In this work, we develop a neural network-based, data-driven, decoupled multiscale scheme for the modeling of structured magnetically soft magnetorheological elastomers (MREs). On the microscale, sampled magneto-mechanical loading paths are imposed on a representative volume element containing spherical particles and an elastomer matrix, and the resulting boundary value problem is solved using a mixed finite element formulation. The computed microscale responses are homogenized to construct a database for the training and testing of a macroscopic physics-augmented neural network model. The proposed model automatically detects the material's preferred direction during training and enforces key physical principles, including objectivity, material symmetry, thermodynamic consistency, and the normalization of free energy, stress, and magnetization. Within the range of the training data, the model enables accurate predictions of magnetization, mechanical stress, and total stress. For larger magnetic fields, the model yields plausible results. Finally, we apply the model to investigate the magnetostrictive behavior of a macroscopic spherical MRE sample, which exhibits contraction along the magnetic field direction when aligned with the material's preferred direction.

翻译：本文提出了一种基于神经网络的、数据驱动的、解耦的多尺度方案，用于模拟结构化软磁磁流变弹性体（MREs）。在微观尺度上，对包含球形颗粒和弹性体基质的代表性体积单元施加采样的磁-机械加载路径，并采用混合有限元公式求解相应的边值问题。计算得到的微观响应经过均匀化处理，构建用于训练和测试宏观物理增强神经网络模型的数据集。所提出的模型在训练过程中自动检测材料的优选方向，并强制满足关键物理原理，包括客观性、材料对称性、热力学一致性，以及自由能、应力和磁化强度的归一化。在训练数据范围内，该模型能够准确预测磁化强度、机械应力和总应力。对于更大的磁场，模型可给出合理的结果。最后，我们将该模型应用于研究宏观球形MRE样品的磁致伸缩行为，当磁场方向与材料优选方向一致时，样品沿磁场方向表现出收缩现象。