Pre-stretched Membrane Research Articles

Investigation of buckling instabilities in fiber-reinforced DEAs

Artificial muscles, designed to replicate the movements of natural biological muscles, hold significant promise in the fields of robotics and prosthetics. Recent advancements have led to the development of fiber-reinforced actuators, drawing inspiration from biological tissues. Dielectric elastomer actuators (DEAs) are a type of electroactive artificial muscle. It is possible to enhance the uni-axial deformation of DEAs by constraining and applying pre-stretch on the actuator membrane. This can be achieved through uni-directional fibers bonded to the DEA that lead to transversely isotropic properties. However, combining membrane pre-stretch and fiber reinforcement may lead to instabilities such as fiber buckling due to the compressive load of the pre-stretched membrane or due to wrinkling during actuation. Understanding these instabilities is crucial as they can significantly impact the performance. A novel model taking into consideration these instabilities is established and experimentally validated. By calculating the force in the fiber direction, the buckling profile such as the wavelength and amplitude can be predicted. The validation of the model presented along with an extensive experimental investigation allow for a comprehensive analysis to explore the impact of fiber buckling on the performance and the force of uni-axial DEAs.

Co-Culture of Schwann Cells with DRG Neurons on a Pre-Stretched Membrane

Co-Culture of Schwann Cells with DRG Neurons on a Pre-Stretched Membrane

Co-Culture of Schwann Cells with DRG Neurons on a Pre-Stretched Membrane

Co-Culture of Schwann Cells with DRG Neurons on a Pre-Stretched Membrane

Bifurcations of a Laminated Circular Cylindrical Shell

In this paper, the stability and local bifurcations of a composite laminated circular cylindrical shell with radially pre-stretched membranes are explored by using analytical and numerical methods. On the basis of the four-dimensional averaged equation in the case of 1:1 internal resonance, three types of critical points are studied in detail. They are characterized as (1) one pair of purely imaginary eigenvalues and two negative eigenvalues; (2) a simple zero and one pair of purely imaginary eigenvalues; (3) two pairs of purely imaginary eigenvalues in nonresonant case. With the aid of normal form theory and Maple software, the steady-state solutions and the stability regions of the initial equilibrium solutions are obtained. The explicit expressions for the critical bifurcation curves leading to static bifurcation and Hopf bifurcation are also presented. The presence of Hopf bifurcation indicates that the circular cylindrical shell will flutter. The results contribute to the design of reasonable structure parameters to avoid flutter. Finally, numerical simulations are also presented to demonstrate the good agreement with the analytical predictions.

Stiffness and pre-stretching estimation from indentation test of hyperelastic membrane

Obtaining precise data on the mechanical properties of soft materials, often in the form of thin, pre-tensioned membranes, is crucial, especially when conventional testing methods have limited applicability. The article focuses on an innovative method for estimating the Young's modulus and pre-stretching the membranes using the indentation method, assuming an isotropic, incompressible hyperelastic material. The parameters were estimated for two models of indenter-membrane contact: with perfect slip and without slip. Experimental tests were performed for pre-stretched latex membranes glued to a stiffer ring to minimize the effect of attachment on membrane deformation. In order to validate the estimation method, the predictions of the model with the determined mechanical parameters were compared with the results of indentation tests with a liquid layer under the membrane. The discussion shows the consistency of the estimation results with the literature results for small latex deformations, and indicates the advantages and numerous limitations of the approach, especially related to the choice of the material model.

Intrinsically Multistable Soft Actuator Driven by Mixed-Mode Snap-Through Instabilities.

Actuators utilizing snap-through instabilities are widely investigated for high-performance fast actuators and shape reconfigurable structures owing to their rapid response and limited reliance on continuous energy input. However, prevailing approaches typically involve a combination of multiple bistable actuator units and achieving multistability within a single actuator unit still remains an open challenge. Here, a soft actuator is presented that uses shape memory alloy (SMA) and mixed-mode elastic instabilities to achieve intrinsically multistable shape reconfiguration. The multistable actuator unit consists of six stable states, including two pure bendingstates and four bend-twist states. The actuator is composed of a pre-stretched elastic membrane placed between two elastomeric frames embedded with SMA coils. By controlling the sequence and duration of SMA activation, the actuator is capable of rapid transition between all six stable states within hundreds of milliseconds. Principles of energy minimization are used to identify actuation sequences for various types of stable state transitions. Bendingand twisting angles corresponding to various prestretch ratios are recorded based on parameterizations of the actuator's geometry. To demonstrate its application in practical conditions, the multistable actuator is used to perform visual inspection in a confined space, light source tracking during photovoltaic energy harvesting, and agilecrawling.

