3D Printable Self-Sensing Magnetorheological Elastomer

Magnetorheological elastomers (MREs) are a category of smart materials composed of a magnetic powder dispersed in an elastomeric matrix. They are characterized by the ability to change their mechanical properties when an external magnetic ﬁeld is applied, called magnetorheological (MR) eﬀect. When a conductive ﬁller is added to a magnetorheological elastomer, the resulting hybrid ﬁller composite showcases both MR and piezoresistive eﬀects. For such a reason, these composites are referred to as self-sensing magnetorheological elastomers. In this case, the synthesized self-sensing magnetorheological elastomers are based on styrene-based thermoplastic elastomers (TPS), carbonyl iron particles (CIP), and carbon black (CB). The hybrid ﬁller concept using various coated CIP and constant CB content showed that above 25 vol.% CIP the resistivity increased rapidly. This work proposes the ﬁrst case of a 3D printable self-sensing magnetorheological elastomer and cyclic mechanical compression and tensile mode analysis at high deformation (up to 20% and 10%, respectively). The results showcase a magnetoresistive change of up to 68% and a piezoresistive change of up to 42% and 98% in compression and tension, respectively. In addition, the magnetostriction of the self-sensing samples has been characterized to be 3.6% and 5.6% in the case of CIP 15 and 30 vol.%, respectively.


Introduction
Magnetorheological elastomers (MREs) are a category of smart materials, [1] and are characterized by an increase in stiffness as a result of an externally applied magnetic field. [2]Such a phenomenon is called magnetorheological (MR) effect. [3,4]All MREs DOI: 10.1002/mame.202300294 are composed of magnetic particles suspended in a non-magnetic elastomeric matrix.Common elastomers that are used as a matrix material for the development of MREs are usually RTV silicones, natural rubbers, [5] and thermoplastic elastomers (TPE) like thermoplastic polyurethane (TPU), [6] and styrene-based TPE (TPS). [7,8]Typically, carbonyl iron particles (CIP) [9] are used as a soft magnetic filler, and the composites can be divided into isotropic and anisotropic MREs: anisotropic MREs are obtained by curing the elastomer within a magnetic field, [10] whereas isotropic MREs can be obtained by curing the material without a magnetic field.Moreover, the concentration, particle size, and particle coating of the magnetic filler strongly affect the MR effect. [11,12]Silicone and TPE-based MRE structures have been fabricated by additive manufacturing like direct ink writing and fused deposition modeling (FDM). [13,14]REs' most common application is in the development of dampers for vibration absorption [15,16] thanks to their real-time tunable mechanical properties.In particular, their ability to act as a low-pass mechanical filter while being able to change the cut-off frequency [17] and the viscous energy losses [18] as a function of the magnetic field makes them exceptionally suitable for highly dynamic environments.In recent years, however, MREs' performance under large deformations [19] has captured the attention of the soft robotics community [20] and they have been utilized as actuators for a wide range of tasks: shape-morphing, [21] locomotion, [22,23] grasping, [24] and tunable mechanical filtering. [25,26]REs can further showcase sensing behavior and serve as force and strain sensors, especially when a second conductive filler is used. [27,28]This hybrid filler concept results in an MRE with combined magnetorheological and piezoresistive effects, which lead to a sensor that can sense both the change in the magnetic field or mechanical load based on the change in electrical resistance, called magnetoresistors. [29,30]Once the externally applied deformation is known, the combination of magnetic and electrical response can be used to inform about the MRE's viscoelastic properties and can lead to self-sensing composite materials.Commonly used carbon fillers are carbon black (CB), [31,32] carbon nanotubes, [33,34] graphite, [35,36] and graphene. [37,38]However, adding conductive carbon fillers such as CB often enhances their mechanical properties (like Young's modulus), Figure 1.Workflow of the performed manufacturing process and characterization.SEBS, CIP, and CB are mixed through melt mixing according to the desired volume fractions.Further details about the mixing method are provided in Section 4.1.Then, the obtained materials are extruded as fibers and manually cut into pellets.Such pellets are fed into a pellet extruder to 3D print samples, and those samples are used to perform mechanical and magnetoresistive tests.
affecting the MR effect, even though these fillers themselves are diamagnetic. [39,40]In turn, this results in a lower MR effect, both in the case of shear [41] and compression [42] tests because of a higher baseline stiffness.
CIP itself showcases a reinforcement effect of TPS composite which is further increased if a small volume fraction of carbonbased nanomaterials is added. [43]By adding carbon-based nanomaterials, the mechanical properties, magnetic sensitivity, and energy generations could be varied in a wide range, depending on the relative volume fraction of the different fillers. [44]Overall, TPS-based hybrid composites' properties are highly tunable and make such MREs a good candidate for a wide plethora of applications.
Self-sensing MREs have been studied as online tunable vibration dampers. [45,46]Such composites provide a real-time feedback signal and closed-loop control algorithms can be used to adjust the MREs' stiffness by tailoring an applied magnetic field, as shown by Komatsuzaki et al. [47] However, all cases of self-sensing MRE reported in the literature are obtained through casting rather than 3D printing.Moreover, the magnetic field was generated using electromagnets: when active, electromagnets can heat up significantly, thus inducing temperature-dependent changes in the material properties, whose role cannot be analyzed independently from the MR effect.
In this work, we propose a 3D printable self-sensing MRE, composed of TPS, SiO 2 -coated CIP, and CB.The proposed composite is mixed, extruded, 3D printed, and characterized by magneto-mechanical methods.In order to avoid any temperature-dependent behavior, the external magnetic field is applied using permanent magnets.Unlike previously reported research studies, [45,46] we propose the analysis of the self-sensing MREs in combined cyclic compression and tension mechanical tests, up to 20% strain.For the first time in scientific literature, we propose a self-sensing MRE printable with a FDM single screw extruder-based print head.Moreover, we provide a method to investigate self-sensing behavior both with mechanical compression and tensile load at higher deformation.As an outcome, we investigated the effect of CIP vol.% both in the magnetostriction and resistivity of the produced 3D printed samples and further studied the MR effect and the Hall effect.In summary, we study different effects of a varying magnetic field and mechanical load, reaching a magnetoresistive change of up to 68% and a piezoresistive change of up to 42% and 98% in compression and tension, respectively.

