Magnetorheological elastomers (MREs) consist of micron-sized magnetizable particles embedded in a rubber matrix. Properties of these magneto-sensitive materials are changed reversibly upon application of external magnetic fields. They exhibit highly non-linear magneto-mechanical response which allows developing new devices and applications. However, the coupled magneto-mechanical behavior makes mathematical modeling of MREs quite complicated. So development of a reliable constitutive framework is essential for further understanding of this coupled behavior as well as simulation of the systems that utilize MREs. In this paper, a finite strain continuum model is developed for MREs where the effect of magnetization on material stiffness is directly introduced in the material shear modulus. It is shown that this approach simplifies the constitutive models and also perceives the magnetic saturation of MREs. Moreover, the coupled effects of magnetization, deformation and particle-chains orientation on the mechanical response are also taken into account in the introduced parameter. This reduces the number of material parameters, the required experimental tests for parameters identification and also simplifies the mathematical formulation of the developed constitutive equations which is beneficial for numerical formulations. A systematic two-step method is then introduced for material parameters identification which assures uniqueness of the parameters set. The predictive capabilities of the proposed model are examined via available mechanical and magneto-mechanical experimental data on both isotropic and anisotropic MRE samples at different configurations of magnetic field and loading with respect to the preferred direction of the samples. It is shown that the model can well predict the magneto-mechanical response of MREs at different deformation modes and magnetic fields.

磁流变弹性体（MRE）由嵌入橡胶基质中的微米级可磁化颗粒组成。这些磁敏材料的性质在施加外部磁场时可逆地改变。它们表现出高度非线性的磁机械响应，从而允许开发新的设备和应用。但是，耦合的磁机械行为使MRE的数学建模变得相当复杂。因此，开发可靠的本构框架对于进一步了解这种耦合行为以及使用MRE的系统的仿真至关重要。在本文中，为MRE建立了有限应变连续模型，其中磁化对材料刚度的影响直接引入材料的剪切模量中。结果表明，该方法简化了本构模型，并且还可以感知MRE的磁饱和。此外，在引入的参数中还考虑了磁化，变形和颗粒链取向对机械响应的耦合作用。这减少了材料参数的数量，减少了参数识别所需的实验测试，还简化了已开发的本构方程的数学公式，这对数值公式很有帮助。然后引入一种系统的两步法来进行材料参数识别，以确保参数集的唯一性。通过关于磁场和载荷相对于样品优选方向的不同配置的各向同性和各向异性MRE样品的可用机械和磁机械实验数据，检验了所提出模型的预测能力。结果表明，该模型能够很好地预测MRE在不同变形模式和磁场下的磁机械响应。