The Modeling of Magnetorheological Elastomers: A State‐of‐the‐Art Review

Abstract

The magnetorheological elastomers (MREs) are novel multifunctional materials wherein their viscoelastic properties can be varied instantly under an application of applied magnetic field. Due to their field‐dependent stiffness and damping properties, MREs are widely used in the development and design of MRE‐based adaptive vibration isolators and absorbers and also biomedical engineering. Moreover, MREs due to their inherent magnetostriction effect have enormous potential for the development of soft actuators. The dynamic behavior of MREs is affected by various material parameters (e.g., matrix and particle types, particle concentration, additives) as well as mechanical and magnetic loading parameters (e.g., frequency, amplitude, temperature, magnetic flux density). Understanding and predicting the effect of materials and loading parameters on the response behavior of MREs are of paramount importance for the design of MRE‐based adaptive structures and systems. This review paper mainly aims to provide a comprehensive study of material constitutive models to predict the nonlinear magnetomechanical behavior of MREs. Particular emphasis is paid to physics‐based models including continuum‐ and microstructure‐based models. Moreover, phenomenological models describing the dynamic magnetoviscoelastic behavior of MREs as well as the effect of temperature on the magnetomechanical behavior of such materials are properly addressed.

The nonlinear theory of magnetoelasticity and the role of the Maxwell stress: a review

“…One such model was derived in Bustamante [44] and involves 10 invariants (nine for incompressibility) in the general case. It was used in the review paper by Saber & Sedhagati [45] in the study of constitutive models of the nonlinear behaviour of MS elastomers, including micro-structural models. where e = tre and the constants μ, λ, ν and ξ are given by the derivatives Ω i and Ω ij being evaluated in B 0 .…”

“…Several slightly different approaches have been developed in the literature, including those by Brigadnov & Dorfmann [41], Kankanala & Triantafyllidis [42], Dorfmann & Ogden [26], and a novel theory based on implicit constitutive equations has been developed by Bustamante & Rajagopal [43]. A constitutive theory for transversely isotropic magnetoelastic materials was proposed by Bustamante [44], and has been used in the review by Saber & Sedaghati [45]. The method of homogenization has been used by Castañeda & Galipeau [46], Chatzigeorgiou et al [47] and Mukherjee et al [48], while the paper by Nadzharya et al [49] examines the influence of different spatial scales on the macroscopic behaviour of MS elastomers.…”

Hard magnetics and soft materials—a synergy

“…Yarali et al [32] presented a review on MERPs, focusing on their synthesis, characterization, and applications. Saber and Sedaghati [111] recently provided a study exclusively devoted to modeling, specifically concentrating on the dynamic and thermal behavior of MREs. Recently, Lu et al [112] presented an exclusive review of mechanics (outlining different constitutive models and principles) and design optimizations in hMSMs with a special focus on magnetic metamaterials.…”

Flutter analysis of laminated fiber-reinforced magnetorheological elastomer sandwich plate resting on an elastic foundation using an improved first-order shear deformation theory

“…Notably, Sun et al [12] have demonstrated that an augmentation in magnetic flux leads to smoother frequency response peaks, attributed to an amplified damping effect within the structure. Several other authors have investigated the viscoelastic modeling of MREs and their application [13][14][15][16][17][18].…”