Coupled magneto-hyperelasticity-thermal behavior of magnetorheological elastomers: A physics-based model and experimental verification

Recently, magnetorheological elastomers (MREs), known as a class of functional materials, have garnered considerable attention. MREs adapt their mechanical properties under external magnetic fields, positioning them as versatile materials for a range of engineering and biomedical applications. Therefore, accurately characterizing and modeling of their response under near-real-life conditions is of paramount importance. In this study, a physics-based model based on nonlinear continuum mechanics framework and total Helmholtz energy function has been formulated to predict the response of soft isotropic MREs under coupled magneto-hyperelasticity-thermal conditions. The deformation gradient, magnetic induction, and temperature are treated as independent variables in the proposed model. Additionally, the state of temperature and its gradient within the medium are examined to assess their influence on both the shear modulus and the total energy function. The Yeoh hyperelastic energy function is modified to incorporate magnetic and magneto-mechanical coupling effects, representing the isothermal component in the total Helmholtz energy function. In addition to the proposed mathematical model, a series of experimental tests are carried out to determine the material parameters and validate the accuracy of the developed model. The experimental results reveal that the fabricated MRE exhibits an increase in shear modulus in linear viscoelastic region with rising temperature. The model is subsequently utilized to study a boundary-value problem addressing a solid cylinder made of MRE subjected to torque-twist loading and under thermal boundary conditions. The effects of temperature and magnetic flux density on the response of the MRE cylinder, specifically torque–twist behavior, material stiffening, and strain softening, are subsequently examined and discussed.