Flow-network-controlled shape transformation of a thin membrane through differential fluid storage and surface expansion

The mechanical properties of a thin, planar material, perfused by an embedded flow network, have been suggested to be potentially changeable locally and globally by fluid transport and storage, which can result in both small- and large-scale deformations such as out-of-plane buckling. In these processes, fluid absorption and storage eventually cause the material to locally swell. Different parts can hydrate and swell unevenly, prompting a differential expansion of the surface. In order to computationally study the hydraulically induced differential swelling and buckling of such a membrane, we develop a network model that describes both the membrane shape and fluid movement, coupling mechanics with hydrodynamics. We simulate the time-dependent fluid distribution in the flow network based on a spatially explicit resistor network model with local fluid-storage capacitance. The shape of the surface is modeled by a spring network produced by a tethered mesh discretization, in which local bond rest lengths are adjusted instantaneously according to associated local fluid content in the capacitors in a quasistatic way. We investigate the effects of various designs of the flow network, including overall hydraulic traits (resistance and capacitance) and hierarchical architecture (arrangement of major and minor veins), on the specific dynamics of membrane shape transformation. To quantify these effects, we explore the correlation between local Gaussian curvature and relative stored fluid content in each hierarchy by using linear regression, which reveals that stronger correlations could be induced by less densely connected major veins. This flow-controlled mechanism of shape transformation was inspired by the blooming of flowers through the unfolding of petals. It can potentially offer insights for other reversible motions observed in plants induced by differential turgor and water transport through the xylem vessels, as well as engineering applications.

Active Surfaces Formed in Liquid Crystal Polymer Networks

There is an increasing interest in animating materials to develop dynamic surfaces. These dynamic surfaces can be utilized for advanced applications, including switchable wetting, friction, and lubrication. Dynamic surfaces can also improve existing technologies, for example, by integrating self-cleaning surfaces on solar cells. In this Spotlight on Applications, we describe our most recent advances in liquid crystal polymer network (LCN) dynamic surfaces, focusing on substrate-based topographies and dynamic porous networks. We discuss our latest insights in the mechanisms of deformation with the "free volume" principle. We illustrate the scope of LCN technology through various examples of photo-/electropatterning, free-volume channeling, oscillating/programmable network distortion, and porous LCNs. Finally, we close by discussing prominent applications of LCNs and their outlook.

Is there only one equilibrium configuration for spontaneous bending of liquid crystal elastomer circular plates with free edges?

In this paper, the spontaneous bending of a liquid crystal elastomer (LCE) circular plate under light illumination is investigated. The large bending deformation configurations for the LCE circular plate with free edges are obtained by minimizing the potential energy. It is found that for an LCE circular plate with random distribution of liquid crystal molecules, if the light intensity is small, there is only one equilibrium configuration for bending of the LCE circular plate. However, when the light intensity reaches a critical value, the circular plate will buckle and there will be three possible equilibrium configurations. On the other hand, for an LCE circular plate with uniform orientation of liquid crystal molecules, the strain induced by light is anisotropic, and there is only one equilibrium configuration. In addition, bending shapes of the LCE circular plate depend on its thickness. These results may be useful for designing light-driven LCE devices.

Curvature Induced by Deflection in Thick Meta-Plates

The design of advanced functional devices often requires the use of intrinsically curved geometries that belong to the realm of non-Euclidean geometry and remain a challenge for traditional engineering approaches. Here, it is shown how the simple deflection of thick meta-plates based on hexagonal cellular mesostructures can be used to achieve a wide range of intrinsic (i.e., Gaussian) curvatures, including dome-like and saddle-like shapes. Depending on the unit cell structure, non-auxetic (i.e., positive Poisson ratio) or auxetic (i.e., negative Poisson ratio) plates can be obtained, leading to a negative or positive value of the Gaussian curvature upon bending, respectively. It is found that bending such meta-plates along their longitudinal direction induces a curvature along their transverse direction. Experimentally and numerically, it is shown how the amplitude of this induced curvature is related to the longitudinal bending and the geometry of the meta-plate. The approach proposed here constitutes a general route for the rational design of advanced functional devices with intrinsically curved geometries. To demonstrate the merits of this approach, a scaling relationship is presented, and its validity is demonstrated by applying it to 3D-printed microscale meta-plates. Several applications for adaptive optical devices with adjustable focal length and soft wearable robotics are presented.

Boundary effect on the spontaneous deformation of a liquid crystal elastomer plate with arbitrary director orientation

Except for director orientation, the deformation modes of constrained liquid crystal elastomer thin plate display specimen geometry size dependence due to the boundary effect. In this paper, the effect of plate geometry size on the spontaneous deformation of a simply supported liquid crystal elastomer plate is studied. The relation between the deformation modes with director orientation and plate geometry size are investigated. Results show that the deformation modes are decided by the director orientation for a certain liquid crystal elastomer, but the geometry size affects the mode transformation with respect to the director. These results are supposed to be used in the design and application of liquid crystal elastomer-based smart actuators or sensors.

