A unified dual modeling framework for soft and hard magnetorheological elastomers
Résumé
Most current magnetorheological elastomers (MREs) are broadly categorized into hard(h-MREs) and soft(s-MREs) depending on the magnetic properties of the underlying particles. The former consist of particles exhibiting strong magnetic dissipation (e.g., NdFeB), while the later are purely energetic (e.g., carbonyl iron). In this work, we present a unified modeling framework for h-MREs including the response of the s-MREs as a limiting case when the dissipation is set to zero. In addition, the proposed framework is dual in the sense of a partial Legendre-Fenchel transform of the magnetic part, i.e., we propose exactly equivalent models in the F − H and F − B variable spaces. Efficient finite element, numerical solutions for various boundary value problems (BVPs) involving hand s-MREs are obtained via incremental variational principles. The calculations for the end-tip deflection of a uniformly pre-magnetized cantilever exhibit excellent agreement with the experimental data. The investigations on the remanent fields and the magnetic actuation performance of hybrid h-/s-MRE rank-1 laminated cantilevers and non-uniformly pre-magnetized, functionally graded beams are also carried out. The analysis shows that pre-magnetization profiling of the h-MRE beams allows to program efficiently the deflection patterns upon subsequent application of a small actuating magnetic field. Furthermore, concentrating the hard-magnetic particles near the beam flanks reduces the actuation field considerably. The proposed F − H and F − B-based modeling frameworks and their numerical implementations serve as useful tools in analyzing the magneto-mechanical performance of the MRE structures made of sand h-MREs.
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