Magnetorheological elastomers (MREs) are ferromagnetic particle-reinforced composites that have a wide application prospect in engineering because of their tunable stiffness with applied magnetic fields. While a large number of experimental efforts have been carried out to characterize the magneto-mechanical properties of MREs, few physics-based quantitative modeling and simulation have been explored. Here a micromechanics-based finite element model and computational homogenization is developed to determine the field-dependent shear moduli of MREs. The magneto-elastic coupling is realized with the magnetic field-induced body forces in the local mechanical field. The three-dimensional body forces are solved with consideration of magnetization and demagnetizing fields. Effects of essential microstructure parameters (particle concentration and particle spacing) are investigated on the effective magneto-mechanical properties of chain-structured MREs. The numerical results demonstrate that the microstructures and demagnetizing field have significant effects on the field-induced moduli of MREs. RVEs with appropriate microstructures are selected to compare our model predictions of magneto-mechanical properties with multiple groups of experiment data in the literature, showing the capability and validity of the proposed model.

磁流变弹性体（MRE）是铁磁颗粒增强复合材料，由于其刚度随外加磁场可调而在工程中具有广泛的应用前景。虽然已经进行了大量的实验工作来表征 MRE 的磁力学特性，但很少探索基于物理的定量建模和模拟。这里开发了基于微力学的有限元模型和计算均匀化，以确定 MRE 的场相关剪切模量。磁弹性耦合是通过局部机械场中的磁场感应体力实现的。考虑了磁化场和去磁场，求解了三维体力。研究了基本微观结构参数（粒子浓度和粒子间距）对链状结构 MRE 的有效磁力学性能的影响。数值结果表明，微结构和退磁场对MRE的场致模量有显着影响。选择具有适当微观结构的 RVE 将我们对磁力学性能的模型预测与文献中的多组实验数据进行比较，显示所提出模型的能力和有效性。