Magneto-sensitive elastomers in a homogeneous magnetic field: a regular rectangular lattice model

A theory of mechanical behaviour of the magneto-sensitive elastomers is developed in the framework of a linear elasticity approach. Using a regular rectangular lattice model, different spatial distributions of magnetic particles within a polymer matrix are considered: isotropic, chain-like and plane-like. It is shown that interaction between the magnetic particles results in the contraction of an elastomer along the homogeneous magnetic field. With increasing magnetic field the shear modulus for the shear deformation perpendicular to the magnetic field increases for all spatial distributions of magnetic particles. At the same time, with increasing magnetic field the Young's modulus for tensile deformation along the magnetic field decreases for both chain-like and isotropic distributions of magnetic particles and increases for the plane-like distribution of magnetic particles.Comment: 38 pages, 15 figure

Magneto-Mechanical Coupling in Magneto-Active Elastomers

In the present work, the magneto-mechanical coupling in magneto-active elastomers is investigated from two different modeling perspectives: a micro-continuum and a particle–interaction approach. Since both strategies differ significantly in their basic assumptions and the resolution of the problem under investigation, they are introduced in a concise manner and their capabilities are illustrated by means of representative examples. To motivate the application of these strategies within a hybrid multiscale framework for magneto-active elastomers, their interchangeability is then examined in a systematic comparison of the model predictions with regard to the magneto-deformation of chain-like helical structures in an elastomer surrounding. The presented results show a remarkable agreement of both modeling approaches and help to provide an improved understanding of the interactions in magneto-active elastomers with chain-like microstructures

A nonlinear theory for fibre-reinforced magneto-elastic rods

We derive a model for the finite motion of a magneto-elastic rod reinforced with isotropic (spherical) or anisotropic (ellipsoidal) inclusions. The particles are assumed weakly and uniformly magnetised, rigid and firmly embedded into the elastomeric matrix. We deduce closed form expressions of the quasi-static motion of the rod in terms of the external magnetic field and of the body forces. The dependences of the motion on the shape of the inclusions, their orientation, their anisotropic magnetic properties and the Young modulus of the matrix are analysed and discussed. Two case studies are presented in which the rod is used as an actuator suspended in a cantilever configuration. This work can foster new applications in the field of soft-actuators

A review on magneto-mechanical characterizations of magnetorheological elastomers

Magnetorheological elastomers (MREs) are a class of recently emerged smart materials whose moduli are largely influenced when exposed to an external magnetic field. The MREs are particulate composites, where micro-sized magnetic particles are dispersed inside a non-magnetic polymeric matrix. These elastomers are known for changing their mechanical and rheological properties in the presence of a magnetic field. This change in properties is widely known as the magnetorheological (MR) effect. The MR effect depends on a number of factors such as type of matrix materials, type, concentration and distribution of magnetic particles, use of additives, working modes, and magnetic field strength. The investigation of MREs’ mechanical properties in both off-field and on-field (i.e. the absence and presence of a magnetic field) is crucial to deploy them in real engineering applications. The common magneto-mechanical characterization experiments of MREs include static and dynamic compression, tensile, and shear tests in both off-field and on-field. This review article aims to provide a comprehensive overview of the magneto-mechanical characterizations of MREs along with brief coverage of the MRE materials and their fabrication methods

Field-Induced Transversely Isotropic Shear Response of Ellipsoidal Magnetoactive Elastomers

Magnetoactive elastomers (MAEs) claim a vital place in the class of field-controllable materials due to their tunable stiffness and the ability to change their macroscopic shape in the presence of an external magnetic field. In the present work, three principal geometries of shear deformation were investigated with respect to the applied magnetic field. The physical model that considers dipole-dipole interactions between magnetized particles was used to study the stress-strain behavior of ellipsoidal MAEs. The magneto-rheological effect for different shapes of the MAE sample ranging from disc-like (highly oblate) to rod-like (highly prolate) samples was investigated along and transverse to the field direction. The rotation of the MAE during the shear deformation leads to a non-symmetric Cauchy stress tensor due to a field-induced magnetic torque. We show that the external magnetic field induces a mechanical anisotropy along the field direction by determining the distinct magneto-mechanical behavior of MAEs with respect to the orientation of the magnetic field to shear deformation

