Modeling Magneto-Active Elastomer Composites Using the Finite Element Method

Effect of isotropy and anisotropy: toward understanding the fracture behavior of magnetoactive elastomers

The influence of residual plastic deformation on the bending deformation of a magnetoactive elastomer (MAE) beam with non-coercive superparamagnetic manganite (La0.6Ag0.2Mn1.2O3) nanoparticles induced by a transverse uniform magnetic field has been studied. It was found that the MAE bending induced by the magnetic field switching-on/switching-off is mainly cyclic elastic. Plastic deformation leads to the emergence of residual bending and hysteresis in the field dependence of the bending. It was shown that the residual bending that appears after the first magnetic field switch-on eliminates the uncertainty of the bending direction at the next magnetization. Due to the residual plastic deformation, the bending direction of the superparamagnetic MAE with nanoparticles does not change when the direction of the applied magnetic field is inverted, in contrast to the MAE with microparticles where the uncertainty of the bending direction is eliminated due to the residual magnetization of weakly coercive ferromagnetic microparticles; therefore, the bending direction changes its sign with magnetic field reversion. In the low fields, the bending value for the MAEs with superparamagnetic particles is proportional to the square of the magnetic field strength. Model estimates on the residual deformation influence on the beam bending at beam magnetization reversal were obtained.

A Magnetorheological Elastomer (MRE) can be categorized as a smart material as it can respond when it is subjected to a magnetic field against itself. Shrinking and changing shape in MRE is due to the displacement of magnetic particle in the MRE matrix. However, the lack of understanding of the magnetic flow through magnetic particle in the elastomer matrix causes difficulties to improve the best MRE matrix type and a magnetic circuit for use in MRE devices. In this paper, a finite element magnetic method (FEMM) software has been used to investigate and to study the effect of the magnetic flow when the angle of the magnetic particle in the MRE changed. The analysis was conducted in two-dimensional cross-section (axisymmetric type) with two magnetic particles in the elastomer matrix and the magnetic core. The result shows by changing the angle of the magnetic particle, the value of the magnetic flow and magnetic flux density also change. As a conclusion, the magnetic particle arrangement in the elastomer matrix plays a vital role in designing the MRE matrix layer and MRE device. By understanding the magnetic flow through the magnetic particle, one can improve the method in the preparation of MRE matrix and MRE magnetics circuit.

Significant deformations of bodies made from compliant magnetoactive elastomers (MAE) in magnetic fields make these materials promising for applications in magnetically controlled actuators for soft robotics. Reported experimental research in this context was devoted to the behaviour in the quasi-static magnetic field, but the transient dynamics are of great practical importance. This paper presents an experimental study of the transient response of apparent longitudinal and transverse strains of a family of isotropic and anisotropic MAE cylinders with six different aspect ratios in time-varying uniform magnetic fields. The time dependence of the magnetic field has a trapezoidal form, where the rate of both legs is varied between 52 and 757 kA/(s·m) and the maximum magnetic field takes three values between 153 and 505 kA/m. It is proposed to introduce four characteristic times: two for the delay of the transient response during increasing and decreasing magnetic field, as well as two for rise and fall times. To facilitate the comparison between different magnetic field rates, these characteristic times are further normalized on the rise time of the magnetic field ramp. The dependence of the normalized characteristic times on the aspect ratio, the magnetic field slew rate, maximum magnetic field values, initial internal structure (isotropic versus anisotropic specimens) and weight fraction of the soft-magnetic filler are obtained and discussed in detail. The normalized magnetostrictive hysteresis loop is introduced, and used to explain why the normalized delay times vary with changing experimental parameters.

