Creasing-wrinkling transition in elastomer films under electric fields

Mechanics of Surface Instabilities in Soft Dielectrics Subject to Electromechanical Loading

As a category of polymeric materials, soft dielectrics, such as most elastomers and rubber-like materials, have shown great potential for extensive applications in various fields. Owing to their intriguing electromechanical coupling behaviors, the morphological instabilities in soft dielectrics have been an active research field in recent years. In this work, the recent progress in experimental and theoretical research on their electromechanical morphological instabilities is reviewed, especially regarding the theoretical aspect. First, we revisit the theoretical framework for the electroelasticity of soft dielectrics. Then, the typical configurations of soft dielectric membranes used to generate two typical types of surface instabilities, namely wrinkles and creases, are introduced. Three commonly used modeling approaches (i.e., the stress balance method, the incremental method, and the energy method) for surface instabilities are reviewed with specific examples. Moreover, discussions on the difference between these methods and the corresponding critical loading conditions are presented. Furthermore, this review also covers the relation and transition between wrinkling and creasing phenomena.

Harnessing Gravity‐Induced Instability of Soft Materials: Mechanics and Application

This work offers a comprehensive overview of how gravity affects soft materials, with a particular emphasis on gravity‐induced instability. Soft materials, including biological tissues, elastomers, and gels, are characterized by low elastic moduli and the ability to undergo significant deformations. These large deformations can lead to instabilities and the emergence of distinctive surface patterns when even small perturbations are introduced. An in‐depth understanding of these gravity‐induced instabilities in soft materials is of paramount importance for both fundamental scientific research and practical applications across diverse domains. The underlying mechanisms governing these instabilities are delved in and elucidate the techniques employed to study and manipulate them. Further, the gravity‐induced wrinkling and the Rayleigh‐Taylor (RT) instability in soft materials are zoomed in, highlighting how altered gravity environments impact natural and synthetic systems. Lastly, current and potential applications are underscored where gravity‐induced instabilities are already making an impact or may hold promise in the near future. In sum, the exploration of gravity‐induced instabilities in soft materials paves the way for innovative applications and advancements in a wide range of fields.

Nonlinear electromechanical coupling in graded soft materials: Large deformation, instability, and electroactuation

Subject to an applied electric field, soft dielectrics with intrinsic low moduli can easily achieve a large deformation through the so-called electrostatic Maxwell stress. Meanwhile, the highly nonlinear electromechanical coupling between the mechanical and electric loads in soft dielectrics gives a variety of failure modes, especially pull-in instability. These failure modes make the application of soft dielectrics highly limited. In this paper, we investigate the large deformation, pull-in instability, and electroactuation of a graded circular dielectric plate subject to the in-plane mechanical load and the applied electric load in the thickness direction. The results obtained herein cover, as special cases, the electromechanical behaviors of homogeneous dielectrics. There is a universal physical intuition that stiffer dielectrics can sustain higher electromechanical loads for pull-in instability but achieve less deformation, and vice versa. We show this physical intuition theoretically in different homogeneous dielectrics and graded dielectrics. Interestingly, we find that the ability to sustain a high electric field or a large deformation in a stiff or soft homogeneous circular dielectric plate can be achieved by just using a graded circular dielectric plate. We only have to partly change the modulus of a circular plate, with a stiff or soft outer region. The change makes the same electromechanical behavior as that of a homogeneous dielectric, even increases the maximum electroactuation stretch from 1.26 to 1.5. This sheds light on the effects of the material inhomogeneity on the design of advanced dielectric devices including actuators and energy harvestors.

Emergent magnetoelectricity in soft materials, instability, and wireless energy harvesting

Magnetoelectric materials that convert magnetic fields into electricity and vice versa are rare and usually complex, hard crystalline alloys. Recent work has shown that soft, highly deformable magnetoelectric materials may be created by using a strain-mediated mechanism. The electromagnetic and elastic deformation of such materials is intricately coupled, giving rise to a rather rich instability and bifurcation behavior that may limit or otherwise put bounds on the emergent magnetoelectric behavior. In this work, we investigate the magneto-electro-mechanical instability of a soft dielectric film subject to mechanical forces and external electric and magnetic fields. We explore the interplay between mechanical strain, electric voltage and magnetic fields and their impact on the maximum voltage and the stretch the dielectric material can reach. Specifically, we present physical insights to support the prospects to achieve wireless energy harvesting through remotely applied magnetic fields.

