Deformation Of Elastomers Research Articles

Magnetorheological effect in elastomers containing uniaxial ferromagnetic particles

The description of the collective magnetorheological effect induced by magnetic field in magnetoactive elastomers is proposed. The condition of consistency is used between magnetic and mechanic momenta of forces exerted on magnetically uniaxial ferromagnetic particles in elastomer at their magnetization. The study shows that even in the case of small concentration of particles, the value of magnetically-induced shear can be anomalously large, reaching up to tens of percent. The deformation of magnetoactive elastomer can evolve critically, as a second-order phase transition, if magnetic field is aligned along the easy axis of particles.

УСТОЙЧИВОСТЬ СОСТАВНОЙ ТОЛСТОЙ ПЛИТЫ С НЕОДНОРОДНЫМ ПОЛЕМ ПРЕДВАРИТЕЛЬНЫХ НАПРЯЖЕНИЙ

Using methods of spatial nonlinear elasticity we consider the static stability of a rectangular two-layered plate. This problem has a peculiarity which relates to the appearance of nonhomogeneous initial stresses. Each layer of the plate was obtained as a result of straightening of the sector of a cylindrical shell. As a result we have the self-equilibrated initial stresses. The main aim of the paper is the analysis of these initial stresses on the pl ate buckling. The stability was analyzed with linearization method. The method consists of the determination of such critical parameters of deformations for which the linearized boundary-value problem has nonzero or nontrivial solutions. We use the Treloar model as a constitutive relation. This model describes properly deformations of incompressible elastomers up to hundreds percent. Within the linearization approach we derive the linearized boundary-value problem. Using Fourier technique we obtain its nontrivial solutions. To this end we use the representation of solutions in series of sine and cosine functions. On the principal stretches plane we show the stability region. It is demonstrated that the initial stresses may significantly deform this region. In particular, instability can be a result of initial stresses only, that is without action of external loadings. Considered problems can be used for modelling of elements of so-called stretchable electronics, which use multi-layered structures manufactured by deposition of metallic films on an elastic flexible substrate. The internal stresses may result in wrinkling of the elements and to the increase of their flexibility.

Wetting of soap bubbles on soft elastomers with surface stress and gravity

Surface stress and gravitational force have significant effects on the deformation of soft elastomers. By considering surface stress and gravity of the soft elastomer, we study wetting behaviors of soap bubbles on a semi-space elastomer through the surface Green’s function method. The normal surface displacement of the elastomer caused by the surface tension and Laplace pressure is calculated. The normal surface displacement in the contact zone monotonously increases from the center to the triple line, and the contact zone is divided into concave zone and convex zone. The results show that surface stress and gravity have significant influence on the normal surface deformation caused by the wetting of the soap bubble. In general, surface stress and gravity suppress the amplitude of the normal surface displacement. With the increase of surface stress, the amplitude of the normal surface displacement in the concave and convex zones decreases. However, with the increase of gravity, the amplitude of the normal surface displacement in the concave zone decreases, while that in the convex zone increases. This counterintuitive phenomenon can be understood by the superimposition of displacements. The results have potential applications in the fields of adhesion, indentation, evaporation, cell migration on soft materials, etc.

Deformation and Elastic Recovery of Acrylate-Based Liquid Crystalline Elastomers

Liquid crystalline elastomers (LCEs) are well known for their stimuli-responsive behavior. Of interest to the work presented here is the distinctive, nonlinear deformation of these materials to load. Here, we assess the cyclic deformation and elastic recovery of acrylate-based LCEs synthesized by chain-transfer reactions. Mechanical deformation of the LCEs (prepared with this synthetic approach) beyond a threshold strain value does not elastically recover, unless heat-treated. The thermomechanical actuation of these materials exhibits limited hysteresis over five cycles. Exploration of the deformation mechanics and elastic recovery extends the understanding of this material composition and informs its potential use in applications.