We consider magnetoactive elastomer samples based on the elastic matrix and magnetizable particle inclusions. The application of an external magnetic field to such composite samples causes the magnetization of particles, which start to interact with each other. This interaction is determined by the magnetization field, generated not only by the external magnetic field but also by the magnetic fields arising in the surroundings of interacting particles. Due to the scale invariance of magnetic interactions ( in dimensions), a comprehensive description of the local as well as of the global effects requires a knowledge about the magnetization fields within individual particles and in mesoscopic portions of the composite material. Accordingly, any precise calculation becomes technically infeasible for a specimen comprising billions of particles arranged within macroscopic sample boundaries. Here, we show a way out of this problem by presenting a greatly simplified, but accurate approximation approach for the computation of magnetization fields in the composite samples. Based on the dipole model to magnetic interactions, we introduce the cascading mean-field description of the magnetization field by separating it into three contributions on the micro-, meso-, and macroscale. It is revealed that the contributions are nested into each other, as in the Matryoshka’s toy. Such a description accompanied by an appropriate linearization scheme allows for an efficient and transparent analysis of magnetoactive elastomers under rather general conditions.

Magnetoactive elastomers (MAEs) are composites made of an elastomeric matrix and a magnetizable filler material. The combination of their properties enables a MAE to undergo a change of its rheological respective damping behavior. Furthermore, it is expected that such a magnetic field can lead to an actuation of a MAE. This actuation causes actuation forces perceptible on the surfaces of MAEs. For the investigation of the induced actuation forces different MAE-probes are characterized in a first step. The resulting forces of these MAE-probes are measured by generating a variable external magnetic field in a suitable test setup. Subsequently, a finite element analysis (FEA) is carried out to investigate the behavior from a theoretical point of view by introducing an appropriate continuum mechanical model approach based on the Kelvin force. Therefore, a coupling of magnetism and structural-mechanics domain is developed and implemented using the FEA-tool Comsol Multiphyisics. Finally, the experimental and numerical results of the actuation forces are compared showing a good accordance.

In this work, the resonance enhancement of magnetoelectric (ME) coupling at the two lowest bending resonance frequencies was investigated in layered cantilever structures comprising a magnetoactive elastomer (MAE) slab and a commercially available piezoelectric polymer multilayer. A cantilever was fixed at one end in the horizontal plane and the magnetic field was applied horizontally. Five composite structures, each containing an MAE layer of different thicknesses from 0.85 to 4 mm, were fabricated. The fundamental bending resonance frequency in the absence of a magnetic field varied between roughly 23 and 55 Hz. It decreased with the increasing thickness of the MAE layer, which was explained by a simple theory. The largest ME voltage coefficient of about 7.85 V/A was measured in a sample where the thickness of the MAE layer was ≈2 mm. A significant increase in the bending resonance frequencies in the applied DC magnetic field of 240 kA/m up to 200% was observed. The results were compared with alternative designs for layered multiferroic structures. Directions for future research were also discussed.

Hollow cathode discharge (HCD) is widely used in material processing and plasma emission spectroscopy due to several advantages over other plasma sources. Basically, the HCD consists of a cathode with a hollow structure (cavity, hole, or parallel faces) and an anode of arbitrary shape. In this investigation, experimental studies on low-pressure plane-parallel HCD operated at different process conditions are reported. Herein, we investigate the dependence of the discharge current on the product of the gas pressure and inter-cathode distance (pD). In addition, the electron temperature and density were inferred from the current-voltage characteristics of a single cylindrical Langmuir probe positioned between the cathodes, on the discharge axis. The measurements were carried out at different gas pressures, magnetic field intensities, working gases, inter-cathode distances, cathode materials, and discharge voltages. The results showed that, at different gas pressures, the maximum discharge current (Id,max) is not only a function of the product pD, but also of the pressure itself. Application of a uniform longitudinal magnetic field improved plasma confinement between cathodes, leading to a substantial increase in Id,max in most of the situations considered in this study. However, for oxygen discharge, a strong discharge current reduction after the application of the magnetic field was observed. In relation to the Langmuir probe studies, it was observed that the uniform longitudinal magnetic field reduced the electron temperature, but this behavior depends strictly on pD. The typical values of electron density and electron temperature in the case of the nitrogen discharge were ne = 1017 m−3 and Te = 2.5 eV, respectively. Finally, our experiments showed that the pD range for hollow cathode effects was between 0.2–5 Pa m.

