Bottom-up multiscale modeling of yield stress for magnetorheological fluids based on close-packed BCT configuration

Current computational models for solving the yield stress of magnetorheological fluids (MRFs) still struggle to balance computational accuracy and efficiency. In this work, we proposed a bottom-up multi-scale yield stress model by integrating macroscopic parameters with a microscale framework rooted in the closest-packed body-centered tetragonal (BCT) configuration. All unknown parameters in the model are uniformly expressed as explicit functions of particle concentration and external field strength, significantly improving the computational efficiency while facilitating the establishment of the constitutive model of MRFs. Specifically, the modeling of the closest-packed BCT configuration considers multi-body and multi-pole interactions via a three-dimensional finite element method to improve computational accuracy. The applied reduced magnetic field formula and affine deformation ensure the periodic boundary conditions. To avoid computational domain overlap of the BCT configuration during shear deformation, a lateral offset displacement is introduced to the particles based on the energy minimization principle. The improvement in model prediction accuracy is achieved by introducing an effective chain coefficient, which is identified from experimental data using the least squares method. The calculation results are in good agreement with the experimental data measured by a rotational rheometer, which verifies the accuracy of the model. By combining the established yield stress model with the existing viscosity model for particle suspensions, a constitutive model of MRFs is established and further applied to the damping force modeling of dampers. This constitutive model provides theoretical guidance for the matching and development of suitable MRFs in the damper design stage.