Abstract
When a liquid crystal elastomer layer is bonded to an elastic layer, it creates a bilayer with interesting properties that can be activated by applying traction at the boundaries or by optothermal stimulation. Here, we examine wrinkling responses in three-dimensional nonlinear systems containing a monodomain liquid crystal elastomer layer and a homogeneous isotropic incompressible hyperelastic layer, such that one layer is thin compared to the other. The wrinkling is caused by a combination of mechanical forces and external stimuli. To illustrate the general theory, which is valid for a range of bilayer systems and deformations, we assume that the nematic director is uniformly aligned parallel to the interface between the two layers, and that biaxial forces act either parallel or perpendicular to the director. We then perform a linear stability analysis and determine the critical wave number and stretch ratio for the onset of wrinkling. In addition, we demonstrate that a plate model for the thin layer is also applicable when this is much stiffer than the substrate.
Highlights
Liquid crystal elastomers (LCEs) are complex materials that combine the elasticity of polymeric solids with the self-organisation of liquid crystalline structures [31, 38]
We find that: (a) When the LCE is at high temperature cooled, it extends along the director and contracts in the perpendicular direction causing wrinkling parallel to the director, as sketched in figure 1; (b) When the LCE is at low temperature heated, it contracts along the director and extends in the perpendicular direction causing wrinkling perpendicular to the director, as sketched in figure 2; (c) At constant temperature, if the nematic layer is compressed along the director, it can lead to reorientation of the director until it aligns perpendicular to the compressive force, after which, further compression produces wrinkling parallel to the rotated director
We conducted a linear stability analysis for the onset of wrinkling in nonlinear two-layer systems formed from a hyperelastic film on a LCE substrate, or a LCE film on a hyperelastic substrate
Summary
Liquid crystal elastomers (LCEs) are complex materials that combine the elasticity of polymeric solids with the self-organisation of liquid crystalline structures [31, 38]. Bilayer film-substrate systems of neo-Hookean materials with different stiffness ratios, subjected to combined compression and growth conditions were studied systematically in [45]. For a growing soft layer subjected to equi-biaxial compression, in [26], a weakly nonlinear analysis of the wrinkling instability was performed using the multiple-scale perturbation method applied to the incremental theory in finite elasticity. For ideal monodomain LCEs, where the mesogens are uniformly aligned throughout the material, a general formulation is provided by the phenomenological neoclassical strain-energy function proposed in [14, 86, 89] This model is based on the molecular network theory of rubber elasticity [77], and its parameters are directly measurable experimentally or derived from macroscopic shape changes [87, 88]. We draw concluding remarks and outline some potential future developments
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