Shape transformations of soft matter governed by bi-axial stresses

Responsive materials architected in space and time

Rationally designed architected materials have attained previously untapped territories in materials property space. The properties and behaviours of architected materials need not be stagnant after fabrication; they can be encoded with a temporal degree of freedom such that they evolve over time. In this Review, we describe the variety of materials architected in both space and time, and their responses to various stimuli, including mechanical actuation, changes in temperature and chemical environment, and variations in electromagnetic fields. We highlight the additive manufacturing methods that can precisely prescribe complex geometries and local inhomogeneities to make such responsiveness possible. We discuss the emergent physics phenomena observed in architected materials that are analogous to those in classical materials, such as the formation and behaviour of defects, phase transformations and topologically protected properties. Finally, we offer a perspective on the future of architected materials that have a degree of intelligence through mechanical logic and artificial neural networks.

Mechanical Adaptability of Patterns in Constrained Hydrogel Membranes

Pattern formation and dynamic restructuring play a vital role in a plethora of natural processes. Understanding and controlling pattern formation in soft synthetic materials is important for imparting a range of biomimetic functionalities. Using a three-dimensional gel Lattice spring model, we focus on the dynamics of pattern formation and restructuring in thin thermoresponsive poly(N-isopropylacrylamide) membranes under mechanical forcing via stretching and compression. A mechanical instability due to the constrained swelling of a polymer network in response to the temperature quench results in out-of-plane buckling of these membranes. The depth of the temperature quench and applied mechanical forcing affect the onset of buckling and postbuckling dynamics. We characterize formation and restructuring of buckling patterns under the stretching and compression by calculating the wavelength and the amplitude of these patterns. We demonstrate dynamic restructuring of the patterns under mechanical forcing and characterize the hysteresis behavior. Our findings show that in the range of the strain rates probed, the wavelength prescribed during the compression remains constant and independent of the sample widths, while the amplitude is regulated dynamically. We demonstrate that significantly smaller wavelengths can be prescribed and sustained dynamically than those achieved in equilibrium in the same systems. We show that an effective membrane thickness may decrease upon compression due to the out-of-plane deformations and pattern restructuring. Our findings point out that mechanical forcing can be harnessed to control the onset of buckling, postbuckling dynamics, and hysteresis phenomena in gel-based systems, introducing novel means of tailoring the functionality of soft structured surfaces and interfaces.

Reconfiguring Gaussian Curvature of Hydrogel Sheets with Photoswitchable Host-Guest Interactions

Photoinduced shape morphing has implications in fields ranging from soft robotics to biomedical devices. Despite considerable effort in this area, it remains a challenge to design materials that can be both rapidly deployed and reconfigured into multiple different three-dimensional forms, particularly in aqueous environments. In this work, we present a simple method to program and rewrite spatial variations in swelling and, therefore, Gaussian curvature in thin sheets of hydrogels using photoswitchable supramolecular complexation of azobenzene pendent groups with dissolved α-cyclodextrin. We show that the extent of swelling can be programmed via the proportion of azobenzene isomers, with a 60% decrease in areal swelling from the all trans to the predominantly cis state near room temperature. The use of thin gel sheets provides fast response times in the range of a few tens of seconds, while the shape change is persistent in the absence of light thanks to the slow rate of thermal cis-trans isomerization. Finally, we demonstrate that a single gel sheet can be programmed with a first swelling pattern via spatially defined illumination with ultraviolet light, then erased with white light, and finally redeployed with a different swelling pattern.

Computational analysis of hygromorphic self-shaping wood gridshell structures

Bi-layered composites capable of self-shaping are of increasing relevance to science and engineering. They can be made out of anisotropic materials that are responsive to changes in a state variable, e.g. wood, which swells and shrinks by changes in moisture. When extensive bending is desired, such bilayers are usually designed as cross-ply structures. However, the nature of cross-ply laminates tends to prevent changes of the Gaussian curvature so that a plate-like geometry of the composite will be partly restricted from shaping. Therefore, an effective approach for maximizing bending is to keep the composite in a narrow strip configuration so that Gaussian curvature can remain constant during shaping. This represents a fundamental limitation for many applications where self-shaped double-curved structures could be beneficial, e.g. in timber architecture. In this study, we propose to achieve double-curvature by gridshell configurations of narrow self-shaping wood bilayer strips. Using numerical mechanical simulations, we investigate a parametric phase-space of shaping. Our results show that double curvature can be achieved and that the change in Gaussian curvature is dependent on the system's geometry. Furthermore, we discuss a novel architectural application potential in the form of self-erecting timber gridshells.

