Hard Magnetic Particles Research Articles

Drop-on-Demand 3D Printing of Programable Magnetic Composites for Soft Robotics

Soft robotics have become increasingly popular as a versatile alternative to traditional robotics. Magnetic composite materials, which respond to external magnetic fields, have attracted significant interest in this field due to their programmable two-way actuation and shape-morphing capabilities. Additive manufacturing (AM), also known as 3D printing, allows for the incorporation of different functional composite materials to create active components for soft robotic systems. However, current AM methods have limitations, especially when it comes to printing smart composite materials with high functional material content. This is a key requirement for enhancing responsiveness to external stimuli. Commonly used AM methods for smart magnetic composites, such as direct ink writing (DIW), confront challenges in achieving discontinuous printing, and enabling multi-material control at the voxel level, while some AM techniques are not suitable for producing composite materials. To address these limitations, we employed high-viscosity drop-on-demand (DoD) jetting and developed versatile programmable magnetic composites filled with micron-sized hard magnetic particles. This method bridges the gap between conventional ink-jetting and DIW, which require inks with viscosities at opposite ends of the spectrum. This high-viscosity DoD jetting enables continuous, discontinuous, and non-contact printing, making it a versatile and effective method for printing functional magnetic composites even with micron-sized fillers. Furthermore, we demonstrated stable magnetic domain programming and two-way shape-morphing actuations of printed structures for soft robotics. In summary, our work highlights high-viscosity DoD jetting as a promising method for printing functional magnetic composites and other similar materials for a wide range of applications.

Exploring the effect of exchange coupling in (SrFe9.8Al2La0.2O19)1-x/(Co0.7Zn0.3Fe2O4)x nanocomposites synthesised by sol–gel auto combustion method

Extensive research has been conducted over the last decade to develop permanent magnets utilizing less rare earth materials. Exchange-coupled nanocomposite magnets are a fascinating development in the field of permanent magnets. They involve the combination of hard and soft ferrites, resulting in a unique and evolving magnet. Here we present an in-depth structural, morphological and magnetic characterization of ferrite-based nanostructures obtained through a bottom-up sol−gel approach. The combination of high coercivity of a hard phase SrFe9.8Al2La0.2O19 (SFALO) and high saturation magnetization of a soft phase, Co0.7Zn0.3Fe2O4 (CZFO), allowed us to develop exchange-coupled bi-magnetic nanocomposites by varying the mass percentage (x = 0, 0.1, 0.2, 0.3, 0.4, 1). Thermogravimetric analysis (TGA) up to 1200 °C was used to investigate the material’s thermal properties with the phase formation temperature. Detailed atomic/nano-scale structural characterizations of these nanocomposites were performed by X-ray diffraction and Transmission Electron Microscopy. The average particle size was calculated from the SEM analysis and it was observed that most of the composites with ratio x = 0.1, 0.3 & 0.4 was 145 nm and x = 0.2 was 165 nm. The Switching Field Distribution (SFD) curve revealed the exchange coupling between soft and hard magnetic particles. The findings indicate that the inclusion of a soft magnetic phase has a considerable impact on the exchange coupling between the hard and soft ferrite phases. As the spinel concentration increased, in the composite the saturation magnetization increased from 18 emu/g to 48 emu/g. From the stroner-wholfrathmodel, the decrease in the remanence ratio below 0.5 concludes the crystallites are randomly oriented. The nanocomposite with the ratio x = 0.1 was observed with the high magneto crystalline anisotropy of 2183.23 × 102 (J/m3) and a high energy product (BH)max of 5.5 kJ/m3. The aforementioned features of nanocomposites demonstrate their potential for use in permanent magnet applications.