Method of Measuring Deformations of Magnetoactive Elastomers under the Action of Magnetic Fields

Magnetic deformation is a change in the size and shape of a sample under the action of a uniform external magnetic field. The study of this effect in various materials provides deep understanding of the nature of magnetic and mechanical interactions. Moreover, magnetic deformation is of great interest from an engineering point of view for designing new devices. In magnetoactive elastomers containing magnetic microparticles in the polymer matrix, a giant deformation is detected under the action of an external magnetic field. The generally accepted methods for measuring magnetic deformation in magnetoactive soft materials are now practically absent. The article describes the installation for the study of the magnetomechanical characteristics of magnetoactive elastomers and demonstrates its experimental capabilities. The installation allows to measure deformations in the range from 0 to 12.5 mm with a resolution of 1 micron. The deformation curves obtained using these installations are required for developing actuators and sensors based on magnetoactive elastomers, and also for improving their manufacturing technologies.

Experimental and theoretical analysis of laterally pre-stretched pure shear deformation of dielectric elastomer

Recently laterally pre-stretched pure shear deformation is considered as the most compatible and easier way of achieving higher actuation performances of dielectric elastomer actuator due to improvement of its dielectric strength and pull-in stability. However, an accurate experimental investigation and modelling criteria of dielectric elastomer under various lateral pre-stretches up to failure have still not been reported in details. In the present work, different pre-stretch levels are incorporated in commonly used material, VHB 4910 under pure shear loading at sufficiently slow strain rate to obtain stress-stretch curves up to failure. It has been also established that Ogden model parameters obtained by fitting pure shear test data are more accurate for pre-stretched pure shear modelling than those obtained from commonly used uniaxial pull test.

Effects of local rearrangement of magnetic particles on deformation in magneto-sensitive elastomers.

Based on the dipole-dipole approach for magnetic interactions we present a comprehensive analysis of spatial rearrangement of magnetic particles under a magnetic field and its effect on the magneto-induced deformation of magneto-sensitive elastomers. The presented formalism allows analyzing non-affine displacements of magnetic particles in a general way and reveals how the local rearrangement of particles under a magnetic field affects the magneto-induced deformation. The formalism includes two contributions: (1) displacements due to elastic coupling with a deformed matrix and (2) rearrangements on the background of the deformed matrix due to magnetic interactions between the particles. We show that in the linear response regime the sign of deformation is defined by the first contribution and the second one amplifies the magnitude of deformation. The sign and magnitude of deformation depend on the factors cos2 θ and cos4 θ, where averaging is over mutual pairs of particles and θ is the angle between the vector connecting the particles and the direction of the magnetic field. We test the new formalism on isotropic-like lattice distributions with cos2 θ = 1/3 and show that the difference in the sign of their deformation is defined by the difference in the factor cos4 θ. The results are compared for 3-dimensional and 2-dimensional systems, which are shown to have a similar behavior as a function of the aspect ratio of a sample.

Field-induced surface deformation of magnetoactive elastomers with anisometric fillers: a single-particle model.

Surface relief of magnetoactive elastomers (MAEs) based on soft polymer matrices filled with anisometric magnetically hard fillers is studied theoretically in magnetic fields applied perpendicular to the MAE surface. A single-particle 2D cell model describing the rotation of one individual elliptical particle in a near-surface MAE layer is developed. The equilibrium rotation angle of particles is defined by a balance between Zeeman, magnetic anisotropy and elastic (generated in the polymer matrix) energy increments. The Stoner-Wohlfarth model is used to describe magnetic properties of the filler particles while the elastic energy as a function of the particle rotation angle is evaluated numerically using FEM simulations. A representative surface MAE system is constructed via superposition of single-particle cells with field-driven magnetic particles, and surface relief characteristics are derived for various sets of geometric and statistical parameters. Limitations of the proposed approach have been discussed.

Multi-cycle deformation of supramolecular elastomers: Constitutive modeling and structure-property relations

