Shape-programmable cantilever made of a magnetoactive elastomer of mixed content

Abstract

This work presents an approach to the macroscopic field-controlled mechanics of magnetoactive elastomers of mixed content, which are a special type of smart materials made of an elastic composite and a combination of two essentially different ferromagnetic fillers. High-coercive particles of NdFeB-alloy powder for the magnetically hard filler and carbonyl iron powder particles with nearly zero coercivity for the magnetically soft filler are usually used. The magnetically hard particles are tens-of-micron in size and impart to the elastomer a remanent magnetisation, whereas due to the magnetically soft particles of several microns in size, the elastomer acquires a high magnetic susceptibility. Since large magnetically hard particles once magnetised in a strong field possess their own fields to which the magnetically soft particles are susceptible, the overall elastomer magnetisation as well as its mechanical response greatly depends on the relative concentration of both fillers. This work particularly studies the bending deformation of horizontally fixed magnetoactive cantilevers with the permanent magnetisation along the length axis under the action of gravity and a vertically applied uniform magnetic field. The cantilevers of the same geometry and fixed NdFeB content but different carbonyl iron concentration are considered. The magnetomechanical model is developed based on the finite-strain theory assuming the plane-stress approximation of the two-dimensional cantilever of infinite width. The magnetic energy comprises two magnetic terms, one of which is qualitatively linear and the other one is quadratic in the applied field strength. The numerically calculated field-programmed equilibrium bending shapes of the cantilevers are compared with the experimentally observed shapes. The model provides good agreement with the experiment up to moderate concentrations of the magnetically soft filler, when the coefficients of customary interpolation formulas for the concentration dependencies of elastic modulus and magnetic susceptibility are properly adjusted.

Spontaneous change of symmetry in a magnetoactive elastomer beam at its critical bending induced by a magnetic field

“…The magnitude of the torque of elastic forces must be equal to that of the torque created by the beam magnetization. In a low field, the latter torque has two components associated with the field action on the remanent MAE magnetization and the MAE magnetization induced by the field [70,71]. For a small bend, δ ≪ 1, and at H ≪ H cr , the Euler-Bernoulli equation [63] for the rotation angle φ can be written in the form where J = bc 3 /12 is the moment of inertia with respect to the z-axis, and S = bc is the beam cross-section area.…”