Nonlinear free vibration analysis of ionic liquid enhanced soft composite membrane

Due to their electromechanical coupling properties, ionic liquid (IL)-enhanced dielectric elastomer composites are promising for applications in soft robotics and implantable actuators. However, their structural vibration behaviors subjected to electric fields remain unclear. This work investigates the nonlinear vibration of IL-enhanced soft composite (ILESC) membranes subjected to electric loading through theoretical modeling and numerical simulation. The effective properties of ILESC membrane are determined by a developed micromechanical model considering the physical mechanisms as involved. Governing equations for the nonlinear vibration of a pre-stretched circular membrane made of ionic liquid/poly (dimethylsiloxane) (IL/PDMS) are established, which are solved by Taylor series expansion (TSE) and differential quadrature (DQ) methods. The developed model and numerical results are verified by comparing present results to existing studies and finite element analysis. The influences of the size of the membrane, the direct current (DC) voltage and alternating current (AC) frequency of the electric field, and the attributes of the IL fillers and matrix on the nonlinear vibration of the structure are investigated. The voltage-induced nonlinearity is highly sensitive to the content, size and shape of the IL fillers. The performances of the structure within various AC frequency bands can be tuned by changing the geometry of the IL fillers as well as the surface charge density of the matrix. This study aims to provide guidelines for predicting and optimizing the structural behaviors of ILESC membranes, accelerating their applications in engineering demanding flexibility and voltage-dependent responses.

Multi-stability of fiber reinforced polymer frames with different geometries

Shape adaptable structures are desired in many fields of application such as aerospace, soft robotics, and architecture. Multi-stable structures can enable shape adaptation as they possess multiple stable morphologies that can be held without the need of external work. Many concepts to realize multi-stable systems have been proposed in the last decades. However, the vast majority of multi-stable structures exhibit minimal changes in shape or high coupling between stable states, which limits their applicability. Recently, a novel class of multi-stable composite structures has been investigated, showing that a periodic arrangement of square frames combined with pre-stretched membranes enables many stable states together with large shape transformations. To investigate how this new class can be employed in a broader range of applications, this study extends the design space to any N-sided regular polygon frame. The multi-stability is investigated through experiments and finite element (FE) analysis. The polygonal frames and their respective periodic arrangements possess a large number of stable states, with similar behavior to that of the square frames. Moreover, neutral stability is observed for the limit case of a circular polygonal frame. This study proves that the concept is highly flexible in terms of design, thus opening up new possibilities for applications of multi-stable composite structures.

Effect of geometrical parameters on the nonlinear behavior of DE-based minimum energy structures: Numerical modeling and experimental investigation

This work presents a finite element framework for simulating the quasi-static response of dielectric elastomer-based minimum energy structure (DEMES). The DEMES is an actuator formed by combining an inextensible frame and pre-stretched dielectric membrane that exhibits the unique shape-morphing characteristics of the actuator. A continuum strain energy-based model is implemented to investigate the impact of the different geometrical parameters on the performance of the DEMES actuator. Finite element analyses are performed using user-defined element (UEL) in ABAQUS for determining the equilibrium shape of the actuators and further investigating their electromechanical response. Experiments are performed using the commercially available VHB-4910 acrylic tape and the PET frames. 3D-printed reinforcements are used to impart anisotropy in the specimen. The findings of the model solutions provide preliminary insights on the alteration of the initial and final configurations of the DEMES affected by different geometrical parameters. It is observed that the shape of the electrode (rectangular, circular and triangular), compliant frame (rectangular, circular and triangular) and implemented stiffeners appreciably alter the attained initial configuration, final configuration and actuation range of the DEMES actuator. In general, this investigation can find its potential use in designing the futuristic DEMES through topological optimization of the compliant electrode and frame geometry together with material anisotropy of the elastomer.