Modeling magnetic soft continuum robot in nonuniform magnetic fields via energy minimization

The emerging magnetic soft continuum robots (MSCRs) – a type of slender and soft rods with embedded hard-magnetic particles – hold great promise in endovascular intervention via remote magnetic actuation. Although numerous advantages of using permanent magnets have been demonstrated for manipulating MSCRs (e.g., simple systems with high actuation force, large operating workspace), the magneto-mechanical behavior of MSCRs in nonuniform magnetic fields, particularly those generated by permanent magnets, remains largely unexplored. In this work, a systematic study of MSCRs in the nonuniform field is presented, which includes theoretical modeling using hard-magnetic elastica theory, numerical analyses by energy minimization method, finite element simulations using ABAQUS user element (UEL), and experimental validation. Without solving governing differential equations, the large deflection of MSCRs is efficiently obtained via the minimization of the total potential energy using sequential quadratic programming (SQP). This efficient modeling method offers insights into the control of MSCRs using nonuniform magnetic fields. Two practical strategies are provided for precisely controlling MSCRs by manipulating a cubic magnet through the adjustment of the actuation distance, rotation angle, and spin angle, laying the foundation for applications of magnetically-assisted endovascular intervention.

The magnetic properties of packings of cylinders

Powders of magnetic particles are used e.g. in additive manufacturing of magnets, necessitating an investigation of the properties of such powders. In this work we consider hard magnetic particles modeled as infinitely long cylinders in 2D and randomly packed in a square container. The particles have a nonlinear magnetization curve with defined remanence and coercivity and their radii follow a lognormal distribution with the standard deviation distinguishing different packings. Using a finite element approach we calculate the average and standard deviation of the magnetization of the individual particles in the packings and from these subtract the value of the corresponding regions in a solid square box to remove the shape demagnetization effect of the overall packing. We find that at applied fields close to the coercivity the average magnetization of the individual particles have the highest probability to deviate 5% from the average magnetization in the corresponding regions in the box. Away from the coercivity the packings have an near-identical magnetization to the solid box. Considering the magnetization internally in each particle, near the coercivity the standard deviation of the magnetization has the highest probability to deviate 10% from the standard deviation in magnetization in the corresponding region in the box. Thus while the overall magnetization in a packing appear to be the same as in a solid box, near the coercivity there is a larger variation of magnetization both between and within the magnetic particles, compared to a solid box.

Dynamic modeling and simulation of hard-magnetic soft beams interacting with environment via high-order finite elements of ANCF

Hard-magnetic soft (HMS) beams made of soft polymer matrix embedded with hard-magnetic particles can generate large and fast deformation under magnetic stimulation. Dynamic modeling and simulation of HMS beams interacting with complex environment are challenging in terms of computational accuracy and efficiency. This paper presents a method for high-order modeling and efficient computation of HMS beams. The major contribution of the method is a new three-node HMS beam element of absolute nodal coordinate formulation (ANCF), which applies to two material models of nonlinear and linear elasticities (i.e. neoHookean and St. Venant-Kirchhoff) coupled with magnetic energy. To improve the efficiency of the method, the paper presents how to derive the generalized internal forces and their Jacobians via invariant tensors, and how to determine the generalized external forces to model dynamic loads and interactions including gravity, hydrodynamics in fluids, and frictional contact in pipelines. Afterwards, the paper gives both static and dynamic equations with Rayleigh damping and discusses the numerical algorithms. Finally, the paper makes a comparison of static analysis and the experimental observation to validate the accuracy of the proposed modeling method. The paper also discusses the dynamic simulations, including forced vibration, swimming motion, crawling locomotion, and navigating motion to demonstrate the predictive capability and efficacy of the proposed method for dynamic problems.

Development of a novel fractional magneto-viscoelastic dynamic model for an adaptive beam featuring functional composite magnetoactive elastomers: Simulations and experimental studies

Recently, the rapid emergence of functional composite magnetoactive elastomers with integrated hard magnetic particles (known as hard magnetoactive elastomers) has attracted significant interest in fields such as soft robotics and material science. It is of paramount importance to develop an efficient model that can accurately predict the nonlinear dynamic behavior of adaptive structures for their practical application and the synthesis of effective control strategies. In this study, a novel nonlinear fractional magneto-viscoelastic model of an adaptive cantilevered beam featuring hard magnetoactive elastomers has been developed. This model effectively characterizes the beam’s nonlinear and rate-dependent response behavior under magnetic stimuli of varying frequencies and magnitudes. Considering the fractional Kelvin-Voigt energy dissipation model and large deformation nonlinearity, the governing equations for the cantilevered hard-magnetic soft beam were derived using the Hamilton principle. The finite difference method, combined with the Galerkin modal decomposition scheme, was subsequently utilized to discretize the time and space domains, respectively. A hardware-in-the-loop experimental framework was finally designed to experimentally investigate the beam’s nonlinear response behavior and validate the simulation results. The simulated nonlinear quasi-static responses of the beam, subjected to magnetic loading up to 30 mT, exhibited excellent agreement with the experimental data collected. Moreover, the simulated dynamic responses of the beam, subjected to various amplitudes of the applied magnetic field and magnetic frequencies up to 2 Hz, were thoroughly investigated. These included time-histories, phase-plane, and hysteretic responses, all demonstrating strong alignment with the experimental observations.

