Abstract:This paper reveals the effects of the variable cross section and the gradient magnetic field on the large deformations of hard magnetic soft (HMS) beams, which may provide theoretical guidance for the development of advanced magnetoactive devices and systems. Based on the principle of minimum potential energy, a theoretical model is established to calculate the static deformation of the HMS beam with a variable cross section under the gradient magnetic field. The effect of the variable cross section on the buckling instability behavior of the HMS beam is analyzed by using a linear stability theory. The nonlinear analysis method is employed to study the effects of the variable cross section and the magnetic field gradient on bending deformations of the HMS beam. It is found that the variable section parameter plays a significant role on the critical buckling load of the HMS beam, i.e. the buckling stability of the beam can be well tuned by changing the variable section parameter. When the bending deformation is relatively small, the effect of the variable section parameter on the post-buckling configuration of the HMS beam is obvious. Such effect becomes weak when the beam’s bending deformation tends to saturation. The increase of the magnetic field gradient parameter will lead to a larger static deformation of the HMS beam with a variable section. When the magnetic field force exceeds the critical buckling load, the variable-section HMS beam will not suffer the pre-buckling deformation, but directly translates to a nonlinear post-buckling deformation. The results also show that the accuracy of the magnetic deflection at the free end of the variable-section HMS beam can be improved by increasing the parameter value of the magnetic field gradient, which can increase the control effectiveness of the magnetic steering of the HMS beam with a variable section. This work may be useful for the design of deployable flexible structures, flexible electronic devices and soft robots based on HMS materials.