Analytical pressure–deflection curves for the inflation of pre-stretched circular membranes

The inflation of circular membranes is a benchmark problem in finite elasticity. Due to its mathematical complexity, so far most efforts have been focused on numerical solutions whereas analytical solutions are still lacking. The present work proposes an analytical formula to compute the pressure–deflection curves of pre-stretched circular membranes. The Mooney–Rivlin hyperelastic model is assumed as constitutive law. Following the semi-inverse method, an analytical model assuming spherical deformed configurations is developed and a pressure–deflection relation is derived. Due to the simplifying hypothesis on the kinematics, the analytical expression for the pressure is not always accurate and requires an adjustment. Two corrective polynomial functions are implemented in the formula to capture the effect of the pre-stretch, which affects the pressure–deflection response depending on the magnitude of deformation and material parameters. The polynomial coefficients are calibrated by fitting numerical solutions of the differential equilibrium equations of the exact theory. The calibration is performed over a wide range of material parameters and pre-stretch, covering all the values of practical interest. As a result, an accurate and ready-to-use pressure–deflection relation for practical applications is obtained. The proposed formula is validated by finite element simulations. Differently from other solutions in literature, our formula holds for both compressible and incompressible materials. Experimental bulge tests on pre-stretched rubber membranes are carried out and the proposed formula is used for the calibration of material parameters. A code developed in the software Mathematica is made available upon request to directly compute the proposed formula.

Effect of stretch limit change on hyperelastic dielectric actuation of styrene–ethylene/butylene–styrene (SEBS) copolymer organogels

Harder dielectric elastomers are structurally stronger than soft ones but hardly actuate under electrostatic pressure. It remains unclear which property limits harder dielectric elastomers from producing as large actuation as soft ones. This study shows that the change in stretch limit rather than modulus bounds the ultimate dielectric actuation. A larger ultimate stretch warrants a pre-stretched membrane to further thin down and expand biaxially relative to the pre-stretch state. Theory and experiments showed that pre-stretch alters the maximum stretchability and ultimate dielectric actuation. An optimal pre-stretch helps maximize the ultimate actuation close to times radially so long as the corresponding total stretch did not exceed the elastomer’s fracture limit. Hence, a stretchy harder dielectric elastomer stands a chance of producing as large ultimate actuation as soft ones do. To validate the theory, we tested three commercial grades of styrene–ethylene/butylene–styrene copolymers (SEBS) organogels with different oil content and shore hardness. The tests showed that a 20 A-hardness organogel of low toughness actuated less ultimately, but a 10 A-hardness organogel of greater toughness actuated as much as an 8 A-hardness organogel does. This 10 A-hardness SEBS organogel showed an ultimate elongation of 1192%, and 3.1 times the shear modulus and seven times the tensile strength of 3 M VHB 4910. When being optimally pre-stretched for 3.5 times radially, it produced a substantial hyperelastic dielectric actuation up to 104% active areal strain at 277 MV m−1, comparable to the actuation generated by the over-stiffened VHB DEAs. Unlike VHB DEAs, these harder SEBS DEAs generated hyperelastic actuation free from severe viscoelastic drift. The high performance of SEBS organogels can potentially meet the need for forceful artificial muscles to drive bio-inspired robots.

Instability-driven shape forming of fiber reinforced polymer frames

Thin fiber reinforced polymer (FRP) composites are widely implemented in adaptive and morphing structures. However, realization of the necessary complex 3-dimensional FRP structures requires the use of expensive molds thereby limiting the design space and flexibility. Using the elastic strain energy of pre-stretched membranes holds potential for addressing this challenge. In this work, a novel manufacturing technique for fabricating 3-dimensional FRP structures moldlessly is presented where pre-stretched membranes are used to drive out-of-plane buckling instabilities of FRP composite shells. To explore the potential of this approach, a simple square frame design is investigated. An analytical model based on high deformation beam buckling theory is developed for understanding the parameters driving the out-of-plane behavior of these structures. Experimental and finite element results are used for model validation and reveal excellent agreement, with errors less than 10% over a large portion of the design space. Analytical and finite element models demonstrate that the out-of-plane deformation can be tailored by varying the structure’s geometric and material parameters. A new design space for FRP composite laminates is characterized, enabling highly flexible design. The manufacturing and modeling techniques can be extended to other geometries for the realization and analysis of arbitrarily complex surfaces.

Modeling and analysis of a magnetoelastic annular membrane placed in an azimuthal magnetic field

This work presents the development of a 2D nonlinear magnetoelastic framework for a thin membrane undergoing large deformations. An asymptotic theory is obtained, starting from the 3D variational magnetostatic and force balance equations for a weakly magnetizable material. The model is subsequently specialized to axisymmetry and applied to a pre-stretched annular membrane deforming under azimuthal magnetic field and transverse pressure loading. Parametric studies are performed by varying the pre-stretch, magnetic field, and transverse pressure inputs.

