Modeling of magnetic hystereses in soft MREs filled with NdFeB particles

Abstract

Herein, we investigate the structure-property relationships of soft magnetorheological elastomers (MREs) filled with remanently magnetizable particles. The study is motivated from experimental results which indicate a large difference between the magnetization loops of soft MREs filled with NdFeB particles and the loops of such particles embedded in a comparatively stiff matrix, e.g. an epoxy resin. We present a microscale model for MREs based on a general continuum formulation of the magnetomechanical boundary value problem which is valid for finite strains. In particular, we develop an energetically consistent constitutive model for the hysteretic magnetization behavior of the magnetically hard particles. The microstructure is discretized and the problem is solved numerically in terms of a coupled nonlinear finite element approach. Since the local magnetic and mechanical fields are resolved explicitly inside the heterogeneous microstructure of the MRE, our model also accounts for interactions of particles close to each other. In order to connect the microscopic fields to effective macroscopic quantities of the MRE, a suitable computational homogenization scheme is used. Based on this modeling approach, it is demonstrated that the observable macroscopic behavior of the considered MREs results from the rotation of the embedded particles. Furthermore, the performed numerical simulations indicate that the reversion of the sample’s magnetization occurs due to a combination of particle rotations and internal domain conversion processes. All of our simulation results obtained for such materials are in a good qualitative agreement with the experiments.

Modeling and Simulation of Hysteresis Effects in Magnetorheological Elastomers

“…After a few load cycles, the magnetic hysteresis loops of the MRE are significantly smaller compared to the initial one, see Figure 1(a). This effect occurs due to rotations of the particles which are induced by local magnetic torques and is in qualitative accordance with experimental results [2,5]. In the effective mechanical stress response of the system, butterfly hystereses appear.…”

“…The analyzed MREs are described by a microscopic model, i. e. the heterogeneous microstructure consisting of magnetizable inclusions and polymer matrix is taken into account explicitly. Since the coupling effects within the particles are neglected, the specific free energy function is divided into mechanical and magnetic part: Ψ = Ψ mech + Ψ mag , where Ψ mag is zero within the polymer [1][2][3]. In both components, the mechanical part is defined by a compressible neo-Hookean potential.…”

“…In this contribution the behavior of such magnetically hard MREs is investigated by means of a finite strain modeling approach which is based on a general magneto-mechanical continuum formulation as presented in Kalina et al [1,2].…”

Reversible magnetomechanical collapse: virtual touching and detachment of rigid inclusions in a soft elastic matrix

“…To test our theoretical conclusions and the consequences of our approximations, we performed additional FE simulations. They are based on a coupled magnetomechanical continuum formulation including nonlinear contributions to the magnetic and elastic properties of the magnetic particles and elastic matrix, respectively [72,90]. In addition to the theoretical approaches above, the magnetic field is spatially resolved also within the two particles.…”

“…Here, the superscript T denotes the transpose. Since f mag (r) can be expressed as the divergence of the magnetic stress tensor σ mag (r), the balance of linear momentum is given by the relation [72,[90][91][92] ∇ · σ tot (r) = 0 withn(r) · σ tot (r) = 0 on S d .…”