The nonlinear elastic response of magnetorheological elastomers

Magnetorheological elastomers (MREs), consisting of a soft elastomeric matrix embedded with rigid (and typically magnetized) particles such as NdFeB, are increasingly used in mechanical and biomedical applications. Accurate modeling of their magneto-mechanical behavior requires first predicting their purely mechanical response. Traditionally, this mechanical prediction has relied on directly measuring the macroscopic response of MREs, either numerically or experimentally, for each particle fraction of interest, a procedure that is both time-consuming and labor-intensive. In this study, we replace that procedure with a simple computational framework that requires only a single measurement on the unfilled elastomer.The framework treats MREs as general incompressible filled elastomers and predicts their nonlinear elastic response by integrating several established modeling techniques. For any physically admissible particle volume fraction, it analytically predicts the macroscopic nonlinear response from the measured properties of the unfilled elastomer. We validate the framework experimentally across a wide range of cross-link densities in the elastomeric matrices, particle volume fractions (0%–28%), and specimen geometries, subjected to both uniform and highly localized large deformations (with local strains up to ∼ 600%). The experimental results show excellent agreement with the computational predictions, confirming the framework as a fast and reliable tool for predicting the nonlinear elastic response of MREs. Consequently, this study offers a practical tool for streamlining the modeling and design of MRE-based structures.