Magnetic field gradient and sample size effect on magnetomechanical response for magnetic elastomers

We studied the size effect of disk-shaped magnetic elastomers, which were placed on a permanent magnet, on their magnetomechanical response for the permanent magnet. The diameter of the magnetic elastomers varied from 14 to 40 mm, whereas the diameter of the permanent magnet was constant at 30 or 35 mm. The smallest magnetic elastomer did not exhibit magnetomechanical response for both 30- and 35-mm-diameter permanent magnets; however, a clear response was observed when the diameter of the magnetic elastomer equaled that of the permanent magnet. Magnetic field distribution revealed a steep gradient of magnetic fields at the fringe of permanent magnets. Image analyses indicated that the bottom of magnetic elastomers was restricted to deform along the horizontal direction under compression. In the vertical direction, the magnetostriction due to the magnetic attractive force from permanent magnets was negligibly small. Therefore, the size-dependent behavior of magnetomechanical response is considered a pinning effect wherein the bottom of magnetic elastomers was restricted by the magnetic field gradient in the horizontal direction. We also analyzed the magnetomechanical response of magnetic elastomers when magnetic fields were applied by square- or ring-shaped permanent magnets.