Physically motivated modelling of magnetoactive elastomers

Magnetoactive elastomers (MAEs) are polymer composites containing magnetically soft or hard particles incorporated into an elastomer matrix during the crosslinking procedure. In the presence of a magnetic field, the induced magnetic interactions and the corresponding particle rearrangements significantly alter the mechanical properties in dependence on the initial particle distribution and sample shape. In addition, applying magnetic fields also changes the macroscopic shape of an MAE. This thesis investigates the magneto-mechanical coupled behaviour of MAEs by means of analytical and numerical methods. The effects of particle distribution and sample shape have been studied with the help of a physically motivated model of MAEs that considers dipole-dipole interactions between magnetizable particles. The presence of a magnetic field leads to a mechanical anisotropy in MAEs with isotropic particle distribution, and the induced anisotropy is directed along the orientation of the field. Thus, MAEs exhibit direction-dependent mechanical properties with distinct elastic moduli along and perpendicular to the field direction when the MAE sample is subjected to uniaxial deformation. A good agreement is reported between the physically motivated approach and conventional transversely isotropic material models. Furthermore, we investigate the important interplay between the particle distribution and the sample shape of MAEs, where a simple analytical expression is derived based on geometrical arguments to describe the particle distribution inside MAEs. We show that the enhancement of elastic moduli arises not only from the induced dipole-dipole interactions but also considerably from the change in the particle microstructure. Moreover, the magneto-mechanical behaviour of isotropic MAEs under shear deformations is studied. Three principal geometries of shear deformation are investigated with respect to the orientation of the applied magnetic field. We show that the Cauchy stress tensor of MAEs is not always symmetric due to the generation of a magnetic torque acting on an anisometric MAE sample under shear loadings. The theoretical study of magneto-mechanical behaviour of MAEs confirms that the effect of sample shape is quite significant and cannot be neglected. On the other hand, the initial particle distribution and presumed rearrangements due to the magnetic field additionally influence the material response of MAEs. Finally, the physically motivated model of MAEs could be transformed into an invariants-based model enabling its implementation in commercial finite element software. Therefore, we have uncovered a new pathway to model MAEs based on dipole-dipole interactions, leading to a constitutive relation analogous to the macro-scale continuum approach and revealing a synergy between both modelling strategies

Magnetostriction in elastomers with mixtures of magnetically hard and soft microparticles: effects of non-linear magnetization and matrix rigidity

In this contribution a magnetoactive elastomer (MAE) of mixed content, i.e., a polymer matrix filled with a mixture of magnetically soft and magnetically hard spherical particles, is considered. The object we focus at is an elementary unit of this composite, for which we take a set consisting of a permanent spherical micromagnet surrounded by an elastomer layer filled with magnetically soft microparticles. We present a comparative treatment of this unit from two essentially different viewpoints. The first one is a coarse-grained molecular dynamics simulation model, which presents the composite as a bead-spring assembly and is able to deliver information of all the microstructural changes of the assembly. The second approach is entirely based on the continuum magnetomechanical description of the system, whose direct yield is the macroscopic field-induced response of the MAE to external field, as this model ignores all the microstructural details of the magnetization process. We find that, differing in certain details, both frameworks are coherent in predicting that a unit comprising magnetically soft and hard particles may display a non-trivial re-entrant (prolate/oblate/prolate) axial deformation under variation of the applied field strength. The flexibility of the proposed combination of the two complementary frameworks enables us to look deeper into the manifestation of the magnetic response: with respect to the magnetically soft particles, we compare the linear regime of magnetization to that with saturation, which we describe by the Fr\"{o}hlich-Kennelly approximation; with respect to the polymer matrix, we analyze the dependence of the re-rentrant deformation on its rigidity

A microstructural-based approach to model magneto-viscoelastic materials at finite strains

