  In this study, we perform a critical examination of the phenomenon where the
magnetization is stretch-independent in incompressible hard-magnetic
magnetorheological elastomers (h-MREs), as observed in several recent
experimental and numerical investigations. We demonstrate that the fully
dissipative model proposed by Mukherjee et al. (2021) may be reduced, under
physically consistent assumptions, to that of Yan et al. (2023), but not that
of Zhao et al. (2019). In cases where the h-MRE solid undergoes non-negligible
stretching, the model of Zhao et al. (2019) provides predictions that are in
disagreement with experimental observations, given that, by construction, that
model produces a magnetization response that is not stretch-independent. By
contrast, the other two models are able to describe this important feature
present in h-MREs, as well as in incompressible magnetically soft s-MRES. Note
that in cases where stretching is negligible, such as for inextensible slender
structures under bending deformation, the Zhao et al. (2019) model provides
accurate predictions despite its underlying assumptions. Additionally, our
analysis reveals two key points about the magnetization vector in the context
of the more general, fully dissipative model. First, the magnetization can be
related to an internal variable in that theory. However, it cannot be formally
used as an internal variable except in the special case of an ideal magnet,
and, as such, it is subject to constitutive assumptions. Furthermore, we
clarify that the magnetization vector alone is insufficient to describe
entirely the magnetic response of an MRE solid; instead, the introduction of
one of the original Maxwell fields is always necessary for a complete
representation.