Fault-Tolerant Electro-Responsive Surfaces for Dynamic Micropattern Molds and Tunable Optics

Electrically deformable surfaces based on dielectric elastomers have recently demonstrated controllable microscale roughness, ease of operation, fast response, and possibilities for programmable control. Potential applications include marine anti-biofouling, dynamic pattern generation, and voltage-controlled smart windows. Most of these systems, however, exhibit limited durability due to irreversible dielectric breakdown. Lowering device voltage to avoid this issue is hindered by an inadequate understanding of the electrically-induced wrinkling deformation as a function of the deformable elastic film thickness. Here we report responsive surfaces that overcome these shortcomings: we achieve fault-tolerant behavior based on the ability to self-insulate breakdown faults, and we enhance fundamental understanding of the system by quantifying the critical field necessary to induce wrinkles in films of different thickness and comparing to analytical models. We also observe new capabilities of these responsive surfaces, such as field amplification near local breakdown sites, which enable actuation and wrinkle pattern formation at lower applied voltages. We demonstrate the wide applicability of our responsive, fault-tolerant films by using our system for adjustable transparency films, tunable diffraction gratings, and a dynamic surface template/factory from which various static micropatterns can be molded on demand.

Two-field surface pattern control via marginally stable magnetorheological elastomers

The stability and post-bifurcation of a non-linear magnetoelastic film/substrate block is experimentally exploited to obtain active control of surface roughness. The non-intuitive interplay between magnetic field and elastic deformation owes to material and geometry selection, namely a ferromagnetic particle composite film bonded on a compliant passive foundation. Cooperation of the two otherwise independent loading mechanisms-mechanical pre-compression and magnetic field-allows one to bring the structure near a marginally stable state and then destabilize it with either magnetic or mechanical fields. We demonstrate for the first time that the critical magnetic field is a decreasing function of pre-compression and vice versa. The experimental results are then probed successfully with full-field finite element simulations at large strains and magnetic fields. The magnetoelastic coupling allows for reversible on/off control of surface wrinkling under adjustable critical magnetic and mechanical fields, thus this study constitutes a first step towards realistic active haptic and morphing devices.

Electro-elastocapillary Rayleigh-plateau instability in dielectric elastomer films

We demonstrate, using both finite element simulations and a linear stability analysis, the emergence of an electro-elastocapillary Rayleigh-plateau instability in dielectric elastomer (DE) films under 2D, plane strain conditions. When subject to an electric field, the DEs exhibit a buckling instability for small elastocapillary numbers. For larger elastocapillary numbers, the DEs instead exhibit the Rayleigh-plateau instability. The stability analysis demonstrates the critical effect of the electric field in causing the Rayleigh-plateau instability, which cannot be induced solely by surface tension in DE films. Overall, this work demonstrates the effects of geometry, boundary conditions, and multi-physical coupling on a new example of Rayleigh-plateau instability in soft solids.

Buckling of elastomer sheets under non-uniform electro-actuation

Dielectric elastomer sheets undergo in-plane expansion when stimulated by a transverse electric field. We study experimentally how dielectric plates subjected to a non-uniform voltage distribution undergo buckling instabilities. Two different configurations involving circular plates are investigated: plates freely floating on a bath of water, and plates clamped on a frame. We describe theoretically the out-of-plane deformation of the plates within the framework of weakly non-linear plate equations. This study constitutes a first step of a route to control the 3D activation of dielectric elastomers.

