Magnetoactive Elastomers Research Articles

Effect of magnetic-field-induced restructuring on the elastic properties of magnetoactive elastomers

Composite materials where magnetic micrometer-sized particles are embedded into a compliant polymer matrix are known as magnetorheological (or magnetoactive) elastomers (MAEs). They are distinguished by huge variations in their physical properties, when in a magnetic field, which is commonly attributed to the restructuring of the filler. The process of the magnetic-field-induced restructuring in a magnetorheological elastomer is interpreted as progression towards percolation. Such a physical model was previously used to explain the dependence of the magnetic permeability and dielectric permittivity of MAEs on the magnetic field strength. Based on this hypothesis, the magnetorheological effect in MAEs is considered theoretically. The theoretical approach is built upon a self-consistent effective-medium theory for the elastic properties, extended to the variable (field dependent) percolation threshold. The proposed model allows one to describe the large variations (over several orders of magnitude) of the effective elastic moduli of these composite materials, known as the giant magnetorheological (MR) and field-stiffening effects. The existence of a giant magnetic Poisson effect is predicted. The relation of the proposed model to the existing theories of the MR effect in MAEs is discussed. The results can be useful for applications of MAEs in magnetic-field-controlled vibration dampers and isolators.

Induced anisotropy in composite materials with reconfigurable microstructure: Effective medium model with movable percolation threshold

In composite materials, with field-dependent restructuring of the filler material (changes in the mutual arrangement of inclusions), the presence of an external magnetic field induces anisotropy of the dielectric properties, even if the composite is isotropic in the absence of an external field. A modified effective medium approximation is proposed for the calculation of the components of effective permittivity within a class of composites with reconfigurable microstructure, where both phases (the filler and the matrix) are isotropic and the inclusions have spherical shape. The effective physical properties are calculated in the parallel and perpendicular directions to an applied field. The appearance of the anisotropy of the permittivity is simulated by the introduction of two not-equal, possibly variable (field-dependent) percolation thresholds. The implications, of the proposed theoretical approach, are demonstrated for the case of the dielectric properties of magnetoactive elastomers (MAEs). In MAEs with soft polymer matrices, the mutual arrangement of micrometer-sized magnetic inclusions can significantly change in an applied magnetic field. A reasonable agreement between theory and experiment at a measurement frequency of 1 kHz is found, and is improved in comparison to the previous models. The components of the effective permittivity tensor, characterizing the dielectric properties along the direction of the applied magnetic field and in the orthogonal direction, grow with an increasing field. This growth is more pronounced for the permittivity component in the field direction. The possible extensions of the theoretical model and future directions of research are discussed. The presented theoretical approach can be useful for the application-driven development of a number of smart materials, in particular electro- and magnetorheological gels, elastomers and fluids.

Giant Extensional Strain of Magnetoactive Elastomeric Cylinders in Uniform Magnetic Fields.

Elongations of magnetoactive elastomers (MAEs) under ascending–descending uniform magnetic fields were studied experimentally using a laboratory apparatus specifically designed to measure large extensional strains (up to 20%) in compliant MAEs. In the literature, such a phenomenon is usually denoted as giant magnetostriction. The synthesized cylindrical MAE samples were based on polydimethylsiloxane matrices filled with micrometer-sized particles of carbonyl iron. The impact of both the macroscopic shape factor of the samples and their magneto-mechanical characteristics were evaluated. For this purpose, the aspect ratio of the MAE cylindrical samples, the concentration of magnetic particles in MAEs and the effective shear modulus were systematically varied. It was shown that the magnetically induced elongation of MAE cylinders in the maximum magnetic field of about 400 kA/m, applied along the cylinder axis, grew with the increasing aspect ratio. The effect of the sample composition is discussed in terms of magnetic filler rearrangements in magnetic fields and the observed experimental tendencies are rationalized by simple theoretical estimates. The obtained results can be used for the design of new smart materials with magnetic-field-controlled deformation properties, e.g., for soft robotics.

