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Magnetic microfibers are fibers that behave as a flexible paramagnetic body, for example, polymer fibers filled with superparamagnetic particles. A cantilevered magnetic microfiber will bend in response to an applied magnetic field. In a nonuniform field, generated for example by a single electromagnet or by a magnetic dipole, a magnetic microfiber displays position hysteresis as the field strength increases and decreases. This paper presents a model for determining stable shapes of a cantilevered magnetic microfiber in a nonuniform magnetic field. The model determines stable shapes by finding local minima of the potential energy using a Rayleigh-Ritz method. The model predicts the position hysteresis behavior observed in magnetic microfibers. Experimental data ware collected using two electromagnets with different geometries. The model simulation and experimental data compare well both qualitatively and quantitatively. The model will be useful for designing actuators based on magnetic microfibers and for characterizing the magnetic properties of fabricated fibers. A rigid bar model is also introduced, which captures the qualitative behavior of the fiber and illustrates the source of the position hysteresis behavior.

Bending and Position Hysteresis of Magnetic Microfibers in Nonuniform Magnetic Fields