In this study, 3D printed magnetorheological (MR) elastomer has been characterized through a force vibration testing. The 3D printed MR elastomer is a composite consisting three different materials, magnetic particles and two different elastomers. The MR elastomers were printed layer-by-layer by encapsulating MR fluid within the polymeric elastomer and then allowed to cure at room temperature. The 3D printing allowed to print various patterns of magnetic particles within the elastomeric matrix. In the presence of an external magnetic field, both elastic and damping properties of the 3D printed MR elastomers were changed. Natural frequency, stiffness, damping ratio, damping coefficient, and shear modulus were increased with increasing magnetic field. For the single degree-of-freedoms system, shear mode MR elastomers suppressed the transmitted vibration amplitude up to 31.4% when the magnetic field was 550 mT. The results showed that the 3D printed MR elastomer could be used as a tunable spring element for vibration absorption or isolation applications. However, further optimization of the magnetic particles’ configurations should be performed to obtain the higher MR effect.

The linear viscoelastic behaviour of magnetorheological elastomers is analysed in this work according to their formulation and working conditions. This study comprised both the synthesis of different magnetorheological elastomers and the strain and frequency sweep characterization under different magnetic fields and temperatures. The characterization was performed by a Physica MCR 501 rheometer from Anton Paar, equipped with a magnetorheologic cell 70/1T MRD. In the synthesis with a given elastomeric matrix, samples with different magnetic particle content are studied with two types of curing conditions: under the action of a magnetic field (anisotropic magnetorheological elastomers) and without a magnetic field (isotropic magnetorheological elastomers). The working conditions are excitation frequency, temperature and the applied external magnetic field. In this work, a new procedure to determine the linear viscoelastic behaviour is proposed; the loss factor is analysed in addition to analysing the storage modulus to determine the linear viscoelastic region of each sample. The results show that high temperatures and magnetorheological elastomers with higher volume fraction of magnetic particles restrict the linear viscoelastic behaviour of magnetorheological elastomers.

Soft magnetoactive elastomers (MAEs) are smart materials that respond to external magnetic fields by dynamically altering their mechanical properties. They are composed of magnetically responsive microparticles embedded within a soft polymer matrix, exhibiting an effective shear modulus of up to 100 kPa. In recent decades, MAEs' bulk properties have been successfully exploited for applications such as dynamic vibration damping, vibration sensing, and actuation in soft robotics. Recent research has shifted to their surface properties, revealing promising results on tunable surface features such as roughness, adhesion, and wetting. Even the transport of small solid and fluid objects was demonstrated. The associated surface effects can be significantly enhanced through the precise engineering of surface topography. In this article, an efficient laser micromachining technique, with a resolution of 15 µm, is presented, which enables rapid prototyping of MAE surfaces. It allows the creation of various complex shapes and offers functionality beyond the one achievable with traditional molding techniques. Additionally, the approach is versatile and can be applied to any polymer that sufficiently absorbs the laser light. As an example, a lamellar surface micro-pattern fabrication process and its characterization by optical and scanning electron microscopies are shown. Its response to a magnetic field is demonstrated. The technique provides a flexible and fast solution for optimizing polymer surface design across a wide range of applications.

We explore the possibility of creating an effective retinal fixator on the basis of magnetoactive elastomers (MAEs) and systems of permanent magnets. MAEs consist of silicone elastomer matrix with embedded magnetic iron microparticles. We study theoretically and experimentally magnetic forces acting between MAE samples and permanent magnets in various configurations. The theoretical model is based around classical magnetostatics and Maxwell equations with different parameters accounting for peculiarities of the material and the setup. Approximation of the experimentally measured magnetization curves for MAE samples was used to find input parameters for the theoretical model. To test the model, we conducted a series of experimental measurements of magnetic forces accompanied by model predictions for the system of one cylindrical magnet and a cuboid MAE sample. Calculated dependences of the average pressure arising from magnetic interactions on the distance between the closest faces of MAE samples and a permanent magnet are in a good agreement with the experimental data. The proof on concept for smaller magnetic systems required for eye surgery includes data for 10 magnets configuration and a thin MAE band. This research demonstrates high prospects of using MAE as an element of a magnetic fixator for treatment of complicated retinal detachments.