Effect of mesoscopic magnetomechanical hysteresis on magnetization curves and first-order reversal curve diagrams of magnetoactive elastomers

Magnetoactive elastomers may display magnetic hysteresis, even if they are filled only with magnetically soft particles. In this work we discuss application of the first-order reversal curve (FORC) analysis to identify and study hysteresis of that kind. To obtain theoretical magnetization curves and FORC diagrams for the composites in question, a simple model comprising two magnetically soft particles embedded in an elastic environment is proposed. Elucidation of the features present in FORC diagrams is conducted using computer simulation. Despite the simplicity of the model, it allows one to explain the origin of diagonal ridge patterns, which turn up in the FORC diagrams of elastomer composites with magnetically soft filler, and to quantify the experimental results. As the ridge pattern of the diagrams is inherently exclusive to such types of materials, it could be useful for their diagnostics.

Field-induced interactions in magneto-active elastomers - A comparison of experiments and simulations

In this contribution, field-induced interactions of magnetizable particles embedded into a soft elastomer matrix are analyzed with regard to the resulting mechanical deformations. By comparing experiments for two-, three- and four-particle systems with the results of finite element simulations, a fully coupled continuum model for magneto-active elastomers is validated with the help of real data for the first time. The model under consideration permits the investigation of magneto-active elastomers with arbitrary particle distances, shapes and volume fractions as well as magnetic and mechanical properties of the individual constituents. It thus represents a basis for future studies on more complex, realistic systems. Our results show a very good agreement between experiments and numerical simulations—the deformation behavior of all systems is captured by the model qualitatively as well as quantitatively. Within a sensitivity analysis, the influence of the initial particle positions on the systems’ response is examined. Furthermore, a comparison of the full three-dimensional model with the often used, simplified two-dimensional approach shows the typical overestimation of resulting interactions in magneto-active elastomers.

Low-Modulus Elastomeric Matrices for Magnetoactive Composites with a High Magnetic Field Response

Magnetoactive elastomers based on polydimethylsiloxane functional oligomers with a concentration of magnetic iron microparticles of 70, 75, and 80 wt % are synthesized. Soft samples with low (about 2 kPa) elastic moduli are obtained by introducing side chains into the polymer network without using a low molecular weight oil. It is shown that the rigidity of the matrix can be controlled by varying the concentration of only the crosslinking agent. The obtained magnetoactive elastomers have a high magnetic field response: the relative growth of the real part of the dynamic shear modulus of soft samples exceeds two orders of magnitude and reaches 400 in a magnetic field of 1 T. The contact angle of water with the surface of the composites increases to 140° in a magnetic field of the order of 400 mT.

Finite deformation analysis of isotropic magnetoactive elastomers

In this study, the large deformation analysis of the magnetoactive elastomers based on continuum mechanics approach has been conducted. First, the governing differential equations for the spatial configuration are presented. Stored energy density function defined with respect to the invariants of the right or left Cauchy–Green deformation tensor and the magnetic field induction vector is adopted to develop a material model for finite deformation of isotropic magnetoactive elastomers (MAEs). An isotropic magnetoactive sample with 15% iron particle volume fraction is then fabricated, and a test setup has been designed to measure its magnetic permeability. Using an advanced magnetorheometer, quasi-static tests are then carried out on MAE circular cylindrical samples to find their torque-twist response under various magnetic fields. The experimental results are then effectively utilized to identify the unknown parameters in the proposed material model. The accuracy of the proposed constitutive model in predicting the response behavior of the MAE is then demonstrated through comparison of theoretical results with those obtained experimentally.

