Magneto-Mechanical Coupling in Magneto-Active Elastomers

Effects of Filler Anisometry on the Mechanical Response of a Magnetoactive Elastomer Cell: A Single-Inclusion Modeling Approach

A finite-element model of the mechanical response of a magnetoactive elastomer (MAE) volume element is presented. Unit cells containing a single ferromagnetic inclusion with geometric and magnetic anisotropy are considered. The equilibrium state of the cell is calculated using the finite-element method and cell energy minimization. The response of the cell to three different excitation modes is studied: inclusion rotation, inclusion translation, and uniaxial cell stress. The influence of the magnetic properties of the filler particles on the equilibrium state of the MAE cell is considered. The dependence of the mechanical response of the cell on the filler concentration and inclusion anisometry is calculated and analyzed. Optimal filler shapes for maximizing the magnetic response of the MAE are discussed.

Effect of microstructure evolution on the mechanical behavior of magneto-active elastomers with different matrix stiffness

Evolution of microstructure in magneto-active elastomers (MAEs) which can be caused by an applied magnetic field is a fascinating phenomenon with a significant impact on the mechanical behavior of the composite. To gain insight into the underlying mechanisms of this phenomenon, it is essential to create a model that can appropriately describe the field induced change in the particle distribution and its mechanical implications. The magneto-mechanical coupling is driven by magnetic interactions between the particles in the applied field. These magnetic interactions can result in macroscopic deformation of the sample and also in rearrangement of the microstructure, i.e. the local positions of the particles. In the case of initially isotropic MAEs made with a sufficiently soft matrix, this leads to the formation of chains of magnetized particles, creating a significant increase in the mechanical moduli along the field direction. In this paper, we implement a transversely isotropic Neo-Hookean material model to account for such anisotropic elastic behavior. A dipolar mean field approach is used to describe magnetic interactions between the particles. A penalty term is introduced to compensate for the micro-mechanical elastic energy required to move the particles inside the cross-linked elastomer. The resulting model can predict the huge magneto-rheological effects observed in experiments, and improves our understanding of how microstructure evolution affects magnetically induced deformation and stiffness of MAEs.

Switching-field and first-order-reversal-curve distribution measurements in magnetic elastomers by molecular dynamics simulations: Accounting for polydispersity

In this work we employ molecular dynamics simulations to investigate the first-order-reversal-curve distribution and switching-field distribution of magnetic elastomers. We model magnetic elastomers in a bead-spring approximation with permanently magnetized spherical particles of two different sizes. We find that a different fractional composition of particles affects the magnetic properties of elastomers obtained as a result. We prove that the hysteresis of the elastomer can be attributed to the broad energy landscape with multiple shallow minima and caused by dipolar interactions.

Multiferroic Cantilevers Containing a Magnetoactive Elastomer: Magnetoelectric Response to Low-Frequency Magnetic Fields of Triangular and Sinusoidal Waveform

In this work, multiferroic cantilevers comprise a layer of a magnetoactive elastomer (MAE) and a commercially available piezoelectric polymer-based vibration sensor. The structures are fixed at one end in the horizontal plane and the magnetic field is applied vertically. First, the magnetoelectric (ME) response to uniform, triangle-wave magnetic fields with five different slew rates is investigated experimentally. Time and field dependences of the generated voltage, electric charge, and observed mechanical deflection are obtained and compared for four different thicknesses of the MAE layer. The ME responses to triangular and sinusoidal wave excitations are examined in contrast. Second, the ME response at low frequencies (≤3 Hz) is studied by the standard method of harmonic magnetic field modulation. The highest ME coupling coefficient is observed in the bias magnetic field strength of ≈73 kA/m and it is estimated to be about 3.3 ns/m (ME voltage coefficient ≈ 25 V/A) at theoretically vanishing modulation frequency (f→0 Hz). Presented results demonstrate that the investigated heterostructures are promising for applications as magnetic-field sensors and energy harvesting devices.

Field-Induced Transversely Isotropic Shear Response of Ellipsoidal Magnetoactive Elastomers

Magnetoactive elastomers (MAEs) claim a vital place in the class of field-controllable materials due to their tunable stiffness and the ability to change their macroscopic shape in the presence of an external magnetic field. In the present work, three principal geometries of shear deformation were investigated with respect to the applied magnetic field. The physical model that considers dipole-dipole interactions between magnetized particles was used to study the stress-strain behavior of ellipsoidal MAEs. The magneto-rheological effect for different shapes of the MAE sample ranging from disc-like (highly oblate) to rod-like (highly prolate) samples was investigated along and transverse to the field direction. The rotation of the MAE during the shear deformation leads to a non-symmetric Cauchy stress tensor due to a field-induced magnetic torque. We show that the external magnetic field induces a mechanical anisotropy along the field direction by determining the distinct magneto-mechanical behavior of MAEs with respect to the orientation of the magnetic field to shear deformation.

Benchmark for the Coupled Magneto-Mechanical Boundary Value Problem in Magneto-Active Elastomers

Within this contribution, a novel benchmark problem for the coupled magneto-mechanical boundary value problem in magneto-active elastomers is presented. Being derived from an experimental analysis of magnetically induced interactions in these materials, the problem under investigation allows us to validate different modeling strategies by means of a simple setup with only a few influencing factors. Here, results of a sharp-interface Lagrangian finite element framework and a diffuse-interface Eulerian approach based on the application of a spectral solver on a fixed grid are compared for the simplified two-dimensional as well as the general three-dimensional case. After influences of different boundary conditions and the sample size are analyzed, the results of both strategies are examined: for the material models under consideration, a good agreement of them is found, while all discrepancies can be ascribed to well-known effects described in the literature. Thus, the benchmark problem can be seen as a basis for future comparisons with both other modeling strategies and more elaborate material models.

A Cascading Mean-Field Approach to the Calculation of Magnetization Fields in Magnetoactive Elastomers

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 (O(r−3) in d=3 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.