Light-induced spontaneous bending of a simply supported liquid crystal elastomer rectangular plate

Designing the director alignment of a liquid crystal elastomer (LCE) is a key tuning approach for LCE based smart devices. In this paper, the spontaneous strain of the LCE with arbitrary three-dimensional director orientation is derived, and the governing equation for a simply supported LCE rectangular plate is established. By using the finite difference method, the bending configurations are obtained. Different from the freestanding case, three bending modes, that is, unimodal, bimodal, and trimodal modes, are observed for the simply supported rectangular LCE plate. The relation between the bending modes and the director orientation is established. This paper enhances the understanding and facilitates the design of LCE based intelligent light driven devices.

Tunable wrinkling of thin nematic liquid crystal elastomer sheets

Instabilities in thin elastic sheets, such as wrinkles, are of broad interest both from a fundamental viewpoint and also because of their potential for engineering applications. Nematic liquid crystal elastomers offer a new form of control of these instabilities through direct coupling between microscopic degrees of freedom, resulting from orientational ordering of rodlike molecules, and macroscopic strain. By a standard method of dimensional reduction, we construct a plate theory for thin sheets of nematic elastomer. We then apply this theory to the study of the formation of wrinkles due to compression of a thin sheet of nematic liquid crystal elastomer atop an elastic or fluid substrate. We find the scaling of the wrinkle wavelength in terms of material parameters and the applied compression. The wavelength of the wrinkles is found to be nonmonotonic in the compressive strain due to the presence of the nematic. Finally, due to soft modes, the critical stress for the appearance of wrinkles can be much higher than in an isotropic elastomer and depends nontrivially on the manner in which the elastomer was prepared.

Patterning nonisometric origami in nematic elastomer sheets

Nematic elastomers dramatically change their shape in response to diverse stimuli including light and heat. In this paper, we provide a systematic framework for the design of complex three dimensional shapes through the actuation of heterogeneously patterned nematic elastomer sheets. These sheets are composed of nonisometric origami building blocks which, when appropriately linked together, can actuate into a diverse array of three dimensional faceted shapes. We demonstrate both theoretically and experimentally that the nonisometric origami building blocks actuate in the predicted manner, and that the integration of multiple building blocks leads to complex, yet predictable and robust, shapes. We then show that this experimentally realized functionality enables a rich design landscape for actuation using nematic elastomers. We highlight this landscape through examples, which utilize large arrays of these building blocks to realize a desired three dimensional origami shape. In combination, these results amount to an engineering design principle, which provides a template for the programming of arbitrarily complex three dimensional shapes on demand.

Smart Muscle-Driven Self-Cleaning of Biomimetic Microstructures from Liquid Crystal Elastomers

Muscle-driven actuation of biomimetic microfibrillar structures is achieved using integrative soft-lithography on a backing splayed liquid-crystal elastomer (LCE). Variation in the backing LCE layer thickness yields different modes of thermal deformation from a pure bend to a twist-bend. Muscular motion and dynamic self-cleaning of gecko toe pads are mimicked via this mechanism.

Response of constrained glassy splay-bend and twist nematic sheets to light and heat

A general approach is proposed to analyze the complex photo- or thermo-response of glassy splay-bend and twist nematic sheets with boundary constraints. The governing equations are two-dimensional, as in the classical plate theory. However, the solution can generate exact three-dimensional displacement and stress distributions within the interior of the sheets, except the boundary layer whose width is of the same order of the sheet thickness.

Mechanical frustration and spontaneous polygonal folding in active nematic sheets

We analyze the bending response to light or heat of a solid nematic disk with a director twisted from being radial on the upper surface to be azimuthal on the lower. We find a number of curl lobes determined purely by the geometry of the mechanical frustration that arises during the response.

Mechanical and optical bending of nematic elastomer cantilevers

We describe how bend imposed on a nematic elastomer cantilever can be accommodated with little or no internal stress by the director rotating. Thus, for a range of imposed curvatures that we calculate, there is no countertorque. Equally nonclassically, in such beams there is associated transverse curvature (clasticity). When instead bend is induced by illumination which causes spatially dependent contractions, director rotation can also act to vitiate stresses, but then (anti-)clasticity and its suppression has to be resolved, sometimes at the cost of stress creation.

Shape selection of twist-nematic-elastomer ribbons

How microscopic chirality is reflected in macroscopic scale to form various chiral shapes, such as straight helicoids and spiral ribbons, and how the degree of macroscopic chirality can be controlled are a focus of studies on the shape formation of many biomaterials and supramolecular systems. This article investigates both experimentally and theoretically how the chiral arrangement of liquid crystal mesogens in twist-nematic-elastomer films induces the formation of helicoids and spiral ribbons because of the coupling between the liquid crystalline order and the elasticity. It is also shown that the pitch of the formed ribbons can be tuned by temperature variation. The results of this study will facilitate the understanding of physics for the shape formation of chiral materials and the designing of new structures on basis of microscopic chirality.

Gaussian curvature from flat elastica sheets

We discuss methods of reversibly inducing non-developable surfaces from flat sheets of material at the micro-scale all the way to macroscopic objects. We analyse the elastic ground states of a nematic glass in the membrane approximation as a function of temperature for disclination defects of topological charge +1. An aim is to show that by writing an appropriate director field into such a solid, one could create a surface with Gaussian curvature, dynamically switchable from flat sheets while avoiding stretch energy. In addition to the prospect of programmable structures, such surfaces offer actuation via stretch in thin systems since when illumination is subsequently removed, unavoidable stretches return.