  We investigate the mechanics of bistable, hard-magnetic, elastic beams,
combining experiments, finite element modeling (FEM), and a reduced-order
theory. The beam is made of a hard magneto-rheological elastomer, comprising
two segments with antiparallel magnetization along the centerline, and is set
into a bistable curved configuration by imposing an end-to-end shortening.
Reversible snapping is possible between these two stable states. First, we
experimentally characterize the critical field strength for the onset of
snapping, at different levels of end-to-end shortening. Second, we perform 3D
FEM simulations using the Riks method to analyze high-order deformation modes
during snapping. Third, we develop a reduced-order centerline-based beam theory
to rationalize the observed magneto-elastic response. The theory and
simulations are validated against experiments, with an excellent quantitative
agreement. Finally, we consider the case of combined magnetic and
mechanical-indentation loading, examining how the applied field affects the
bistability and quantifying the maximum load-bearing capacity. Our work
provides a set of predictive tools for the rational design of one-dimensional,
bistable, magneto-elastic structural elements.
