Optimized neural network framework for MRE fabrication with targeted stiffness and damping

Abstract Magnetorheological elastomers (MRE) are versatile smart materials capable of modulating their mechanical properties under external magnetic fields, unlocking transformative potential for applications demanding adaptive stiffness and damping. This work introduces a novel two-phase approach—a forward modelling phase followed by a design optimization phase—to design MREs with precisely tailored viscoelastic properties. Seven MRE samples, spanning isotropic and anisotropic configurations, are fabricated by varying chain orientations and curing magnetic fields. Extensive rheological characterization is conducted under multiple temperatures, magnetic fields, and frequencies, generating a dataset of 4200 points. In the first phase, a Multilayer Perceptron (MLP) neural network is trained on this dataset, with its architecture optimized using two metaheuristic algorithms: Particle Swarm Optimization (PSO) and the Whale Optimization Algorithm (WOA). Results reveal that the three-hidden-layer MLP, optimized by PSO, outperforms other configurations with a minimum Root Mean Squared Error (RMSE) of 1571.3, surpassing the R 2 = 0.97 achieved by a parametric fractional model on the same dataset. Conversely, WOA demonstrates a marginal edge in the four-hidden-layer configuration. Subsequently, the best-performing forward model among the tested configurations serves as a surrogate in the second-phase design procedure. PSO is reapplied to determine the optimal parameters—namely temperature, operating and preparatory magnetic fields, chain orientation, and angular frequency—to achieve the desired storage and loss moduli. Four new MRE samples are fabricated according to two of these optimized parameters, while the remaining parameters are applied during rheological testing. The final experimental results confirm that the maximum discrepancy between the designed and desired moduli is limited to ±7.5%. This framework streamlines MRE customization, minimizing trial and error efforts and significantly reducing fabrication costs and time. Its robustness paves the way for advanced applications in vibration isolation, soft robotics, and adaptive devices requiring precise stiffness and damping modulation.