Results and Discussion
To achieve self-sensing magnetorheological elastomers (MREs), in this work, we have used a very soft TPS, based on SEBS, with Shore hardness 75 VLRH, and ferromagnetic and conductive fillers, namely carbonyl iron particles (CIP) and carbon black (CB), respectively (see Section 4).The main aims of this work are to showcase the first reported case of 3D-printed self-sensing MRE at high strain and to characterize the magnetostrictive, magnetorheological (MR), piezoresistive, and magnetoresistive effects.Figure 1 illustrates the workflow from the materials' mixing to the mechanical and magnetoresistive tests, performed on 3D-printed testing samples.

Fibers' Electrical Resistivity
To investigate the electrical resistivity of the self-sensing MREs, the resistance of all extruded fibers has been assessed in the absence and presence of a magnetic field 302 mT, as shown in Figure 2. Commercial CIP are made by the chemical reaction of carbon monoxide with iron in the presence of a catalyst. [48]The resulting product is a fine conductive iron powder with a diameter of only a few micrometers.Like normal iron, CIP are conductive.However, non-conductive CIPs are commercially available and those are coated with a thin silicon oxide layer. [8]As a first approach, non-coated and coated CIP were mixed with SEBS ma-trix in four different volume fractions, namely 15, 30, 45, and 60 vol.%.As shown in Figure 2A, only with the highest concentration of uncoated CIP a resistivity of 1.3 Ωm could be observed in the absence of a magnetic field.However, due to the high filler content, the fibers got brittle and therefore the composite would not be practical for real-world applications, such as soft robotics.
As expected even at high concentrations of coated CIP the resistivity of the MRE exceeded 10 3 Ωm, which is above typical values for conductive materials.Tagliabue et al. [8] investigated the static and dynamic magnetorheological properties of uncoated and coated CIPs and they observed that the composite based on TP and coated CIP resulted in a significantly higher MR effect.Therefore, we selected the coated CIP for further investigation.Based on previous studies, [49,50] SEBS-based TPS with 15 vol.%CB was used to avoid a yield point, which indicates plastic deformation, and to ensure a low initial resistivity.In this study, a resistivity of 10 −3 Ωm could be achieved by adding 15 vol.% of CB into TPS (see Figure 2A).As expected, the sample containing only CB as a filler showcases no difference in resistivity when measured in the absence and presence of the magnetic field.
Based on Achur et al., [51] polymers with carbon fillers show diamagnetic properties, which means that they are weakly repelled by a magnetic field, due to the induced magnetic moment that is opposite in direction to the applied field.However, in the absence of CIP filler the self-sensing MRE results in a composite whose resistivity was unaffected by the applied magnetic field due to the weak diamagnetic response of carbon material in a static magnetic field.Several volume fractions of coated CIP have been tested, from 10 to 35 vol.%, every 5%, using a constant CB content of 15 vol.%.The results of the resistive measurements are reported in Figure 2A,B.Specifically, Figure 2B showcases the effect of the CIP concentration on the resistivity maintaining a 15% CB volume fraction in the absence and presence of a magnetic field.In the presence of an external magnetic field, the resistivity drops significantly for all compositions containing both fillers.Moreover, the more CIP is added, the greater the magnetic-induced resistivity decrease is measured.