Analytical solutions for inflation of pre-stretched elastomeric circular membranes under uniform pressure

Elastomeric membranes are frequently used in several emerging fields such as soft robotics and flexible electronics. For convenience of the structural design, it is very attractive to find simple analytical solutions to well describe their elastic deformations in response to external loadings. However, both the material/geometrical nonlinearity and the deformation inhomogeneity due to boundary constraints make it much challenging to get an exact analytical solution. In this paper, we focus on the inflation of a pre-stretched elastomeric circular membrane under uniform pressure, and derive an approximate analytical solution of the pressure–volume curve based upon a reasonable assumption on the shape of the inflated membrane. Such an explicit expression enables us to quantitatively design the material and geometrical parameters of the pre-stretched membrane to generate a target pressure–volume curve with prescribed peak point and initial slope. This work would be of help in the simplified mechanical design of structures involving elastomeric membranes.

Andronov-Hopf bifurcations, Pomeau-Manneville intermittent chaos and nonlinear vibrations of large deployable space antenna subjected to thermal load and radial pre-stretched membranes with 1:3 internal resonance

Abstract Andronov-Hopf bifurcations, Pomeau-Manneville intermittent chaos and nonlinear vibrations of the large deployable space antenna (LDSA) subjected to the thermal load with the case of 1:3 internal resonance are studied for the first time. The frequencies and vibration modes of the LDSA are analyzed by using the finite element method. It is found that there may exist an approximate threefold relationship between the fourth-order and first-order frequencies of the LDSA. The LDSA is simplified to a composite laminated equivalent cylindrical shell clamped along a generatrix and with the radial pre-stretched membranes at two ends subjected to the thermal load. Considering the case of 1:3 internal resonance, four-dimensional nonlinear averaged equations are obtained by using the method of multiple scales. The amplitude-frequency response curves and amplitude-force response curves are obtained for the LDSA subjected to the thermal load through the prediction-correction continuation algorithm. The fold bifurcation and Andronov-Hopf bifurcation points are located on these resonant response curves. The equivalent model of the LDSA has the hardening spring characteristics. The thermal load has very significant influences on the stability of the LDSA. The nonlinear dynamics of the equivalent model for the LDSA are investigated by using the fourth-order Runge-Kutta algorithm. These nonlinear dynamic behaviors are described by the bifurcation diagrams, waveforms, phase plots, and Poincare maps. The periodic doubling bifurcation and Pomeau-Manneville type intermittent chaos appear in this nonlinear dynamical system. According to the topological evolution of the phase trajectories, the phase-locking phenomenon and a special evolution path of the chaotic attractors are found.

Dielectric Elastomer Actuator Driven Soft Robotic Structures With Bioinspired Skeletal and Muscular Reinforcement.

Natural motion types found in skeletal and muscular systems of vertebrate animals inspire researchers to transfer this ability into engineered motion, which is highly desired in robotic systems. Dielectric elastomer actuators (DEAs) have shown promising capabilities as artificial muscles for driving such structures, as they are soft, lightweight, and can generate large strokes. For maximum performance, dielectric elastomer membranes need to be sufficiently pre-stretched. This fact is challenging, because it is difficult to integrate pre-stretched membranes into entirely soft systems, since the stored strain energy can significantly deform soft elements. Here, we present a soft robotic structure, possessing a bioinspired skeleton integrated into a soft body element, driven by an antagonistic pair of DEA artificial muscles, that enable the robot bending. In its equilibrium state, the setup maintains optimum isotropic pre-stretch. The robot itself has a length of 60 mm and is based on a flexible silicone body, possessing embedded transverse 3D printed struts. These rigid bone-like elements lead to an anisotropic bending stiffness, which only allows bending in one plane while maintaining the DEA's necessary pre-stretch in the other planes. The bones, therefore, define the degrees of freedom and stabilize the system. The DEAs are manufactured by aerosol deposition of a carbon-silicone-composite ink onto a stretchable membrane that is heat cured. Afterwards, the actuators are bonded to the top and bottom of the silicone body. The robotic structure shows large and defined bimorph bending curvature and operates in static as well as dynamic motion. Our experiments describe the influence of membrane pre-stretch and varied stiffness of the silicone body on the static and dynamic bending displacement, resonance frequencies and blocking forces. We also present an analytical model based on the Classical Laminate Theory for the identification of the main influencing parameters. Due to the simple design and processing, our new concept of a bioinspired DEA based robotic structure, with skeletal and muscular reinforcement, offers a wide range of robotic application.