Soft Elastomers with Ionic Liquid-Filled Cavities as Strain Isolating Substrates for Wearable Electronics

Managing the mechanical mismatch between hard semiconductor components and soft biological tissues represents a key challenge in the development of advanced forms of wearable electronic devices. An ultralow modulus material or a liquid that surrounds the electronics and resides in a thin elastomeric shell provides a strain-isolation effect that enhances not only the wearability but also the range of stretchability in suitably designed devices. The results presented here build on these concepts by (1) replacing traditional liquids explored in the past, which have some nonnegligible vapor pressure and finite permeability through the encapsulating elastomers, with ionic liquids to eliminate any possibility for leakage or evaporation, and (2) positioning the liquid between the electronics and the skin, within an enclosed, elastomeric microfluidic space, but not in direct contact with the active elements of the system, to avoid any negative consequences on electronic performance. Combined experimental and theoretical results establish the strain-isolating effects of this system, and the considerations that dictate mechanical collapse of the fluid-filled cavity. Examples in skin-mounted wearable include wireless sensors for measuring temperature and wired systems for recording mechano-acoustic responses.

Nucleation and propagation of voltage-driven wrinkles in an inflated dielectric elastomer balloon

Dielectric elastomer (DE) transducers frequently undergo voltage-induced large deformation, which may lead to mechanical instabilities. Here, we investigate wrinkle formation and propagation on the surface of a DE membrane mounted on an air chamber and subjected to a step voltage. Our experiments show that the geometric characteristics of the wrinkle morphology and the nucleation sites depend on the inflation pressure and the applied voltage. As the inflation pressure increases, the critical voltage used to nucleate the wrinkle decreases, while the location where the wrinkle nucleates shifts from the center to the boundary of the membrane. Moreover, by increasing the amplitude of the applied voltage, wrinkle morphology changes from stripe-like wrinkles to labyrinth-like wrinkles. Furthermore, we develop an analytical model to validate the experimental observations and map out the various wrinkle morphologies as a function of the applied pressure and voltage. A three dimensional phase diagram is constructed to help design new soft actuators.

Electrical perturbations of ultrathin bilayers: role of ionic conductive layer

The effect of electrostatic force on the dynamics, morphological evolution, and drainage time of ultrathin liquid bilayers (<100 nm) are investigated for perfect dielectric-perfect dielectric (PD-PD) and ionic liquid-perfect dielectric (IL-PD) bilayers. The weakly nonlinear "thin film" equation is solved numerically to obtain spatiotemporal evolution of the liquid-liquid interface responses to transverse electric field. In order to predict the electrostatic component of conjoining/disjoining pressure acting on the interface for IL-PD bilayers, an analytical model is developed using the nonlinear Poisson-Boltzmann equation. It is found that IL-PD bilayers with electric permittivity ratio of layers (lower to top), εr, greater than one remain stable under an applied electric field. An extensive numerical study is carried out to generate a map based on εr and the initial mean thickness of the lower layer. This map is used to predict the formation of various structures on PD-PD bilayer interface and provides a baseline for unstable IL-PD bilayers. The use of an ionic liquid (IL) layer is found to reduce the size of the structures, but results in polydispersed and disordered pillars spread over the domain. The numerical predictions follow similar trend of experimental observation of Lau and Russel. (Lau, C. Y.; Russel, W. B. Fundamental Limitations on Ordered Electrohydrodynamic Patterning; Macromolecules 2011, 44, 7746-7751).

Miniaturized pattern formation in elastic films cast on sinusoidally patterned substrates

The various morphologies that are formed when van der Waals forces or electric field is induced between film cast on a sinusoidal substrate and in contact proximity with a contactor or electrode are studied. Remarkably smaller length scales are achieved (λc < 2.96h) than those obtained with films cast on flat substrates. With van der Waals interactions, the patterns are uniformly formed throughout the film but are not regularly ordered. When electric field is used at critical voltage, more ordered, localized patterns are formed at the zones of large local interaction strengths. When these patterns are evolved by increasing the applied voltage, coexistence of all three phases-cavities, stripes, and columns-is observed throughout the film. The localized patterns that are initially formed vary with the voltage applied and strongly dictate the phases of evolution. A patterned substrate/patterned contactor assembly can be made to operate like its unpatterned counterpart by making the interaction strength same everywhere and yet yield uniform, regularly ordered, highly miniaturized patterns. Such patterns are very useful in various applications like microfluidics; they are formed with great ease and can be morphologically tuned by tuning the externally applied electric field.

