Photosensitive Liquid Crystal Elastomer, The Constitutive Behavior And Photoinduced Bending Behavior

Liquid crystal elastomer is a kind of soft matter,which is synthesized by crosslinking liquid crystal polymer.Liquid crystal elastomer combines the hyperelasticity of elastomers with the special physical properties of liquid crystals.It has rich and complex mechanical behaviors and properties,for example, thermal-mechanical-order coupling behaviors,anisotropy and soft elasticity. Especially,in 2001,a kind of new photochromic liquid crystal elastomer is developed. It can deform largely under light,and even bend.This photochromic liquid crystal elastomer has the potential applications for micro-opto-sensors and actuators.In this paper,we study and model the constitutive behavors and the light-induced bending of the photochromic liquid crystal elatomers.First,the total free energy of the liquid crystal elatomer is assumed as a function of the deformation gradient,order tensor and temperature.According to the continumm mechanics,totally in the tensor frame,we derive the constitutive equations of stress and entropy,and the equilibrium state for the order tensor.Then we assume the total free energy as the combination of the anisotropic neo-Hookean elastic energy and the Landau-de Gennes nematic energy,and obtain the specific constitutive equations.Liquid crystal elastomer is anisotropic,with special symmetry, so we define an effective left Cauchy-Green tensor to describe the deformation.We still introduce a metric tensor,which relates the macroscopic deformation scale and the microscopic order scale.As a result,when we don't consider the inner couple,the Cauthy stress tensor is symmetric,which is coaxial to the metric tensor and the effective left Cauchy-Green tensor.The deviatoric stress changes the order parameter and the biaxiality.We further analyze the stress-free configuration.Liquid crystal elastomers can deform spontaneously with the change of the temperature.Even when the temperature doesn't change,the director can freely rotate without stress,which is a kind soft behavior.Then,with the inverse method,we solve the deformation gradient for the typical mechanical loadings,such as the unaxial stretch and the pure shear in any directions. As a result,the stress,strain,temperature,order parameter,biaxiality and the direction of the director of the liquid crystal elastomer couple with each other.When the liquid crystal elastomer is sheared or stretched in the direction unparallel to the director,the director of the liquid crystal elastomer will rotate,and the biaxility is induced.Due to the coupling of the mechanics and order,the Young's modulus of the liquid crystal elastomer is anistropic.The Young's modulus perpendicular to the director is smaller than the paralle one,but both are smaller than the one of the neo-Hookean materials. Both the shear moduli perpendicular or parallel to the director are zero under infinite deformation,which represents soft property.Considering the photoisomerization of the photochromic liquid crystal molecules and the nematic-isotropic transition,we introduce the light intensity and temperature into the constitutive equations of liquid crystal elastomers and obtain the opto-mechanical constitutive model.As a result,light changes the order parameter of the liquid crystal elastomer,and therefore induces contraction and the variation of the elastic constants.The light intensity decays through the liquid crystal elastomer sample due the absorption.Thus the inhomogeneous light-induced contraction can cause the bending.Light also makes the liquid crystal elastomer a kind of gradient material.Under the plane section assumption,we construct the small deflection and large deflection simple beam light-induced bending model.The effect of light is equivalent to a bending moment.Then we can solve the deflection curve by the deflection curve differential equation.We calculate the deflection curve under the uniform or non-uniform illumination with the different boundary conditions.Then we further obtain the stress distribution through the thickness.As a result,in our model,light and temperature can jointly control the light-induced bending of the liquid crystal elastomer.The effective optical moment is nonmonotic with the increase of the illumination time,light intensity,and the ratio of the thickness and decay distance. The stress distribution through the thickness for the light-induced bending is nonlinear. When the film stress is zero,there are two or three zero-stress planes.While when the liquid crystal elastomer sample is constrained by the boundary condition,which causees a film stress,the film stress will strongly constrain the bending deflection.At this time,the small deflection model is no longer correct,and we must use the large deflection model.The illumination position and the illumination width also strongly affect the bending.In this paper,we also use the finite element method to model the light-induced bending.At first,we linearize the nonlinear opto-mechanical constitutive relation of liquid crystal elastomer.As a result,the stress is not only a function of the symmetric part of the displacement gradient,but also related to the unsymmetric part.Due to the speciality of the opto-mechanical constitutive equation of the liquid crystal elastomer, we have to write the weak form of the finite element analysis with FEPG software by ourselves,and introduce the opto-mechanical constitutive relation.We model the plane stress problem of the light-induced bending.The results of this finite element method model are in accord with the ones of simple beam model.However,when the ratio of the beam thickness and the decay distance is large,the total strain distribution is nonlinear and the plane section assumption is no longer applicable.At this time, even the illumination is uniform,the stress distribution along the length is non-uniform.