhomogeneous light-induced strain, membrane force and boundary effects lead to the unconventional nonsymmetric buckling behavior that is rarely observed under traditional mechanical or thermal loading.

Light-induced bending and smart control of photochromic liquid crystal elastomers

Light-induce bending of photochromic LCEs is a newly found phenomenon, with potential applications such as artificial muscles, nano actuators and remote-controllable implements. To simulate this, light-induced bending models of straight and curved beams can be derived from the simple beam theory. The effect of the light is substituted as an effective bending moment. Several examples, with different approximations, boundary conditions, under uniform or nonuniform illuminations, are demonstrated to calculate the curvature, the restraining force or the deflection. Especially, under weak light intensities and low temperature, the analytical expression of the curvature is obtained. A simplified remote controllable grip hand is simulated by the curved beam bending model. We calculate the grip force of the hand to hold a body, controlled by light and heat. The simulation shows that the largest value of grip stress can be about 1Mpa. In order to optimize the light-induced bending, the effects on the effective moment of the parameters, such as the light intensity, the thickness of the beam and the decay distance of the material are further analyzed. It is found that the effective moment is not a monotonic function of these parameters. Therefore, proper light intensity, material and thickness must be chosen to get the largest bending.

BIFURCATION AND STABILITY OF MARTENSITIC TRANSFORMATION DYNAMICS

In this paper, we have studied the mathematical properties and their physical implications of a system of nonlinear ordinary differential equations with two variables and six parameters, which was proposed to model the martensitic transformation of shape memory alloys. While the system could not have limit cycles, bifurcation to hysteresis was found in load and/or temperature controlled processes with large enough interfacial energies. This agrees qualitatively quite well with the experimental observation and theoretical understandings of the stress-strain-temperature hysteresis of the alloys. A three-dimensional bifurcation diagram was identified. Nonhyperbolic equilibrium points were found as saddle nodes and high order node points. The local behavior was studied and the phase portrait of the system was obtained for the load and temperature parameters. Accordingly, a stable node represents the stable martensitic or austenitic phase, a saddle stands for the unstable phase mixture, and a saddle node corresponds to the beginning or the end of the transformation. Therefore, for a thermal-mechanical loading path, the martensitic transformation process accords with the qualitative changes of the equilibrium points.