Materials as Machines

Machines are systems that harness input power to extend or advance function. Fundamentally, machines are based on the integration of materials with mechanisms to accomplish tasks-such as generating motion or lifting an object. An emerging research paradigm is the design, synthesis, and integration of responsive materials within or as machines. Herein, a particular focus is the integration of responsive materials to enable robotic (machine) functions such as gripping, lifting, or motility (walking, crawling, swimming, and flying). Key functional considerations of responsive materials in machine implementations are response time, cyclability (frequency and ruggedness), sizing, payload capacity, amenability to mechanical programming, performance in extreme environments, and autonomy. This review summarizes the material transformation mechanisms, mechanical design, and robotic integration of responsive materials including shape memory alloys (SMAs), piezoelectrics, dielectric elastomer actuators (DEAs), ionic electroactive polymers (IEAPs), pneumatics and hydraulics systems, shape memory polymers (SMPs), hydrogels, and liquid crystalline elastomers (LCEs) and networks (LCNs). Structural and geometrical fabrication of these materials as wires, coils, films, tubes, cones, unimorphs, bimorphs, and printed elements enables differentiated mechanical responses and consistently enables and extends functional use.

Blueprinting Photothermal Shape-Morphing of Liquid Crystal Elastomers

Liquid crystal elastomers (LCEs) are an attractive platform for dynamic shape-morphing due to their ability to rapidly undergo large deformations. While recent work has focused on patterning the director orientation field to achieve desired target shapes, this strategy cannot be generalized to material systems where high-resolution surface alignment is impractical. Instead of programming the local orientation of anisotropic deformation, an alternative strategy for prescribed shape-morphing by programming the magnitude of stretch ratio in a thin LCE sheet with constant director orientation is developed here. By spatially patterning the concentration of gold nanoparticles, uniform illumination leads to gradients in photothermal heat generation and therefore spatially nonuniform deformation profiles that drive out-of-plane buckling of planar films into predictable 3D shapes. Experimentally realized shapes are shown to agree closely with both finite element simulations and geometric predictions for systems with unidirectional variation in deformation magnitude. Finally, the possibility to achieve complex oscillatory motion driven by uniform illumination of a free-standing patterned sheet is demonstrated.

Dual-gradient enabled ultrafast biomimetic snapping of hydrogel materials

The design of materials that can mimic the complex yet fast actuation phenomena in nature is important but challenging. Herein, we present a new paradigm for designing responsive hydrogel sheets that can exhibit ultrafast inverse snapping deformation. Dual-gradient structures of hydrogel sheets enable the accumulation of elastic energy in hydrogels by converting prestored energy and rapid reverse snapping (<1 s) to release the energy. By controlling the magnitude and location of energy prestored within the hydrogels, the snapping of hydrogel sheets can be programmed to achieve different structures and actuation behaviors. We have developed theoretical model to elucidate the crucial role of dual gradients and predict the snapping motion of various hydrogel materials. This new design principle provides guidance for fabricating actuation materials with applications in tissue engineering, soft robotics, and active medical implants.

Nonlinear mechanics of thin frames

The dramatic effect kirigami, such as hole cutting, has on the elastic properties of thin sheets invites a study of the mechanics of thin elastic frames under an external load. Such frames can be thought of as modular elements needed to build any kirigami pattern. Here we develop the technique of elastic charges to address a variety of elastic problems involving thin sheets with perforations, focusing on frames with sharp corners. We find that holes generate elastic defects (partial disclinations), which act as sources of geometric incompatibility. Numerical and analytic studies are made of three different aspects of loaded frames-the deformed configuration itself, the effective mechanical properties in the form of force-extension curves, and the buckling transition triggered by defects. This allows us to understand generic kirigami mechanics in terms of a set of force-dependent elastic charges with long-range interactions.

