Soft active materials that show a response under external stimuli such as light, electricity, heat and magnetic fields have wide applications in the fields of soft robotics, flexible electronics, biomedicine, etc. Recently developed hard-magnetic soft (HMS) materials that undergo rapid transformations under magnetic actuations belong to a new class of soft active materials. In order to fulfill the potential applications of HMS structures, it is of great importance to investigate their mechanical responses. In this work, based on the principle of minimum potential energy, a theoretical model for HMS beams with the consideration of exact geometric nonlinearity is proposed, which is capable of characterizing the complex transformations of the HMS beam. The Galerkin method is utilized to solve the governing equation of the system. By comparing with the recent simulation and experimental data, the proposed model is validated. It is found that with the designed residual magnetic flux density in the HMS beam, the initially straight beam would deform into complex configurations under specified magnetic actuation. Interestingly, the crawling of inchworms, grasping of tongs and slithering of snakes can be well imitated by the HMS beam as a consequence. The developed theoretical model could serve as a benchmark for the analyses of HMS beams in the future, and the observed phenomena could shed light on the design of soft robotic devices used in extreme environments based on HMS structures.

In this work, the nonlinear behaviors of soft cantilevered pipes containing internal fluid flow are studied based on a geometrically exact model, with particular focus on the mechanism of large-amplitude oscillations of the pipe under gravity. Four key parameters, including the flow velocity, the mass ratio, the gravity parameter, and the inclination angle between the pipe length and the gravity direction, are considered to affect the static and dynamic behaviors of the soft pipe. The stability analyses show that, provided that the inclination angle is not equal to π, the soft pipe is stable at a low flow velocity and becomes unstable via flutter once the flow velocity is beyond a critical value. As the inclination angle is equal to π, the pipe experiences, in turn, buckling instability, regaining stability, and flutter instability with the increase in the flow velocity. Interestingly, the stability of the pipe can be either enhanced or weakened by varying the gravity parameter, mainly dependent on the value of the inclination angle. In the nonlinear dynamic analysis, it is demonstrated that the post-flutter amplitude of the soft pipe can be extremely large in the form of limit-cycle oscillations. Besides, the oscillating shapes for various inclination angles are provided to display interesting dynamical behaviors of the inclined soft pipe conveying fluid.