Basic magnetic properties of magnetoactive elastomers of mixed content

The results of theoretical and experimental investigations of the polymer composites that belong to a class of magnetoactive elastomers with mixed magnetic content (MAEs-MC) are presented. The fundamental distinction of such composites from ordinary magnetoactive elastomers is that the magnetic filler of MAEs-MC comprises both magnetically soft (MS) particles of size 3–5 µm and magnetically hard (MH) particles whose size is an order of magnitude greater. Since MH particles of the magnetic filler are mixed into a composition in a non-magnetised state, this can ensure preparation of samples with fairly homogeneous distribution of the filler. The ‘initiation’ process of a synthesised MAE-MC is done by its magnetisation in a strong magnetic field that imparts to the sample unique magnetic and mechanical properties. In this work, it is shown that the presence of MS particles around larger MH particles, firstly, causes an augmentation of magnetic moments, which the MH particles acquire during initiation, and secondly, enhances the magnetic susceptibility and remanent magnetisation of MAEs-MC. These magnetic parameters are evaluated on the basis of the macroscopic magnetostatics from the experimental data of spatial scanning of the field over the space around MAEs-MC made in the shape of a spheroid. A set of samples with a fixed MH and varying MS volume contents that are initiated in two different fields, is used. The developed mesoscopic model of magnetic interactions between the MH and MS phases is able to explain the experimentally observed dependencies of the magnetic parameters on the concentration of the MS phase. The problem is solved numerically under the assumption that the elastic matrix of MAEs-MC is rigid, i.e. the mutual displacements of the particles are negligible. The model helps to elucidate the interaction of the magnetic phases and to establish that the MS phase plays thereby a dual role. On the one hand, the MS phase screens out the field acting inside MH particles, and on the other hand, it forms mesoscopic magnetic bridges between adjoining MH particles, which in turn enhance their field. The combined interplay of these contributions defines the resulting material properties of MAEs-MC on the macroscopic scale.

Large Wiedemann effect in a magnetoactive elastomer

Large twists of a soft tube (hollow cylinder) in helical magnetic fields are presented for the first time. Such a phenomenon is usually denoted as the Wiedemann effect. The tube is fabricated from a soft magnetoactive elastomer material with the shear modulus of about 56 kPa. The composite material comprises 80 mass% of micrometer-sized iron particles embedded into a polydimethylsiloxane matrix. The circular magnetic field is generated by an electric current in a straight wire passing through the inner hole of the tube. The maximum value of approximately 350″/cm is observed in a longitudinal magnetic field of a few kA/m overlapped with a circumferential magnetic field of about 1.4 kA/m on the surface of the inner hole. A pronounced hysteresis in the dependence of the Wiedemann effect on the circular magnetic field is found. The ways to enhance the Wiedemann twist in magnetoactive elastomers are discussed. The observed large effect is promising for application in magnetic-field controlled torsional actuators, in particular for soft robotics.

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.

Vibration studies of a magnetoelastic material

This article contains the results of research on the vibration characteristics of elastomer samples. Experimental studies of the dynamic properties of magnetoactive elastomer materials under the action of magnetic fields on a vibration complex are conducted. A kinematic sinusoidal excitation is given on the table of the vibrator from the side of the support on the tested product. The accelerations at the sample output are recorded. Oscillograms of accelerations at the input and output of the sample under the action of a magnetic field are obtained. The range of displacement of resonant frequencies under the influence of a magnetic field is shown. The justification for creating an electromagnet lifting force that overcomes the elastic force of the test material is given. Computational modeling is performed to create an elastic deformation of a magnetoactive elastomer, both static and dynamic, using a magnetic field.

Adaptive elastic metastructures from magneto-active elastomers

Elastic metastructures provide advanced control of elastic wave propagation, particularly through their ability to exhibit frequency band gaps where elastic waves cannot propagate. Several metastructure design strategies to realize band gaps in frequency ranges of interest have emerged in recent years. However, the band gap frequencies are fixed at design time by the metastructure geometry and constituent materials. Here, a tunable metamaterial is developed which utilizes the coupled magneto-mechanical response of magnetoactive elastomers (MAE) to enable active control of the band gap frequencies. It is shown that the band gap of a lattice-based metastructure design can be tuned over a continuous frequency range by remote application of a magnetic field. A direct-ink write fabrication method is introduced to fabricate the metastructures from MAEs, which allows this concept to be extended to a vast design space. Our results suggest that the band gap tunability depends not only on the strength of the applied magnetic field, but also on the interaction of the magnetic field and the metastructure geometry. This implies that the combined effects of geometry and magnetic stiffening represent a new design parameter for tunable metastructures, enabling the creation of new smart structures which feature tunable inherent vibration control.

