  We develop a reduced-order model for thin plates made of hard
magnetorheological elastomers (hard-MREs), which are materials composed of
hard-magnetic particles embedded in a polymeric matrix. First, we propose a new
magnetic potential, as an alternative to an existing torque-based 3D continuum
theory of hard-MREs, obtained by reformulating the remnant magnetization of a
deformed hard-MRE body. Specifically, the magnetizations in the initial and
current configurations are related by the rotation tensor decomposed from the
deformation gradient, independently of stretching deformation. This description
is motivated by recently reported observations in microscopic homogenization
simulations. Then, we derive a 2D plate model through the dimensional reduction
of our proposed rotation-based 3D theory. For comparison, we also provide a
second plate model derived from the existing 3D theory. Finally, we perform
precision experiments to thoroughly evaluate the proposed 3D and 2D models on
hard-magnetic plates under various magnetic and mechanical loading conditions.
We demonstrate that our rotation-based modification of the magnetic potential
is crucial in correctly capturing the behavior of plates subjected to an
applied field aligned with the magnetization, and undergoing in-plane
stretching. In all the tested cases, our rotation-based 3D and 2D models yield
predictions in excellent quantitative agreement with the experiments and can
thus serve as predictive tools for the rational design of hard-magnetic plate
structures.
