Development of New Phenomenological Models for Predicting Magnetic Permeability of Isotropic and Anisotropic Magneto-Rheological Elastomers

Abstract

Designing smart devices based on magneto-rheological elastomers (MREs) is a quite challenging task due to the inherent nonlinear behavior of MREs in the presence of an applied magnetic field. In the early stage of the design process, the magnetic circuit parameters need to be optimized either via analytical approaches or FE simulations. These require a precise nonlinear magnetic permeability model (B-H curve formulation) of MREs. The model should consider the effect of essential design factors (particle volume fraction and anisotropy) and loading conditions (magnetic field and pre-strain). The main contribution of the present study is to formulate a field-dependent novel and reliable nonlinear B-H relation for MREs as functions of the basic design and loading factors. Three batches of isotropic and anisotropic MRE samples were fabricated with different particle volume fractions (15%, 30%, and 45%). Subsequently, a simple methodology was presented to determine the magnetic permeability and then the nonlinear B-H curves of the MREs considering wide variations in pre-strain (0, 12.5%, 25%, 37.5%, and 50%) as well as coil current, ranging from 0.2 A to 8 A. Experimental results showed that the relative magnetic permeability of both types of MREs increased with increasing pre-strain. Phenomenological-based models were consequently developed to estimate the nonlinear B-H curves of the isotropic and anisotropic MREs accurately and efficiently over the entire design and loading conditions considered. The proposed model can be effectively utilized for modeling and design optimization of MRE-based smart devices.