Instability-Induced Pattern Formations in Soft Magnetoactive Composites.

Elastic instabilities can trigger dramatic microstructure transformations giving rise to unusual behavior in soft matter. Motivated by this phenomenon, we study instability-induced pattern formations in soft magnetoactive elastomer (MAE) composites deforming in the presence of a magnetic field. We show that identical MAE composites with periodically distributed particles can switch to a variety of new patterns with different periodicity upon developments of instabilities. The newly formed patterns and postbuckling behavior of the MAEs are dictated by the magnitude of the applied magnetic field. We identify the particular levels of magnetic fields that give rise to strictly doubled or multiplied periodicity upon the onset of instabilities in the periodic particulate soft MAE. Thus, the predicted phenomenon can be potentially used for designing new reconfigurable soft materials with tunable material microstructures remotely controlled by a magnetic field.

Diversifying temporal responses of magnetoactive elastomers

Magnetoactive elastomers(MAEs) are able to deform significantly in response to the application of magnetic fields. Usually, a magnetic field which is harmonic in time usually results in a harmonic mechanical response of the MAEs. To render MAEs with the ability of responding or deforming diversely or anharmonically in time, in this work, we propose a hybrid MAE which is based on a rubber matrix embedded with both soft iron particles and hard NdFeB-alloy particles. Firstly, based on the principle of minimum free energy, we establish a theoretical model to study magnetomechanical behaviors of the proposed hybrid MAEs. Then, through both theoretical and experimental studies, we show that the response of a hybrid MAE sample to the applied magnetic field is usually complex, i.e. the deformation induced by a harmonic magnetic field in time is anharmonic. At last, the effect of two main factors, the state of magnetization and the amplitude of the applied magnetic field, is studied both experimentally and theoretically. This work provides a new idea of diversifying the temporal response of MAEs to the application of harmonic magnetic fields (harmonic in time). The hybrid MAEs may serve as a complement to the recently proposed 3D-printed hard MAEs which are able to deform inhomogeneously in space in response to a uniform magnetic field.

Magnetic peristaltic pumps for stowing operations

Relevance of the work. The use of laying the workings is intended to increase the safety of mining operations, namely, controlling mining pressure, reduce mineral loss during excavation, prevent the occurrence of underground fires, and reduce the risks of destruction of objects in residential areas. Methodology of the work. The article is devoted to the study of the possibility of applying the system of peristaltic transportation of pasty slurries using the energy of a traveling magnetic field to work on the laying of the goaf. Taking into account the features of the materials used as the basis for filling mixtures, the specifics of the process of moving the latter to the place of laying, innovative technologies for transporting filling mixtures are becoming increasingly important. Results and scope. A fundamentally new approach to the transportation of liquid and viscous media is the use of low-frequency magnetic peristaltic pumps. The design of this pump involves the use as an executive body of the working channel, made of a magneto-active elastomer. By its extension under the influence of a traveling magnetic, periodic waves of local deformation pass, moving the filling mixture. Conclusions. The rejection of the traditional roller system, which presses the channel, and the replacement of the main executive body of the pump with the working channel, the structuring flow and preventing its separation, will expand the scope of application of pumping equipment during filling operations. The pressure developed by the pump depends on the energy characteristics of the traveling magnetic field. Studies have shown that the speed of movement of a wave of local deformation when moving various materials is sufficiently stable and slightly depends on the viscosity of a substance.

Development of a small-deformation material model for an isotropic magneto-active elastomer

In the present work, a continuum-based material model has been developed for an isotropic magneto-active elastomer (MAE) to investigate its behavior under small deformations. Firstly, the governing magneto-mechanical equations are formulated for the flexible magneto-active medium. Subsequently, a linearization scheme is used to construct constitutive equations for the small-deformation analysis of MAEs by expressing the magnetic parameters by two constituents involving the rigid-body and perturbation states. The material constants of the constitutive model are estimated from the experiments performed on a right cylindrical sample of a magneto-active material comprising the elastic matrix with 15% volume fraction of carbonyl iron particles.

