Development of a phenomenological model for predicting the viscoelastic response of solid and hybrid MR elastomers

This study presents a phenomenological viscoelastic model for predicting the dynamic compressive behavior of hybrid magnetorheological materials formed by encapsulating magnetorheological fluid within a magnetorheological elastomer shell (MRF–MRE). Cubic specimens with identical geometry (30 mm edge length), including a solid MRE and a hybrid MRF–MRE, were experimentally characterized under uniaxial compression across a range of excitation frequencies, strain amplitudes, and applied magnetic fields. A modified Kelvin–Voigt formulation was developed in which both storage and loss moduli are expressed as coupled functions of magnetic excitation, loading frequency, and strain amplitude. Model predictions show good agreement with experimental measurements, yielding average errors below 5% for both materials. The hybrid MRF–MRE specimen exhibited a markedly enhanced magnetorheological response in compression, achieving an elastic modulus increase of up to 650% under magnetic excitation, compared with approximately 100% for the solid MRE. A similar amplification was observed in dissipative behavior, with the maximum relative change in loss modulus reaching 1340% for the hybrid material, versus 141% for the MRE. The proposed model provides a unified predictive framework for the analysis and design of hybrid magnetorheological materials in adaptive vibration isolation and semi-active control applications.