Soft robotic concepts in catheter design: an on-demand fouling-release urinary catheter

Infectious biofilms are problematic in many healthcare-related devices and are especially challenging and ubiquitous in urinary catheters. This report presents an on-demand fouling-release methodology to mechanically disrupt and remove biofilms, and proposes this method for the active removal of infectious biofilms from the previously inaccessible main drainage lumen of urinary catheters. Mature Proteus mirabilis crystalline biofilms detach from silicone elastomer substrates upon application of strain to the substrate, and increasing the strain rate increases biofilm detachment. The study presents a quantitative relationship between applied strain rate and biofilm debonding through an analysis of biofilm segment length and the driving force for debonding. Based on this mechanism, hydraulic and pneumatic elastomer actuation is used to achieve surface strain selectively within the lumen of prototypes of sections of a fouling-release urinary catheter. Proof-of-concept prototypes of sections of active, fouling-release catheters are constructed using techniques typical to soft robotics including 3D printing and replica molding, and those prototypes demonstrate release of mature P. mirabilis crystalline biofilms (e.g., ≈90%) from strained surfaces. These results provide a basis for the development of a new urinary catheter technology in which infectious biofilms are effectively managed through new methods that are entirely complementary to existing approaches.

Cephalopod-inspired design of electro-mechano-chemically responsive elastomers for on-demand fluorescent patterning

Cephalopods can display dazzling patterns of colours by selectively contracting muscles to reversibly activate chromatophores--pigment-containing cells under their skins. Inspired by this novel colouring strategy found in nature, we design an electro-mechano-chemically responsive elastomer system that can exhibit a wide variety of fluorescent patterns under the control of electric fields. We covalently couple a stretchable elastomer with mechanochromic molecules, which emit strong fluorescent signals if sufficiently deformed. We then use electric fields to induce various patterns of large deformation on the elastomer surface, which displays versatile fluorescent patterns including lines, circles and letters on demand. Theoretical models are further constructed to predict the electrically induced fluorescent patterns and to guide the design of this class of elastomers and devices. The material and method open promising avenues for creating flexible devices in soft/wet environments that combine deformation, colorimetric and fluorescent response with topological and chemical changes in response to a single remote signal.

On-demand hierarchical patterning with electric fields

We report a method to generate hierarchical topographical patterns on demand under the control of applied voltages. The method is implemented by harnessing the electro-creasing instability in multilayerelastomer films. The critical electric field for electro-creasing instability in a layer of elastomer scales with square root of the elastomer's modulus, while the wavelength of instability pattern scales with the layer's thickness. By rationally designing elastomer films with varied modulus and thickness throughout different layers, we control the formation of surface instability patterns with feature sizes of different scales under prescribed voltages. The method is very versatile, giving various types of hierarchical patterns such as randomly oriented, aligned, and gradient ones. A theoretical model is developed and validated to guide the design of hierarchical patterns.

Phase Diagrams of Instabilities in Compressed Film-Substrate Systems

Subject to a compressive membrane stress, an elastic film bonded on a substrate can become unstable, forming wrinkles, creases or delaminated buckles. Further increasing the compressive stress can induce advanced modes of instabilities including period-doubles, folds, localized ridges, delamination, and coexistent instabilities. While various instabilities in film-substrate systems under compression have been analyzed separately, a systematic and quantitative understanding of these instabilities is still elusive. Here we present a joint experimental and theoretical study to systematically explore the instabilities in elastic film-substrate systems under uniaxial compression. We use the Maxwell stability criterion to analyze the occurrence and evolution of instabilities analogous to phase transitions in thermodynamic systems. We show that the moduli of the film and the substrate, the film-substrate adhesion strength, the film thickness, and the prestretch in the substrate determine various modes of instabilities. Defects in the film-substrate system can facilitate it to overcome energy barriers during occurrence and evolution of instabilities. We provide a set of phase diagrams to predict both initial and advanced modes of instabilities in compressed film-substrate systems. The phase diagrams can be used to guide the design of film-substrate systems to achieve desired modes of instabilities.