Changes in Material Behavior according to the Amount of Recycled Magnetic Materials in Polymer-Bonded Magnets Based on Thermoplastics

The applications of polymer-bonded magnets are increasing within drive technology mostly because of new concepts concerning the magnetic excitation of direct current (DC) or synchronous machines. To satisfy this rising demand for hard magnetic filler particles—mainly rare earth materials—in polymer-bonded magnets, a recycling strategy for thermoplastic-based bonded magnets has to be found that can be applied to polymer-bonded magnets. The most important factor for the recycling strategy is the filler material, especially when using rare earth materials, as those particles are associated with limited resources and high costs. However, thermoplastic-based bonded magnets reveal the opportunity to reuse the compound material system without separation of the filler from the matrix. Most known recycling strategies focus on sintered magnets, which leads to highly limited knowledge in terms of strategies for recycling bonded magnets. This paper illustrates the impact of different amounts of recycling material within the material system on material behavior and magnetic properties that can be achieved by taking different flow conditions and varying gating systems into account. The recycled material is generated by the mechanical reuse of shreds. We found that a supporting effect can be achieved with up to 50% recycled material in the material system, which leads to only minimal changes in the material’s behavior. Furthermore, changes in magnetic properties in terms of recycled material are affected by the gating system. To reduce the reduction in magnetic properties, the number of pin points should be as low as possible, and they should located in the middle. The filler orientation of the recycled material is minimally influenced by the outer magnetic field and, therefore, mainly follows the flow conditions. These flow conditions are likely to be affected by elastic flow proportions with increasing amounts of recycled material.

Magnetic field-assisted manufacturing of groove-structured flexible actuators with enhanced performance

Magnetic flexible actuators with hard-magnetic particles (NdFeB) as inlays have attracted widespread attention due to their small size, wireless control capability, and diverse transformation modes. The manufacturing method of these actuators plays a crucial role in their functionality. Here we propose a magnetic field-assisted manufacturing method based on vat photopolymerization (VPP) to produce hard-magnetic flexible actuators with 3D architecture in both geometry structure and magnetization arrangements. The assisting magnetic field enables alignment of hard magnetic particles during manufacturing process, thus obtaining a magnetization arrangement. The VPP method offers the ability to manufacture fine structures and selective curing but has a limitation on the magnetic particle content. To deal with the lack of driving force due to the low available content of magnetic particles, we construct groove structure to enhance the actuators' deformation, which is confirmed by both theoretical and experimental analyses. Flexible actuators with a low magnetic particle content (10 wt%) can be fabricated and fulfill intended functionality. We demonstrate the effectiveness of our method by manufacturing multi-arm grippers, showcasing their transportation capabilities. Moreover, we construct a 2-DOF joint for a crawling robot, significantly improving its motion performance and increasing the average step length to 6.8 times. Finally, we design and manufacture a magnetic diaphragm with complex structure and 3D magnetization arrangements, which is applied to a micro pump, demonstrating its pumping process with a rate of about 3.6 mL/min. These results highlight the potential of the proposed method in designing complex structures and magnetization arrangements of flexible actuators, expanding their functional boundaries.

Shape memory and recovery mechanism in hard magnetic soft materials.

Hard-magnetic soft materials (HMSMs), which combine soft polymer matrices with hard-magnetic particles, have emerged as versatile materials capable of achieving complex deformations under magnetic fields. This work aims to provide a comprehensive understanding of the non-thermal shape memory and recovery mechanisms in HMSMs. By developing a theoretical model, we interpret the transfer of shape information between different field quantities, such as the remanent magnetization vectors and the magnetic forces. The two-dimensional thin beam model developed here implies that the two-way interaction between magnetization patterns and mechanical deformations is the key for the shape memory effect in HMSMs. Experiments also validate the theoretical model and the proposed mechanism for shape memory. Furthermore, the idea is extended to an example of information encryption and retrieval using HMSM thin films. This study offers valuable insights into the control of shape memory effects in HMSMs and presents opportunities for advancements in soft robotics, secure data storage, and responsive materials.