A shape-shifting composite hydrogel sheet with spatially patterned plasmonic nanoparticles

A simple and reliable approach was developed to fabricate thermo-responsive composite hydrogel sheets with spatially patterned regions of plasmonic gold nanoparticles. The same hydrogel exhibited different modes of shape deformation under near-infrared laser irradiation depending on the irradiation direction.

Helical Structures Mimicking Chiral Seedpod Opening and Tendril Coiling

Helical structures are ubiquitous in natural and engineered systems across multiple length scales. Examples include DNA molecules, plants' tendrils, sea snails' shells, and spiral nanoribbons. Although this symmetry-breaking shape has shown excellent performance in elastic springs or propulsion generation in a low-Reynolds-number environment, a general principle to produce a helical structure with programmable geometry regardless of length scales is still in demand. In recent years, inspired by the chiral opening of Bauhinia variegata's seedpod and the coiling of plant's tendril, researchers have made significant breakthroughs in synthesizing state-of-the-art 3D helical structures through creating intrinsic curvatures in 2D rod-like or ribbon-like precursors. The intrinsic curvature results from the differential response to a variety of external stimuli of functional materials, such as hydrogels, liquid crystal elastomers, and shape memory polymers. In this review, we give a brief overview of the shape transformation mechanisms of these two plant's structures and then review recent progress in the fabrication of biomimetic helical structures that are categorized by the stimuli-responsive materials involved. By providing this survey on important recent advances along with our perspectives, we hope to solicit new inspirations and insights on the development and fabrication of helical structures, as well as the future development of interdisciplinary research at the interface of physics, engineering, and biology.

Shape-Morphing Materials from Stimuli-Responsive Hydrogel Hybrids

The formation of well-defined and functional three-dimensional (3D) structures by buckling of thin sheets subjected to spatially nonuniform stresses is common in biological morphogenesis and has become a subject of great interest in synthetic systems, as such programmable shape-morphing materials hold promise in areas including drug delivery, biomedical devices, soft robotics, and biomimetic systems. Given their ability to undergo large changes in swelling in response to a wide variety of stimuli, hydrogels have naturally emerged as a key type of material in this field. Of particular interest are hybrid systems containing rigid inclusions that can define both the anisotropy and spatial nonuniformity of swelling as well as nanoparticulate additives that can enhance the responsiveness and functionality of the material. In this Account, we discuss recent progress in approaches to achieve well-defined shape morphing in hydrogel hybrids. First, we provide an overview of materials and methods that facilitate fabrication of such systems and outline the geometry and mechanics behind shape morphing of thin sheets. We then discuss how patterning of stiff inclusions within soft responsive hydrogels can be used to program both bending and swelling, thereby providing access to a wide array of complex 3D forms. The use of discretely patterned stiff regions to provide an effective composite response offers distinct advantages in terms of scalability and ease of fabrication compared with approaches based on smooth gradients within a single layer of responsive material. We discuss a number of recent advances wherein control of the mechanical properties and geometric characteristics of patterned stiff elements enables the formation of 3D shapes, including origami-inspired structures, concatenated helical frameworks, and surfaces with nonzero Gaussian curvature. Next, we outline how the inclusion of functional elements such as nanoparticles can enable unique pathways to programmable and even reprogrammable shape-morphing materials. We focus to a large extent on photothermally reprogrammable systems that include one of a variety of additives that serve to efficiently absorb light and convert it into heat, thereby driving the response of a temperature-sensitive hydrogel. Such systems are advantageous in that patterns of light can be defined with very high spatial and temporal resolution in addition to offering the potential for wavelength-selective addressability of multiple different inclusions. We highlight recent advances in the preparation of light-responsive hybrid systems capable of undergoing reprogrammable bending and buckling into well-defined 3D shapes. In addition, we describe several examples where shape tuning of hybrid systems enables control over the motion of responsive hydrogel-based materials. Finally, we offer our perspective on open challenges and future areas of interest for the field.