Magneto-active polymers (MAPs) consist of a polymeric matrix filled with magnetisable particles. MAPsmay change their mechanical properties (i.e., stiffness) and/or mechanical deformation upon the applica-tion of an external magnetic stimulus. Mechanical responses of MAPs can be understood as the combinedcontributions of both polymeric matrix and magnetic particles. Moreover, the magnetic response isdefined by the interaction between magnetisable particles and the external field. Common approachesto model MAPs are based on phenomenological continuum models, which are able to predict theirmagneto-mechanical behaviour but sometimes failed to illustrate specific features of the underlying phy-sics. To better understand the magneto-mechanical responses of MAPs and guide their design and man-ufacturing processes, this contribution presents a novel continuum constitutive model originated from amicrostructural basis. The model is formulated within a finite deformation framework and accounts forviscous (rate) dependences and magneto-mechanical coupling. After the formulations, the model is cal-ibrated with a set of experimental data. The model is validated with a wide range of experimental datathat show its predictability. Such a microstructurally-motivated finite strain model will help in designingMAPs with complex three-dimensional microstructures.The authors acknowledge the financial support of the mobility internship for researchers of Carlos III University of Madrid (Spain) (“Programa propio de investigacion - Convocatoria 2020 movilidada”) that facilitates a research visit of the first author to Zienkiewicz Centre for Computational Engineering (ZCCE) at Swansea University, UK. DGG acknowledges support from Programa de Apoyo a la Realizacion de Proyectos Interdiscisplinares de I+D para Jovenes Investigadores de la Universidad Carlos III de Madrid and Comunidad de Madrid (project: BIOMASKIN), support from the Talent Attraction grant (CM 2018-2018-T2/IND-9992) from the Comunidad de Madrid, and support from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 947723). MH acknowledges the funding through an EPSRC Impact Acceleration Award (2020-2021)

Effects of soft and hard magnetic particles on the mechanical performance of ultra-soft magnetorheological elastomers

Magnetorheological elastomers (MREs) mechanically respond to external magnetic stimuli by changing their mechanical properties and/or changing their shape. Recent studies have shown the great potential of MREs when manufactured with an extremely soft matrix and soft-magnetic particles. Under the application of an external magnetic field, such MREs present significant mechanical stiffening, and when the magnetic field is off, they show a softer response, being these alternative states fully reversible. Although softmagnetic particles are suitable for their high magnetic susceptibility, they require the magnetic actuation to remain constant in order to achieve the magneto-mechanical stiffening. Here, we present an alternative solution based on hard-magnetic MREs to provide stiffening responses that can be sustained along time without the need of keeping the external magnetic field on. To this end, we manufacture novel extremely soft hardmagnetic MREs (stiffness in the order of 1 kPa) and characterise them under magneto-mechanical shear and confined magnetic expansion deformation modes, providing a comparison framework with the soft-magnetic counterparts. The extremely soft nature of the matrix allows for easily activating the magneto-mechanical couplings under external magnetic actuation. In this regard, we provide a novel approach by setting the magnetic actuation below the fully magnetic saturating field. In addition, free deformation tests provide hints on the microstructural transmission of torques from the hard-magnetic particles to the viscoelastic carrier matrix, resulting in macroscopic geometrical effects and complex functional morphological changes. Keywords: Magnetorheological elastomers (MREs), Magneto-mechanics, Experimental characterisation, Hard-magnetics MRE, Multifunctional materials, Magnetic propertiesThe authors acknowledge support from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No. 947723, project: 4D-BIOMAP). The authors acknowledge support from MCIN/ AEI /10.13039/501100011033 under Grant number PID2020- 117894GA-I00. MAMM acknowledges support from the Ministerio de Ciencia, Innovacion y Universidades, Spain (FPU19/03874) and DGG acknowledges support from the Talent Attraction grant (CM 2018 - 2018-T2/IND-9992) from the Comunidad de Madrid. MH acknowledges the funding through an EPSRC Impact Acceleration Award (EP/R511614/1)