A microstructure enhancement method for hard magnetic particle chains based on magnetic field oscillation sieve

Magnetic actuation has emerged as a prominent method in soft robots due to its charming advantages on diverse magnetization designs, which heavily rely on the microstructures formed by hard magnetic particles (NdFeB) inside the robot. However, the contradiction between the need for multiple orientations of the particles and the issue of particle agglomeration caused by repeated orientation during fabrication has not been effectively resolved. This limitation prevents additive manufacturing of high-performance magnetic soft robots and hinders further diversification of robot magnetization structures. In this study, we proposed a method that utilizes a dynamic magnetic field to re-disperse agglomerated particles. This method is able to effectively disperse the agglomerates uniformly and enhance the re-oriented particle chains in multiple aspects, including compactness, orientation (∼200 %), and maintenance time (>120 min). Furthermore, this method was utilized to improve the magneto-induced deformation (from 7.71° to 13.89°) of the Magneto-Rheological Elastomer (MRE) samples, which were fabricated with repeatedly orientated magnetizations using magnetic field-assisted Stereo-lithography (SLA). Overall, the proposed method lays the groundwork for the structural complexity of magnetic soft robots and holds significant potential for broadening the fabrication methods of magnetic soft robots.

Facile Synthesis of Nd2Fe14B Hard Magnetic Particles with Microwave-Assisted Hydrothermal Method

The synthesis of Nd-Fe-B magnetic powders via chemical techniques presents significant promise, but poses challenges due to their inherent chemical instability. In this investigation, Nd-Fe-B hard magnetic particles were synthesized utilizing an eco-friendly and simple microwave-assisted hydrothermal synthetic method. The technique involves the synthesis of the Nd-Fe-B oxide precursor using the microwave-assisted hydrothermal method, followed by reduction–diffusion using CaH2. The microwave-assisted hydrothermal technique presents a viable approach for preparing Nd-Fe-B precursor particles, offering advantages such as time and energy efficiency and environmental sustainability. The synthesized Nd-Fe-B particles demonstrated a coercivity of up to 2.3 kOe. These magnetic particles hold significant potential for use in high-performance permanent magnets, and can effectively contribute to developing high-energy density exchange-coupled nanocomposite magnets. This study also offers valuable insights into the design and synthesis of additional magnetic materials based on rare earth elements.

Mechanics of hard-magnetic soft materials: A review

Hard-magnetic soft materials are a class of magnetically responsive composites obtained by embedding hard-magnetic particles into a soft polymeric matrix. They have found widespread applications in shape-morphing systems, soft robotics, biomedical devices, and active metamaterials due to their ability to feature complex, untethered, reversible, and rapid deformations in response to magnetic loads. To guide the rational design of these functional applications, extensive efforts have been devoted to studying the mechanical behavior of hard-magnetic soft materials. In this paper, we review the recent progress in the mechanics of hard-magnetic soft materials. First, we introduce existing constitutive models capable of describing the coupled magneto-elastic deformations of hard-magnetic soft materials. Then, we discuss the mechanical response of structures made of hard-magnetic soft materials, including rods, beams, plates, and shells, under mechanical and magnetic loading. Subsequently, we introduce the design and behavior of magneto-mechanical metamaterials with tunable properties enabled by hard-magnetic soft materials. In addition, optimization-guided inverse design strategies for hard-magnetic soft materials to achieve predefined properties or deformations are also briefly reviewed. Finally, we provide our views on the potential future directions in the field of mechanics of hard-magnetic soft materials. We expect the current review to guide researchers to better understand different theoretical and computational frameworks of mechanics of hard-magnetic soft materials and thus aid with designing functional systems using these materials for various applications.