Supramolecular elastomers are rubber-like polymers with double-network structure formed by chains bridged by covalent and non-covalent bonds. Due to high mobility of temporary bonds, whose rate of recombination is comparable with the strain rate under loading, these materials demonstrate such properties as self-healing and self-recovery at ambient temperature.A constitutive model is developed for the viscoelastic and viscoplastic behavior of supramolecular elastomers. Stress–strain relations and the kinetic equations for plastic deformation are derived from the free energy imbalance inequality for an isothermal three-dimensional deformation. The viscoelastic response reflects breakage and reformation of temporary junctions in an inhomogeneous transient network (transition of chains from their active to dangling state and vice versa). The viscoplastic response reflects slippage of permanent junctions with respect to their reference positions. A junction starts to slide when it becomes unbalanced due to transformation of one of the chains connected by this junction from its active state into the dangling state. The sliding process (plastic flow) proceeds until the junction reaches its new equilibrium state.The model is applied to fit experimental data in tensile relaxation tests, loading-unloading tests, and multi-cycle tests on supramolecular elastomers and triblock copolymers. Numerical simulation shows that the governing equations describe adequately the experimental stress–strain diagrams, the material parameters evolve consistently with chemical composition and experimental conditions, and predictions of the model are in qualitative agreement with observations.

Effect of shear modulus on the performance of prototype un-bonded fiber reinforced elastomeric isolators

Un-bonded fiber reinforced elastomeric isolator (U-FREI) is light weight and facilitates easier installation in comparison to conventional steel reinforced elastomeric isolators (SREI), in which fiber layers are used as reinforcement to replace steel shims as are normally used in conventional isolators. Shear modulus of elastomer has significant influence on the force-displacement relationship of U-FREI. However, a few studies investigated the effect of shear modulus on the horizontal behavior of prototype U-FREI in literature. In this study, effect of shear modulus on performance of prototype U-FREIs is investigated by both experiment and finite element (FE) analysis. It is observed that reduction in horizontal stiffness of U-FREI with increasing horizontal displacement is due to both rollover deformation (or reduction in contact area of isolator with supports) and shear modulus of elastomer. Reasonable agreement is observed between the findings from experiment and FE analysis.
 Keywords: base isolator; prototype un-bonded fiber reinforced elastomeric isolator; rollover deformation; shear modulus; cyclic test.

STATIC FRICTION OF REVERSE STEEL–ELASTOMER SLIDING PAIRS

Sliding cooperation of materials with different hardness (deformability), e.g., a polymeric material cooperating with metallic materials, occurs in machine elements in one of the following two variants: a conventional pair or a reverse pair. In the case of the conventional sliding pair, the deformation area (contact area) of the sliding materials does not move on the surface of the polymer element during their cooperation. In the case of reverse pairs, the contact surface changes its position when moving on the surface of the polymer element. Depending on the variant of the sliding pair, the differences in the friction and wear process of polymer material can be observed. Tribological investigations of chosen sliding pairs (elastomer on steel or steel on elastomer) in the static friction were carried out on the rig. The polymeric materials selected for the tests were thermoplastic elastomers TPU, PUR, and silicone rubber SI. These materials co-operated with C45 steel in the different contact pressures (p = 0.1 – 0.26 MPa) under dry friction or mixed lubrication conditions (hydraulic oil Hipol HLP-68). Based on the recorded value of the friction force Ft, the values of static coefficients of friction μstat were determined. The test results showed a significant influence of the variant of the combination of materials (metal-polymer or polymer-metal) on the value of the friction coefficient. In all tested pairs in which steel sample (pin) slid against elastomeric plates, the friction coefficient was higher than in the case when the elastomeric sample (pins) cooperated with steel counterfaces (plates). The main reason is the considerable value of the deformation component of the friction force. This is probably due to the displacement of the elastomer deformation area in its surface layer and energy dissipation as a result of stress-strain hysteresis in the elastomeric material, as in the case with reversed pairs.

Prediction of the Creep of Elastomers Taking into Account the Forces of Entropic Elasticity of Macromolecules (Prediction of Creep of Elastomers)

ABSTRACTAccounting for the increase in the energy of activation of viscous flow of polymers by an amount proportional to the force of entropic elasticity of the stretched macromolecules, allows for a quantitative description of the curves of deformation of elastomers in the models of Kelvin-Voigt and the standard linear solid. For these models, application of a rubber-like elasticity modulus, increasing with the increase of deformation, enables calculation of Flory's correction factor for the network defects for the deformation curves of a rubber. The curves of creep of silicone rubbers under constant load for various temperatures were measured. For the Kelvin-Voigt model differential equations the dependence of the coefficients of linear approximations of these equations on loadings and temperatures were measured. The possibility to predict the time of achieving given creep values based on the proposed Kelvin-Voigt model equations were demonstrated.

