Modeling Defects, Shape Evolution, and Programmed Auto-Origami in Liquid Crystal Elastomers

Abstract

Liquid crystal elastomers represent a novel class of programmable shape-transforming materials whose shape-change trajectory is encoded in the material's nematic director field. Using three-dimensional non-linear finite element elastodynamics simulation, we model a variety of different actuation geometries and device designs: thin films containing topological defects, patterns that induce formation of folds and twists, and a bas-relief structure. The inclusion of finite bending energy in the simulation model reveals features of actuation trajectory that may be absent when bending energy is neglected. We examine geometries with a director pattern uniform through the film thickness encoding multiple regions of positive Gaussian curvature. Simulations indicate that heating such a system uniformly produces a disordered state with curved regions emerging randomly in both directions due to the film's up/down symmetry. In contrast, applying a thermal gradient by heating the material first on one side breaks up/down symmetry and results in a deterministic trajectory, producing a more ordered final shape. We demonstrate that a folding zone design containing cut-out areas accommodates transverse displacements without warping or buckling, and demonstrate that bas-relief and more complex bent/ twisted structures can be assembled by combining simple design motifs.

Modeling out-of-plane actuation in thin-film nematic polymer networks: From chiral ribbons to auto-origami boxes via twist and topology

“…The well-known relation between disclination defects, topology and curvature272829 can also be implemented in designing and engineering a folding box actuator. A hybrid sample with radial director configuration on the top substrate aligned with an azimuthal director configuration in the bottom substrate, known as the “radial-azimuthal” actuator, distorts its shape via four-fold symmetry bending under external stimulus15.…”

Nematic director fields and topographies of solid shells of revolution

“…Other suitable spirals also give surfaces of constant, but now non-zero curvature (spheres and spherical spindles) [3,4], and these too are found experimentally [5]. Such systems have also been explored numerically by R. Selinger et al [11] for liquid crystal elastomers where a range of curvatures from complex director distributions lead to shells with curvature.…”

Patterning order and disorder with an angle: modeling single-layer dual-phase nematic elastomer ribbons

“…In this work, we perform nite-element elastodynamics simulations for investigating the actuation of these novel singlelayer dual-phase materials given their order-disorder patterned microstructure as well as director conguration in the nematic regions. This numerical method had successfully demonstrated a wide variety of in-plane and out-of-plane actuation behavior in single-phase nematic elastomers including chiral bending, 8 twisting, 8,22 cone and anti-cone (saddle) formation, 21 accordion folds, 9 origami boxes, 11 and bas-relief designs, 21 given by different complex director microstructures. Also, nite element elastodynamics has been implemented for studying the actuation of smectic elastomers.…”

“…Further details on this nite element elastodynamics algorithm can be found in previous work. 11,21,23,25 For modeling dual phase actuators, we use the imprinted director eld conguration to describe the spatial distribution of nematic order and disorder. Director in the nematic regions has a 90 degree twist between top and bottom substrates.…”

“…This simulation setup was designed to replicate the fabrication technique for dual-phase elastomer ribbons described by Liu et al 16 Magnitude of external stimulus is encoded in the parameter adS, in consistency with previous numerical studies implementing nite element elastodynamics in liquid crystal elastomers. 8,9,11,21 External stimulus is applied during a transient time, and then sample is allowed to respond and nd equilibrium. In this work, we use two samples with different lengths: sample 1 has aspect ratio 50-10-1, 13 213 nodes, 61 953 tetrahedral elements; sample 2 has aspect ratio 200-10-1, 65 924 nodes, and 291 711 tetrahedra.…”