Hard magnetorheological elastomers ($h$-MREs) are essentially two phase composites comprising permanently magnetizable metallic inclusions suspended in a soft elastomeric matrix. This work provides a thermodynamically consistent, microstructurally-guided modeling framework for isotropic, incompressible $h$-MREs. Energy dissipates in such hard-magnetic composites primarily via ferromagnetic hysteresis in the underlying hard-magnetic particles. The proposed constitutive model is thus developed following the generalized standard materials framework, which necessitates suitable definitions of the energy density and the dissipation potential. Moreover, the proposed model is designed to recover several well-known homogenization results (and bounds) in the purely mechanical and purely magnetic limiting cases. The magneto–mechanical coupling response of the model, in turn, is calibrated with the aid of numerical homogenization estimates under symmetric cyclic loading. The performance of the model is then probed against several other numerical homogenization estimates considering various magneto–mechanical loading paths other than the calibration loading path. Very good agreement between the macroscopic model and the numerical homogenization estimates is observed, especially for stiff to moderately-soft matrix materials. An important outcome of the numerical simulations is the independence of the current magnetization to the stretch part of the deformation gradient. This is taken into account in the model by considering an only rotation-dependent remanent magnetic field as an internal variable. We further show that there is no need for an additional mechanical internal variable. Finally, the model is employed to solve macroscopic boundary value problems involving slender $h$-MRE structures and the results match excellently with experimental data from literature. Crucial differences are found between uniformly and non-uniformly pre-magnetized $h$-MREs in terms of their pre-magnetization and the associated self-fields.

硬磁流变弹性体（$H$-MREs本质上是两相复合材料，包括悬浮在软弹性基质中的可永久磁化的金属夹杂物。这项工作为各向同性，不可压缩提供了热力学上一致的，微观结构指导的建模框架。$H$-MRE。能量主要通过下面的硬磁颗粒中的铁磁滞后消散在此类硬磁复合材料中。因此，建议的本构模型是根据通用标准材料框架开发的，该框架需要对能量密度和耗散电势进行适当的定义。此外，提出的模型旨在在纯机械和纯磁极限情况下恢复几个众所周知的均质化结果（和界限）。反过来，该模型的磁-机械耦合响应是在对称循环载荷下借助数值均质化估计值进行校准的。然后针对模型的性能针对其他几种数值均质化估计进行探查，其中考虑了除校准加载路径以外的各种磁机械加载路径。观察到宏观模型与数值均化估计值之间有很好的一致性，特别是对于硬到中软的基质材料。数值模拟的重要结果是电流磁化强度与变形梯度的拉伸部分之间的独立性。在模型中通过将仅依赖于旋转的剩余磁场作为内部变量考虑在内。我们进一步表明，不需要额外的机械内部变量。最后，该模型用于解决涉及细长的宏观边值问题 观察到宏观模型与数值均化估计值之间有很好的一致性，特别是对于硬到中软的基质材料。数值模拟的重要结果是电流磁化强度与变形梯度的拉伸部分之间的独立性。在模型中通过将仅依赖于旋转的剩余磁场作为内部变量考虑在内。我们进一步表明，不需要其他机械内部变量。最后，该模型用于解决涉及细长的宏观边值问题 观察到宏观模型与数值均化估计值之间有很好的一致性，特别是对于硬到中软的基质材料。数值模拟的重要结果是电流磁化强度与变形梯度的拉伸部分之间的独立性。在模型中通过将仅依赖于旋转的剩余磁场作为内部变量考虑在内。我们进一步表明，不需要额外的机械内部变量。最后，该模型用于解决涉及细长的宏观边值问题 数值模拟的重要结果是电流磁化强度与变形梯度的拉伸部分之间的独立性。在模型中通过将仅依赖于旋转的剩余磁场作为内部变量考虑在内。我们进一步表明，不需要额外的机械内部变量。最后，该模型用于解决涉及细长的宏观边值问题 数值模拟的重要结果是电流磁化强度与变形梯度的拉伸部分之间的独立性。在模型中通过将仅依赖于旋转的剩余磁场作为内部变量考虑在内。我们进一步表明，不需要其他机械内部变量。最后，该模型用于解决涉及细长的宏观边值问题$H$-MRE结构和结果与文献中的实验数据非常吻合。在均匀和不均匀的预磁化之间发现了关键的差异$H$-MRE在预磁化和相关的自磁场方面。