Shape-programmable magnetic soft matter

Shape-programmable matter is a class of active materials whose geometry can be controlled to potentially achieve mechanical functionalities beyond those of traditional machines. Among these materials, magnetically actuated matter is particularly promising for achieving complex time-varying shapes at small scale (overall dimensions smaller than 1 cm). However, previous work can only program these materials for limited applications, as they rely solely on human intuition to approximate the required magnetization profile and actuating magnetic fields for their materials. Here, we propose a universal programming methodology that can automatically generate the required magnetization profile and actuating fields for soft matter to achieve new time-varying shapes. The universality of the proposed method can therefore inspire a vast number of miniature soft devices that are critical in robotics, smart engineering surfaces and materials, and biomedical devices. Our proposed method includes theoretical formulations, computational strategies, and fabrication procedures for programming magnetic soft matter. The presented theory and computational method are universal for programming 2D or 3D time-varying shapes, whereas the fabrication technique is generic only for creating planar beams. Based on the proposed programming method, we created a jellyfish-like robot, a spermatozoid-like undulating swimmer, and an artificial cilium that could mimic the complex beating patterns of its biological counterpart.

Programmed planar-to-helical shape transformations of composite hydrogels with bioinspired layered fibrous structures

Self-shaping materials have attracted tremendous interest due to their promising applications in soft robotics, and flexible electronics, etc. In this field, a crucial issue is how to construct complex yet elaborate structures in active materials. Here, we present the fabrication of composite hydrogels with both in-plane and out-of-plane structural gradients by multi-step photolithography and the resulting controllable deformations. A patterned gel with a layered fibrous structure like bean pod is developed, which shows programmed deformations from a flat shape to a twisted helix. The parameters of the helix can be deliberately tuned. This approach enables patterning different responsive polymers in specific regions of composite gels, leading to multiple shape transformations under stimulations. The controllability of intricate structures, together with tunable responses of localized gels, facilitates the generation of complex internal stresses and three-dimensional deformations of composite gels toward specific applications.

Grayscale gel lithography for programmed buckling of non-Euclidean hydrogel plates

Shape programmable materials capable of morphing from a flat sheet into controlled three dimensional (3D) shapes offer promise in diverse areas including soft robotics, tunable optics, and bio-engineering. We describe a simple method of 'grayscale gel lithography' that relies on a digital micromirror array device (DMD) to control the dose of ultraviolet (UV) light, and therefore the extent of swelling of a photocrosslinkable poly(N-isopropyl acrylamide) (PNIPAm) copolymer film, with micrometer-scale spatial resolution. This approach allows for effectively smooth profiles of swelling to be prescribed, enabling the preparation of buckled 3D shapes with programmed Gaussian curvature.

Ionoprinted Multi-Responsive Hydrogel Actuators

We report multi-responsive and double-folding bilayer hydrogel sheet actuators, whose directional bending response is tuned by modulating the solvent quality and temperature and where locally crosslinked regions, induced by ionoprinting, enable the actuators to invert their bending axis. The sheets are made multi-responsive by combining two stimuli responsive gels that incur opposing and complementary swelling and shrinking responses to the same stimulus. The lower critical solution temperature (LCST) can be tuned to specific temperatures depending on the EtOH concentration, enabling the actuators to change direction isothermally. Higher EtOH concentrations cause upper critical solution temperature (UCST) behavior in the poly(N-isopropylacrylamide) (pNIPAAm) gel networks, which can induce an amplifying effect during bilayer bending. External ionoprints reliably and repeatedly invert the gel bilayer bending axis between water and EtOH. Placing the ionoprint at the gel/gel interface can lead to opposite shape conformations, but with no clear trend in the bending behavior. We hypothesize that this is due to the ionoprint passing through the neutral axis of the bilayer during shrinking in hot water. Finally, we demonstrate the ability of the actuators to achieve shapes unique to the specific external conditions towards developing more responsive and adaptive soft actuator devices.