  Hard-magnetic soft materials (HMSMs) are particulate composites that consist
of a soft matrix embedded with particles of high remnant magnetic induction.
Since the application of an external magnetic flux induces a body couple in
HMSMs, the Cauchy stress tensor in these materials is asymmetric, in general.
Therefore, the micropolar continuum theory can be employed to capture the
deformation of these materials. On the other hand, the geometries and
structures made of HMSMs often possess small thickness compared to the overall
dimensions of the body. Accordingly, in the present contribution, a
10-parameter micropolar shell formulation to model the finite elastic
deformation of thin structures made of HMSMs and subject to magnetic stimuli is
developed. The present shell formulation allows for using three-dimensional
constitutive laws without any need for modification to apply the plane stress
assumption in thin structures. Due to the highly nonlinear nature of the
governing equations, a nonlinear finite element formulation for numerical
simulations is also developed. To circumvent locking at large distortions, an
enhanced assumed strain formulation is adopted. The performance of the
developed formulation is examined in several numerical examples. It is shown
that the proposed formulation is an effective tool for simulating the
deformation of thin bodies made of HMSMs.