Electromechanical evaluation of sub-micron NiCr-carbon thin films as highly conductive and compliant electrodes for dielectric elastomers

This paper focuses on the electromechanical evaluation of combinations of novel sub-micron metal and carbon thin film electrodes for dielectric elastomers. The thin film electrodes are sputtered either onto 37.5 % biaxially pre-stretched polydimethylsiloxane (PDMS)-foils or on 57.5 % pre-stretched foils under pure shear conditions. The electrodes are wrinkled after relaxing the pre-stretch. The wrinkles in combination with the innovative sputtered sandwich-layers of nickel-chromium and carbon, with a total thin film thickness of 10 nm–40 nm, lead to exceptional electromechanical properties. With an initial resistance of only 500 Ω/square, some electrode configurations tolerate high strain up to 100 % without losing conductivity. 10 million cycles of mechanical load do not cause any major degradation of the thin films and their resistances. The capacitance-strain function is linear as long as the test strain is kept below the previously applied pre-stretch. During all the experiments, no delamination of these compliant thin film electrodes was observed. The force-displacement characteristics of the dielectric elastomer can be altered by applying high voltages on the electrodes, and thus, the actuator working principle is demonstrated. Depending on the kind of pre-stretch, some layer sequences are advantageous and others are disadvantageous when a low resistance at high strain is favored. In general, biaxially pre-stretched membranes with a metallic electrode configuration provide the best properties. Hence, this work proves, that sub-micron sandwich-layers of nickel-chromium and carbon are suitable for electrodes of dielectric elastomer actuators and sensors.

A Novel Full Boundary Element Formulation for Harmonic Analysis of Elastic Membranes Coupled to Acoustics Fluids

A novel full Boundary Element Formulation for the harmonic analysis of elastic membranes coupled to acoustics fluid is presented. The elastic membranes is modeled using the classical linear elastic pre-stretched membrane theory. The acoustic fluid is modeled using the acoustic-wave equation for homogeneous, isotropic, inviscid and irrotational fluids. Elastostatic fundamental solution is used in the boundary element formulation for the elastic membrane. The boundary element formulation for the acoustic fluid is based on the fundamental solution of three dimensional Poisson equation. Domain integrals related to inertial terms and those related with distributed pressure on membrane, were treated using the Dual Reciprocity Boundary Element Method. Fluid-structure coupling equations were established considering the continuity of the normal acceleration of the particles and dynamic pressure at fluid-structure interfaces. Results obtained shows the accuracy and efficiency of the proposed boundary element formulation.

A Novel Full Boundary Element Formulation for Transient Analysis of Elastic Membranes Coupled to Acoustics Fluids

A full time-direct Boundary Element Formulation for the dynamic analysis of elastic membranes coupled to acoustics fluid is presented. The elastic membranes is modeled using the classical linear elastic pre-stretched membrane theory. The acoustic fluid is modeled using the acoustic-wave equation for homogeneous, isotropic, inviscid and irrotational fluids. Elastostatic fundamental solution is used in the boundary element formulation for the elastic membrane. The boundary element formulation for the acoustic fluid is based on the fundamental solution of three dimensional Poisson equation. Domain integrals related to inertial terms and those related with distributed pressure on membrane, were treated using the Dual Reciprocity Boundary Element Method. Fluid-structure coupling equations were established considering the continuity of the normal acceleration of the particles and dynamic pressure at fluid-structure interfaces. The time integration is carried out using the Newmark method. Results obtained shows the accuracy and efficiency of the proposed boundary element formulation.

Mechanics of reversible wrinkling in a soft dielectric elastomer.

A parallel array of wrinkles can be generated in a simple parallel plate capacitor arrangement with a soft dielectric elastomer plate constrained all around its periphery and coated with flexible electrodes. The direction of the wrinkles is predetermined and the phenomenon is reversible in a range of applied potentials. A model of the wrinkled plate as a prestretched neo-Hookean membrane with superposed small out-of-plane bending displacements yields good estimates of the potential range for wrinkling as well as the number of parallel wrinkles. The mechanics is controlled by the thickness and aspect ratios, prestretch, and a nondimensional electric potential.