Athermal Shape Memory Effect in Magnetoactive Elastomers.

Shape memory materials (SMMs) are usually referred to as materials with the ability to recover the original shape via certain thermal stimulations, such as temperature increase. Such shape memory behaviors achieved thermally usually exhibit slow response due to the constraint of thermal conductivity, leaving a big challenge for situations with temperature and speed requirements. In this work, different from previous shape memory mechanisms, an athermal fast-response shape memory effect (SME) based on the manipulation of magnetization profiles is introduced both experimentally and theoretically. Through the new mechanism, the shape information of a hard magnetic-particle-embedded magnetoactive elastomer (H-MAE) can be accurately converted into the distribution of magnetic domains and recorded/memorized in the material. Then, upon the application of an external magnetic field, due to the interactions between magnetic domains and the magnetic field, the recorded shape information can be immediately displayed. To exploit this mechanism, the magnetic actuating properties are analyzed and a new way for information writing and repeatable reading is also realized.

Effective Medium Theory for the Elastic Properties of Composite Materials with Various Percolation Thresholds.

It is discussed that the classical effective medium theory for the elastic properties of random heterogeneous materials is not congruous with the effective medium theory for the electrical conductivity. In particular, when describing the elastic and electro-conductive properties of a strongly inhomogeneous two-phase composite material, the steep rise of effective parameters occurs at different concentrations. To achieve the logical concordance between the cross-property relations, a modification of the effective medium theory of the elastic properties is introduced. It is shown that the qualitative conclusions of the theory do not change, while a possibility of describing a broader class of composite materials with various percolation thresholds arises. It is determined under what conditions there is an elasticity theory analogue of the Dykhne formula for the effective conductivity. The theoretical results are supported by known experiments and show improvement over the existing approach. The introduction of the theory with the variable percolation threshold paves the way for describing the magnetorheological properties of magnetoactive elastomers. A similar approach has been recently used for the description of magneto-dielectric and magnetic properties.

Anomalous magnetorheological effect in unstructured magnetoisotropic magnetoactive elastomers

It was found that the anomalous magnetorheological effect observed in initially unstructured magnetoisotropic magnetoactive elastomers, i.e., the growth of their effective shear modulus in an external magnetic field by almost two orders of magnitude, is a result of the uniaxial magnetic anisotropy induced by the magnetic field. An additional magnetoelastic contribution to the mechanical stress created by the induced magnetic anisotropy counteracts the shear and increases the effective shear modulus of the magnetoactive elastomer when the latter is magnetized. Numerical estimates made for the magnitude of magnetorheological effect are in good agreement with known experimental data.

A Finite Element Framework for Magneto-Actuated Large Deformation and Instability of Slender Magneto-Active Elastomers

In this paper, we present an efficient finite element framework for modeling the finite deformations of slender magneto-active elastomers (MAE) under applied magnetic fields or currents. For the convenience of numerical modeling, magnetic field is defined at fixed spatial coordinates in the background space rather than in the elastic MAEs using material coordinates. The magnetic field will vary with free or localized currents while the spatial distribution of the magnetic field will evolve with the motion or deformation of the MAE materials, which is actuated by the surface or body forces induced by external magnetic fields or equivalent currents. A staggered strategy and a Riks method are introduced to solve the strongly coupled governing equations of the magnetic field and displacement field using finite element method. The mesh distortion along the interfaces between MAE domain and free-space domain is resolved by considering concurrent deformation of the mesh in these two domains. A few 2D numerical examples demonstrate the validity and efficiency of the developed model for simulating large deformation of MAE with non-uniform spatial magnetic field under different actuation sources such as free currents, magnetization or external magnetic field. This framework offers a new solution strategy for modeling mechano-magneto problems of MAEs and will help rational design and analysis of MAE-based actuators and soft robotics in the future.