Length manipulation of hard magnetic particle chains under rotating magnetic fields

Length manipulation of hard magnetic particle chains under rotating magnetic fields

Analytical modeling of a magnetoactive elastomer unimorph

Magnetoactive elastomers (MAEs) are capable of large deformation, shape programming, and moderately large actuation forces when driven by an external magnetic field. These capabilities enable applications such as soft grippers, biomedical devices, and actuators. To facilitate complex shape deformation and enhanced range of motion, a unimorph can be designed with varying geometries, behave spatially varying multi-material properties, and be actuated with a non-uniform external magnetic field. To predict actuation performance under these complex conditions, an analytical model of a segmented MAE unimorph is developed based on beam theory with large deformation. The effect of the spatially-varying magnetic field is approximated using a segment-wise effective torque. The model accommodates spatially varying concentrations of magnetic particles and differentiates between the actuation mechanisms of hard and soft magnetic particles by accommodating different assumptions concerning the magnitude and direction of induced magnetization under a magnetic field. To validate the accuracy of the model predictions, four case studies are considered with various magnetic particles and matrix materials. Actuation performance is measured experimentally to validate the model for the case studies. The results show good agreement between experimental measurements and model predictions. A further parametric study is conducted to investigate the effects of the magnetic properties of particles and external magnetic fields on the free deflection. In addition, complex shape programming of the unimorph actuator is demonstrated by locally altering the geometric and material properties.

A meshfree model of hard-magnetic soft materials

Hard-magnetic soft materials comprising a soft matrix embedded with hard-magnetic particles can exhibit large deformations under external magnetic fields, which have attracted much interest due to their non-contact activation, flexible programmability, and rapid response in various applications such as biomedical devices, soft robotics and flexible electronics. Precise predictions of large deformations of hard-magnetic soft materials would be a key for relevant applications. Given that the rational designs in the programmable shape morphing of ferromagnetic structures requires high precision, here we develop a meshfree model based on the radial point interpolation method to quantitatively predict large deformations of hard-magnetic soft materials. We apply the stabilized conforming nodal integration instead of direct nodal integration to eliminate the influence of zero-energy mode, and the central difference scheme is implemented for the resolution procedure. We explore the bending of a hard-magnetic beam and snap buckling of a bistable hard-magnetic beam under external magnetic stimuli. Uniform and non-uniform discretizations are compared to show the insensitivity of the radial point interpolation method to nodal mesh. To demonstrate the versatile programmability of our model in the design of magnetic robotics, we further simulate complex locomotion (crawling, walking and rolling) of hard-magnetic soft robots under external magnetic excitation. The results could be used to guide rational designs of ferromagnetic structures and soft continuum robots.

Micromechanics-based constitutive modeling of hard-magnetic soft materials

Soft materials exhibit large deformation material nonlinearity when stretched and possess enhanced elongation-at-break strain prior to rupture. As a result, these materials can cater to several state-of-the-art biomedical and microfluidic applications that require cross-domain energy transduction. Furthermore, they are often impregnated with external multi-functional filler materials (e.g., hard-magnetic particles) to result in hard-magnetic soft materials (hMSM). This gives rise to an inherent complexity owing to the multi-physics coupling due to magnetics and solid dynamics (along with geometric and material nonlinearities), which demands a rigorous magneto-mechanical model for a thorough understanding of their large deformation mechanical behavior under magneto-mechanical loads. It is also mandatory to understand their rate-dependent, hyperelastic, and flow behavior that is omnipresent during their deformation process. This paper focuses on the development of a novel thermodynamically-consistent micromechanics-based constitutive model that incorporates all these attributes using the finite deformation theory. A statistical mechanics-based approach has been undertaken to model the mechanics of the elastomer matrix. The plastic behavior due to the elastomer and the dispersed magnetic phases has been further accounted using a double-yield function with a micromechanical approach. The developed model shows a good agreement for a wide range of hMSM subjected to a variety of complex loading conditions. Finally, a parametric study has been carried out to provide physical insights into the different model parameters.

