The quaternion beam model for hard-magnetic flexible cantilevers

The recently developed hard-magnetic soft(HMS)materials manufactured by embedding high-coercivity micro-particles into soft matrices have received considerable attention from researchers in diverse fields,e.g.,soft robotics,flexible electronics,and biomedicine.Theoretical investigations on large deformations of HMS structures are significant foundations of their applications.This work is devoted to developing a powerful theoretical tool for modeling and computing the complicated nonplanar deformations of flexible beams.A so-called quaternion beam model is proposed to break the singularity limitation of the existing geometrically exact(GE)beam model.The singularity-free governing equations for the three-dimensional(3D)large deformations of an HMS beam are first derived,and then solved with the Galerkin discretization method and the trustregion-dogleg iterative algorithm.The correctness of this new model and the utilized algorithms is verified by comparing the present results with the previous ones.The superiority of a quaternion beam model in calculating the complicated large deformations of a flexible beam is shown through several benchmark examples.It is found that the purpose of the HMS beam deformation is to eliminate the direction deviation between the residual magnetization and the applied magnetic field.The proposed new model and the revealed mechanism are supposed to be useful for guiding the engineering applications of flexible structures.

Dynamic analysis and regulation of the flexible pipe conveying fluid with a hard-magnetic soft segment

The recently developed hard-magnetic soft(HMS)materials can play a significant role in the actuation and control of medical devices,soft robots,flexible electronics,etc.To regulate the mechanical behaviors of the cantilevered pipe conveying fluid,the present work introduces a segment made of the HMS material located somewhere along the pipe length.Based on the absolute node coordinate formulation(ANCF),the governing equations of the pipe conveying fluid with an HMS segment are derived by the generalized Lagrange equation.By solving the derived equations with numerical methods,the static deformation,linear vibration characteristic,and nonlinear dynamic response of the pipe are analyzed.The result of the static deformation of the pipe shows that when the HMS segment is located in the middle of the pipe,the downstream portion of the pipe centerline will keep a straight shape,providing that the pipe is stable with a relatively low flow velocity.Therefore,it is possible to precisely regulate the ejection direction of the fluid flow by changing the magnetic and fluid parameters.It is also found that the intensity and direction of the external magnetic field greatly affect the stability and dynamic response of the pipe with an HMS segment.In most cases,the magnetic actuation increases the critical flow velocity for the flutter instability of the pipe system and suppresses the vibration amplitude of the pipe.

A 3D hard-magnetic rod model based on co-rotational formulations

Hard-magnetic soft materials have attracted broad interests because of their flexible programmability,non-contact activation and rapid response in various applications such as soft robotics,biomedical devices and flexible electronics.Such multifunctional materials consist of a soft matrix embedded with hard-magnetic particles,and can exhibit large deformations under external magnetic stimuli.Here,we develop a three-dimensional(3D)rod model to predict spatial deformations(extension,bending and twist)of slender hard-magnetic elastica.The model follows Kirchhoff hypothesis and thus reduces the 3D magneto-elastic energy function to a one-dimensional(1D)form.Besides,the co-rotational formulation is applied to describe rigid body motion,and explicit time integration is adopted for the nonlinear resolution.Moreover,we explore finite bending,post-buckling and twisting of hard-magnetic elastica under external magnetic fields with different directions and amplitudes.Representative examples with various configurations show superior efficiency and accuracy of the model(the difference less than 1%with only a small number of elements)compared to conventional solid element.Our model could be used to guide rational designs on programmable shape morphing of ferromagnetic slender structures.

On the anomalous low-resistance state and exceptional Hall component in hard-magnetic Weyl nanoflakes

Magnetic topological materials, which combine magnetism and topology, are expected to host emerging topological states and exotic quantum phenomena. In this study, with the aid of greatly enhanced coercive fields in high-quality nanoflakes of the magnetic Weyl semimetal Co_(3)Sn_(2)S_(2), we investigate anomalous electronic transport properties that are difficult to reveal in bulk Co_(3)Sn_(2)S_(2) or other magnetic materials. When the magnetization is antiparallel to the applied magnetic field, the low longitudinal resistance state occurs, which is in sharp contrast to the high resistance state for the parallel case. Meanwhile, an exceptional Hall component that can be up to three times larger than conventional anomalous Hall resistivity is also observed for transverse transport. These anomalous transport behaviors can be further understood by considering nonlinear magnetic textures and the chiral magnetic field associated with Weyl fermions, extending the longitudinal and transverse transport physics and providing novel degrees of freedom in the spintronic applications of emerging topological magnets.

Recent developments of rare-earth-free hard-magnetic materials

Recent advances in rare-earth-free hard-magnetic materials including magnetic bulk, thin films, nanocomposites and nanostructures are introduced. Since the costs of the rare-earth metals boosts up the price of the high-performance rare-earth permanent magnets, there is a much revived interest in various types of hard-magnetic materials based on rare-earth-free compounds. The 3d transition metals and their alloys with large coercivity and high Curie temperatures(working temperatures) are expected to overcome the disadvantages of rare-earth magnets. Making rare-earth-free magnets with a large energy product to meet tomorrow's energy needs is still a challenge.

Tunability of Band Gaps of Programmable Hard-Magnetic Soft Material Phononic Crystals

In this paper,the elastic wave band gap characteristics of two-dimensional hard-magnetic soft material phononic crystals(HmSM-PnCs)under the applied magnetic field are studied.Firstly,the relevant material parameters of hard-magnetic soft materials(HmSMs)are obtained by the experimental measurement.Then the finite element model of the programmable HmSM-PnCs is established to calculate its band structure under the applied magnetic field.The effects of some factors such as magnetic field,structure thickness,structure porosity,and magnetic anisotropy encoding mode on the band gap are given.The results show that the start and stop frequencies and band gap width can be tunable by changing the magnetic field.The magnetic anisotropy encoding mode has a remarkable effect on the number of band gaps and the critical magnetic field of band gaps.In addition,the effect of geometric size on PnC structure is also discussed.With the increase of the structure thickness,the start and stop frequencies of the band gap increase.

Dynamic analysis and active control of hard-magnetic soft materials

The hard-magnetic soft materials which can sustain high residual magnetic flux density gradually attract the attention of researchers because of potential applications in soft robotics and biomedical fields.In this work,we focus on the dynamic response of hardmagnetic soft materials.The dynamic motion equations are derived by the Euler-Lagrange equation.The effects of the aspect radio on the nonlinear vibration of the hard-magnetic soft cuboid under the force and applied magnetic fields in different directions are investigated.The amplitude-frequency curves demonstrate that the aspect ratio also has an influence on the frequency and amplitude of the primary resonance.Moreover,to eliminate undesired vibration responses,the PID controller is applied to the vibration of the hardmagnetic soft materials,and the desired results can be obtained.