Development of energy-harvesting system using deformation of magnetic elastomer

In this paper, we propose a power generation method using the deformation of a magnetic elastomer for vibration energy harvesting. The magnetic flux lines in the structure of the magnetic elastomer could be markedly changed if the properly designed structure was expanded and contracted in a static magnetic field. We set a coil on the magnetic elastomer to generate electricity by capturing this change in magnetic flux flow. We fabricated a centimeter-scale device and demonstrated that it generated 10.5 mV of maximum voltage by 10 Hz vibration. We also simulated the change in the magnetic flux flow using finite element analysis, and compared the result with the experimental data. Furthermore, we evaluated the power generation of a miniaturized device.

Pneumatic Muscle: Geometry of the Cylindrical Membrane and The Power Characteristic Prognostic

The pneumatic muscle is a pneumatic motor of the single-acting reciprocating motion. It is designed to create apullingforce. Return of the pneumatic muscle to its original position is provided by elastic deformation of its shell. A cylindrical membrane with the hard bottom and the lid provides the basis of the pneumatic muscle.The membrane cord is formed in the process of helically shaped CU-braid of the threads made from the super-hard synthetic fibres (for example, Kevlar). After the cord is filled with an elastomer, a strong, deformable and elastic shell is formed. An excessive pressure applied to the internal cavity of the membrane arises an extension of the tangent diagonal and a simultaneous shortening of the axial diagonal in the diamond-shaped cell, which is formed as a result of braid of cord threads. This results in pneumatic muscle’s retraction up to 25% of its original length, while creating a sufficiently large contraction force, which depends significantly on the contraction value.Using the cord structure of the MAS series pneumatic muscles of the company “FESTO” as an example, we have investigated a diamond-shaped cell deformation of the membrane and have defined a numerical dependence of its internal diameter and the volume of the internal cavity of the pneumatic muscle on the contraction value. This allowed us to develop a mathematical model of an idealized cylindrical membrane whose dynamics does not take into account a deformation force of the elastomer, filling a diamond-shaped cell.The experimental studies of industrial samples of the MAS 10 family of pneumatic muscles, carried out using a specially designed unit, allowed us to obtain their force characteristics. In the numerical representation, these characteristics turned out to be 2.5 ... 3 times less than the force characteristics of the pneumatic muscle with an idealized membrane, thereby allowing us to draw conclusions that the elastomer deformation forces have a significant influence. There is a proposal to take into account the elastomer deformation effect on the force characteristics of the pneumatic muscle by dint of the correction factor available from a comparative estimate of the force characteristics of the idealized membrane and the normalized force characteristics of the pneumatic muscles of the MAS family.The results of the performed studies allow us to predict the force characteristics of pneumatic muscles at the stage of their design and in-service.

Modelling of magnetic elastomer deformation dependence on magnetic field

The model of magnetic deformable system was developed. The modelling of magnetic elastomer deformation and magnetization dependence on external magnetic field was calculated within the method of movable cellular automata (MCA). It was shown that ordering of magnetic particles substantially effects on elastomer saturation deformation. The maximum orderly elastomer saturation deformation is twice higher the saturation deformation of system with chaotic ordering of magnetic particles.

Developing a visco-hyperelastic material model for 3D finite deformation of elastomers

In this research, using a phenomenological strain energy function, a 3D visco-hyperelastic constitutive equation for the finite deformation of elastomers is developed. For the quasi-static response, a strain energy function, composed of two exponential terms, is employed. The same energy function is considered as the kernel in the hereditary integral approach to derive the visco-hyperelastic model for the time-dependent response. To reduce the number of material parameters, an inverse power-law function between relaxation time and strain rate is proposed. Discretization of the analytical formulation of the visco-hyperelastic model in time is performed to be used in numerical simulations. This approach provides a recursive formulation to update the stress in each time step based on the deformation history. Then, the model is used to study the behavior of elastomeric bushing in radial, torsional and axial deformations. In all these cases, the material parameters are determined by applying a multi-objective optimization algorithm, in which the objective function is the difference between experimental and numerical results. The proposed visco-hyperelastic model shows accurate results for elastomers under 3D quasi-static and time-dependent loadings. Moreover, the accuracy of the results is not dependent on the amount of strain, the strain rate, and modes of deformation.

