Hard magnetorheological elastomers (h-MREs) are essentially two phase composites comprising permanently magnetizable metallic inclusions suspended in a soft elastomeric matrix. This work provides a thermodynamically consistent, microstructurally-guided modeling framework for isotropic, incompressible h-MREs. Energy dissipates in such hardmagnetic composites primarily via ferromagnetic hysteresis in the underlying hard-magnetic particles. The proposed constitutive model is thus developed following the generalized standard materials framework, which necessitates suitable definitions of the energy density and the dissipation potential. Moreover, the proposed model is designed to recover several well-known homogenization results (and bounds) in the purely mechanical and purely magnetic limiting cases. The magneto-mechanical coupling response of the model, in turn, is calibrated with the aid of numerical homogenization estimates under symmetric cyclic loading. The performance of the model is then probed against several other numerical homogenization estimates considering various magneto-mechanical loading paths other than the calibration loading path. Very good agreement between the macroscopic model and the numerical homogenization estimates is observed, especially for stiff to moderately-soft matrix materials. An important outcome of the numerical simulations is the independence of the current magnetization to the stretch part of the deformation gradient. This is taken into account in the model by considering an only rotation-dependent remanent magnetic field as an internal variable. We further show that there is no need for an additional mechanical internal variable. Finally, the model is employed to solve macroscopic boundary value problems involving slender h-MRE structures and the results match excellently with experimental data from literature. Crucial differences are found between uniformly and non-uniformly pre-magnetized h-MREs in terms of their pre-magnetization and the associated self-fields.

To cite this version:Dipayan Mukherjee, Laurence Bodelot, Kostas Danas. Microstructurally-guided explicit continuum models for isotropic magnetorheological elastomers with iron particles. AbstractThis work provides a family of explicit phenomenological models both in the F − H and F − B variable space. These models are derived directly from an analytical implicit homogenization model for isotropic magnetorheological elastomers (MREs), which, in turn, is assessed via full-field numerical simulations. The proposed phenomenological models are constructed so that they recover the same purely mechanical, initial and saturation magnetization and initial magnetostriction response of the analytical homogenization model for all sets of material parameters, such as the particle volume fraction and the material properties of the constituents (e.g., the matrix shear modulus, the magnetic susceptibility and magnetization saturation of the particles). The functional form of the proposed phenomenological models is based on simple energy functions with small number of calibration parameters thus allowing for the description of magnetoelastic solids more generally such as anisotropic (with particle-chains) ones, polymers comprising ferrofluid particles or particle clusters. This, in turn, makes them suitable to probe a large set of experimental or numerical results. The models of the present study show that in isotropic MREs, the entire magnetization response is insensitive to the shear modulus of the matrix material even when the latter ranges between 0.003-0.3MPa, while the magnetostriction response is extremely sensitive to the mechanical properties of the matrix material.two-dimensional MREs. Moreover, in an effort to resolve some of the surrounding air and specimen effects, Kalina et al. (2016) have modeled directly the specimen, the surrounding air and the microstructure at the same scale. While this study has led to satisfactory qualitative agreement with experiments, it did not resolve the different length scales as one goes from specimen to microstructure, since that would require an untractable mesh size. Along this effort, Keip and Rambausek (2015) proposed a two-scale finite element approach in order to solve simultaneously the magneto-mechanical boundary value problem and the microstructural problem by properly resolving the separation of the very different length scales. While this last approach is the more complete one, it still remains numerically demanding, especially if complex unit cells with large number of particles are considered. Moreover, in all these approaches, it is very hard to decouple from the estimated response the relative effect of the specimen geometry and that of the microstructure.In this regard, the recent study of Lefèvre et al. (2017) proposes an alternative view to the problem by first solving the homogenization problem at the RVE scale analytically and then using these estimates at the macroscopic scale to analyze the specimen shape effects. In that effort, the authors obtained a very usef...

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