A mechanics model of hard-magnetic soft rod with deformable cross-section under three-dimensional large deformation

Hard-magnetic soft (HMS) materials are soft active materials prepared by embedding the hard-magnetic particles (e.g. NdFeB) into soft elastomer, which can be actuated by applied magnetic fields. With the ability to retain remnant magnetism, HMS materials have many applications in soft robotics, haptic sensors and other fields. For HMS structures used in soft robotics, mechanics models have been developed for better exploiting the potential of the HMS materials. However, for rod-like structures made of soft materials, the nonlinear stress–strain relation and the areal change of the cross-section have not been considered in previous modeling work. In the present three-dimensional HMS rod model, started with the geometrically exact beam theory, the rigid cross-section assumption is replaced with a planar areal change assumption for soft rods, incompressible neo-Hookean material model is used to model the hyperelastic behavior of elastomers, which will be more accurate than linear relation under large deformation. Consistent with the deformable cross-section assumption, the magneto-elastic energy distribution is formulated and reduced to the line of centroid of the soft rod. To verify the accuracy and efficiency of the model, some simulation examples and experiments are performed. The error between the experimental results and the simulation results calculated by using 5 elements is within 10%. Our model can accurately and efficiently predict the 3D large deformation of the HMS rod, which can reduce the design and optimization cost and shorten the design cycle of HMS structure.

4D printing of hard magnetic soft materials based on NdFeB particles

Magnetic soft materials (MSM) show excellent potential in soft robotics, biomedicine, and sensors because of their excellent magnetic response, reversible deformation, and controlled motion. A hard magnetic soft material (HASM) that can be obtained by adding hard magnetic particles to a soft material matrix. By programing the spatial magnetization profile of the HASM object and manipulating the driving magnetic field, it exhibits excellent shape manipulation performance with unconstrained, reversible deformation transformation and controlled motion. In this study, a HASM ink consisting of hard magnetic NdFeB particles with a soft silicone rubber matrix was prepared. A 4D printing strategy using 3D injection printing technology combined with origami magnetization technology is used to fabricate 3D structured HASM objects for flexible shape programmability. A variety of programed shapes of HASM straight beams with bionic fish tails were fabricated by 4D printing strategy. The HASM straight beam is driven by the magnetic field, which can quickly realize the transformation and change of the preset shape as well as the shape of the HASM beam. The HASM bionic fish tail can swing rapidly under the action of the driving magnetic field. It shows a broad potential in the field of soft and bionic robots.

A Multipole Magnetoactive Elastomer for Vibration-Driven Locomotion.

Smart materials such as magnetoactive elastomers (MAEs) combine elastic and magnetic properties that can be significantly changed in response to a magnetic field and therefore offer enormous potential for applications in both scientific research and engineering. When such an elastomer contains microsized hard magnetic particles, it can become an elastic magnet once magnetized in a strong magnetic field. This article studies a multipole MAE with the aim of utilizing it as an actuation element of vibration-driven locomotion robots. The elastomer beam has three magnetic poles overall with the same poles at the ends and possesses silicone bristles protruding from its underside. The quasi-static bending of the multipole elastomer in a uniform magnetic field is investigated experimentally. The theoretical model exploits the magnetic torque to describe the field-induced bending shapes. The unidirectional locomotion of the elastomeric bristle-bot is realized in two prototype designs using magnetic actuation of either an external or an integrated source of an alternating magnetic field. The motion principle is based on cyclic interplay of asymmetric friction and inertia forces caused by field-induced bending vibrations of the elastomer. The locomotion behavior of both prototypes shows a strong resonant dependency of the advancing speed on the frequency of applied magnetic actuation.

Numerical study on the instabilities of hard-magnetic soft materials with viscoelastic effects

As a type of soft composite material, the hard-magnetic soft materials (HMSM) can retain high residual magnetization due to the high-coercivity of hard-magnetic particles. Meanwhile, the inherent viscoelasticity of the soft polymer matrix usually causes the rate dependent behavior and affects the stability of HMSM. The effects of viscoelasticity on the finite deformation and instability of HMSM are studied in this paper. A numerical model is developed for magneto-mechanical coupled problems of the viscoelastic HMSM. With this model, the instabilities of two typical HMSM structures (i.e. beam and spherical shell) with viscoelastic effects are investigated, including the buckling and snap-through instability. The results show that the viscoelastic effects delay the onset of instability and suppress the snap-back phenomenon during the unloading process. In addition, three different buckling behaviors (i.e. fully relaxed immediate buckling, elastic immediate buckling and the delayed buckling) at different loading rate ranges are observed in both beam and spherical shell. This work provides an effective numerical model to analyze the finite deformation and instabilities of viscoelastic HMSM and may guide the design of HMSM devices.