Temperature-dependent modeling of magnetorheological elastomers: a continuum approach using modified strain energy functions

In recent years, there has been a growing interest in magnetorheological elastomers (MREs) as a type of field-dependent smart composite material. MREs are basically solid analogue of MR fluids in which micro-sized ferromagnetic particles are dispersed into the polymeric medium rather than fluidic carrier. In contrast to MR fluids, stiffness properties of MREs can be substantially varied through application of magnetic field. Beyond internal factors like particle volume fraction and particle arrangement, external conditions such as temperature can also significantly affect the mechanical properties of MRE. This paper aims to formulate a continuum-based model to predict the response of MREs considering environmental temperature as an independent variable. To achieve this, the concept of the Strain Energy Function (SEF) is effectively utilized, and several nonlinear hyperelasticity SEFs are modified to account for magnetic induction, temperature, and deformation gradient as independent parameters. Since temperature can influence MRE behavior through both the initial stiffness and its contribution to the SEF, the proposed model includes a multiplicative function for the initial shear modulus, which depends on magnetic induction, temperature, and axial pressure force. Next, motivated by the lack of existing experimental data on the temperature effect on MRE behavior, a series of torque-twist tests were conducted on a cylindrical MRE sample with a 25% volume fraction of ferromagnetic particles, under a temperature range of -10 to 40 °C. These experimental data were used to identify the unknown parameters and validate the proposed model. Additionally, a discussion is provided on comparison different proposed SEFs and how a simpler SEF can be defined while maintaining acceptable accuracy. The results indicate that a generalized Mooney-Rivlin model, with a reduced number of material constants, can achieve sufficient accuracy.