Stretch-independent magnetization in incompressible isotropic hard magnetorheological elastomers

Recent studies on magnetically hard, particle-filled magnetorheological elastomers ($h$-MREs) have revealed their stretch-independent magnetization response after full pre-magnetization. We discuss this phenomenon, focusing on incompressible, isotropic, particle-filled $h$-MREs. We demonstrate that the fully dissipative model of Mukherjee et al. (2021) for arbitrary loads can be reduced, under physically consistent assumptions, to the energetic model of Yan et al. (2023), but not that of Zhao et al. (2019). The latter two are valid for small magnetic fields around an already known pre-magnetized state. When the pre-magnetized $h-$MRE undergoes non-negligible stretching, the Zhao et al. (2019) model yields predictions that disagree with experiments due to its inherent stretch-dependent magnetization response. In contrast, the Mukherjee et al. (2021) and Yan et al. (2023) models are able to accurately capture this important feature present in pre-stretched $h$-MREs. However, for inextensible slender structures under bending deformation, where stretching is negligible, the Zhao et al. (2019) model provides satisfactory predictions despite its underlying assumptions. Our analysis reveals that, in the fully dissipative model, magnetization can be related to an internal variable but cannot be formally used as one, except for ideal magnets, and is subject to constitutive assumptions. Furthermore, the magnetization vector alone is insufficient to describe the magnetic response of an MRE solid; the introduction of one of the original Maxwell fields is necessary for a complete representation.