The behavior of a fluidized bed of fine magnetite particles as affected by a cross-flow magnetic field is investigated. A distinct feature of this naturally cohesive powder, as compared to noncohesive magnetic grains usually employed in magnetofluidized beds, is that the fluidized bed displays a range of stable fluidization even in the absence of an external magnetic field. Upon application of the magnetic field, the interval of stable fluidization is extended to higher gas velocities and bed expansion is enhanced. We have measured the tensile strength as affected by application of the external magnetic field according to two different operation modes. In the H off-on operation mode, the bed is driven to bubbling in the absence of external magnetic field. Once the gas velocity is decreased below the bubbling onset and the bed has returned to stable fluidization due to natural cohesive forces, the field is applied. In the H on-on mode, the field is maintained during the whole process of bubbling and return to stable fluidization. It is found that the tensile strength of the naturally stabilized bed is not essentially changed by application of the field ( H off-on) since the magnetic field cannot alter the bed structure once the particles are jammed in the stable fluidization state. Magnetic forces within the bulk of the jammed bed are partially canceled as a result of the anisotropic nature of the dipole-dipole interaction between the particles, which gives rise to just a small increment of the tensile strength. On the other hand, when the field is held on during bubbling and transition to stable fluidization ( H on-on mode), the tensile strength is appreciably increased. This suggests the formation of particle chains when the particles are not constrained due to the dipole-dipole attractive interaction which affects the mechanical strength of the stably fluidized bed. Experimental data are analyzed in the light of theoretical models on magnetic surface stresses.

Magnetostriction effect of a spherical sample of a magnetoactive elastomer (MAE) is analyzed. In comparison with the preceding study, the consideration is done on a more realistic basis: taking into account saturation of the MAE magnetization in contrast to the former model where the magnetization was supposed to be linear whatever the field strength. This more thorough investigation has revealed that the striction-induced elongation effect, depending on the material parameters, may occur in two forms. One scenario manifests itself as tapering of the polar zones of the former sphere, where ‘beaks’ are formed, so that the shape of the object drastically deviates from a spheroidal one. The mechanism the underlies the occurrence of beaks is the surface instability of a magnetizable elastic continuum, and the beak nucleation follows the second-order transition pattern; the resulting overall elongation of the body does not display any hysteresis. Another scenario—it is related to MAEs with higher magnetic properties and softer matrices—implies that the beak formation happens simultaneously with a jump-like overall elongation of the former sphere, and this transformation resembles the first-order transition pattern. Upon assessing the chances to observe the predicted effects on the samples of now existing MAEs, one comes to a conclusion that the second scenario is hardly possible, whereas the first one, i.e., beak formation without hysteretic stretching, is much more realizable.

Magnetoactive polymer compositesЁ— polymer matrices with embedded magnetic micro- and/or nanoparticlesЁ— belong to the class of «smart» materials and currently attract significant fundamental and practical interest. This article focuses primarily on magnetoactive elastomers (MAEs) based on chemically crosslinked polymer systems, research on which has been conducted at the Physics Faculty of Moscow State University since the late 1990s. A definition of MAEs is provided, and the properties of their main components — the polymer matrix and magnetic particles — are described. An overview is given of the physical phenomena observed in these materials when an external magnetic field is applied. The influence of the material composition on its magnetic response is discussed in detail, with an emphasis on magnetomechanical properties, which are most critical for practical applications. The results of recent studies related to the synthesis of new matrices for MAEs, the influence of the shape and distribution of magnetic particles in the polymer matrix, as well as contemporary theoretical approaches to describing the behaviour of MAEs in an external magnetic field are analyzed. Finally, the prospects for further advancement in the development of magnetoactive polymer materials and their practical applications are discussed.