Dropwise Condensation on Soft Hydrophobic Coatings.

Promoting dropwise condensation (DWC) could improve the efficiency of many industrial systems. Consequently, a lot of effort has been dedicated to finding durable materials that could sustainably promote DWC as well as finding routes to enhance the heat transfer rate during this phase change process. Motivated by previous reports of substrate softening increasing droplet nucleation rate, here we investigated how mechanical properties of a substrate impact relevant droplet-surface interactions and DWC heat transfer rate. Specifically, we experimentally quantified the effect of hydrophobic elastomer's shear modulus on droplet nucleation density and shedding radius. To quantify the impact of substrate softening on heat transfer through individual droplets, we combined analytical solution of elastomer deformation induced by droplets with finite element modeling of the heat transfer process. By substituting these experimentally and theoretically derived values into DWC heat transfer model, we quantified the compounding effect of the substrate's mechanical properties on the overall heat transfer rate. Our results show that softening of the substrates below a shear modulus of 500 kPa results in a significant reduction in the condensation heat transfer rate. This trend is primarily driven by additional thermal resistance of the liquid posed by depression of the soft substrate.

The mechanism for large-volume fluid pumping via reversible snap-through of dielectric elastomer

Giant deformation of dielectric elastomers (DEs) via electromechanical instability (or the “snap-through” phenomenon) is a promising mechanism for large-volume fluid pumping. Snap-through of a DE membrane coupled with compressible air has been previously investigated. However, the physics behind reversible snap-through of a DE diaphragm coupled with incompressible fluid for the purpose of fluid pumping has not been well investigated, and the conditions required for reversible snap-through in a hydraulic system are unknown. In this study, we have proposed a concept for large-volume fluid pumping by harnessing reversible snap-through of the dielectric elastomer. The occurrence of snap-through was theoretically modeled and experimentally verified. Both the theoretical and experimental pressure-volume curves of the DE membrane under different actuation voltages were used to design the work loop of the pump, and the theoretical work loop agreed with the experimental work loop. Furthermore, the feasibility of reversible snap-through was experimentally verified, and specific conditions were found necessary for this to occur, such as a minimum actuation voltage, an optimal range of hydraulic pressure exerted on the DE membrane and a suitable actuation frequency. Under optimal working conditions, we demonstrated a pumping volume of up to 110 ml per cycle, which was significantly larger than that without snap-through. Furthermore, we have achieved fluid pumping from a region of low pressure to another region of high pressure. Findings of this study would be useful for real world applications such as the blood pump.

Large stable deformation of dielectric elastomers driven on mode of steady electric field

Dielectric elastomers (DEs) are capable of large deformation under the actuation of applied voltage and sprayed charge. Actuation of DE under voltage control is prone to electromechanical instabilities, while the DE under charge control always survives from instabilities with sacrificing a large deformation. In this article, a novel actuation mode of steady electric field is proposed. By tuning applied voltage and sprayed charge during viscoelastic creep, an invariable electric field is generated. Such an actuation method can both avoid the occurrence of electromechanical instabilities and guarantee a large deformation in DE actuation.

誘電エラストマによるアクチュエータ，センサおよび発電素子

Dielectric Elastomer (DE) has a very simple structure comprised of polymer films (elastomers) sandwiched by two electrodes made of a flexible and elastic material, and can operate as an electric control actuator. The operating principle is to use the horizontal deformation of elastomers that is a consequence of the synergistic combination of an electrostatic force and a repulsive force between the electrodes generated when a voltage difference is applied between the two electrodes. Using a DE actuator makes it possible to achieve a highly efficient transduction from electric energy into mechanical energy (the theoretical transduction efficiency is 80-90%), which translates into a considerable energy saving compared to other actuator technologies such as electric motors with gearboxes. At the material level, this material has fast speed of response (over 100,000 Hz has been demonstrated for small strains), with a high strain rate (up to 600%), high pressure (up to 8 MPa), and power density of 1 W/g (for comparison, human muscle is 0.2 W/g and an electric motor with gearbox is 0.05 W/g). The generator mode in DE uses the actuator mode process in reverse, transforming mechanical energy originating from the physical deformation of the elastomer film into electrical energy.