By adding more than 25 vol.%CIP in addition to the 15 vol.%CB, the resistivity of the resulting MRE starts to increase significantly.However, because of the magnetostriction, a decrease in electrical resistivity is still present.It can be assumed that above a certain concentration (e.g., threshold value), the CIP network tends to disturb the CB network and isolate CB particles, increasing the resistivity.This hypothesis is supported by the fact that the mean particle size of the coated CIP is 4.7 μm, [8] and the particle size of the CB is 0.5 μm, [52] therefore CIP is characterized by a diameter about ten times bigger than CB.Based on Mc Geary, it can be assumed that the CB particles are small enough to fill the interstices of the coarse CIP particles when mixing 30 vol.% fine and 70 vol.%coarse particles. [53]Considering the 15 vol.%CB present in our composites, we can observe how above a threshold of 25 vol.%, the CIP starts to effectively shield the CB, increasing the resistivity.
Finally, Figure 2C-I illustrates the side and cross-section views of the obtained self-sensing MREs fibers.Additionally, Figure 2L-O shows those same views for the MREs containing only CIP filler.Increasing the concentration of CIP results in a brighter shade of grey, whilst adding CB tends to drift the resulting color toward black.Moreover, the surface of fibers with a single filler appears much rougher, particularly visible in CIP 30%, whilst hybrid filler produces a smoother surface.The observed clustering in MREs without CB can be caused by the poor interaction between filler and matrix, caused by the low surface area of CIP.Thus, thanks to its large surface area, CB is often used as an additive to limit particle clusters and enhance the composites' mechanical properties. [32]All in all, fibers with hybrid filler content are shown to be quite homogeneous, without visible particle clusters or network separations, with the exception of a few superficial stripes observable in CB 15% CIP 20% and CB 15% CIP 25%.The cross-section views confirm that those rare imperfections are strictly limited to the surface, probably due to the high shear forces at the surface of the capillary die, used for the fabrication of the fibers.

3D Printing
Next, we aim to showcase how the proposed self-sensing MREs can be 3D printed, so to achieve greater design freedom, avoiding the geometrical limitations of other thermoplastic manufacturing techniques, such as injection molding and extrusion.Among the several hybrid filler composites analyzed in Section 2.1, two self-sensing MREs have been selected for 3D printing: CB 15 vol.%CIP 15 vol.% and CB 15 vol.%CIP 30 vol.%.In addition, the TPS with 15 vol.%, and all the TPS with coated CIP have been printed as reference samples.As shown in Figure 3K, the Shore hardness of all samples is too low for using a filament extruder 3D printing head, and therefore a pellet extruder is used in this study.Fibers are cut into pellets and fed into the pellet extruder to print disks for further analysis and geometrically more complex models for characterizing the printing quality.Further details about the printing process and the printed structures are provided in Section 4. Figure 3 showcases the results.
Thermoplastic elastomers result in a high die swell that will affect the resolution of the printed part, therefore the logos of Cambridge University and Empa were printed with the two selected self-sensing MREs (Figure 3A,B).By increasing the hybrid filler content it can be observed that the resolution gets worst.To simultaneously achieve continuous extrusion and avoid overextrusion, the extrusion multiplier has to be tuned for each composition.The extrusion multiplier is a proportionality coefficient for the rotation speed of the screw in the extruder head and it is correlated to the feed rate of the screw. [54]Therefore, the lowest value able to achieve continuous extrusion has been empirically selected for each composition.Figure 3J shows the extrusion value selected for every composition.Moreover, Figure 3K shows the measured Shore hardness of the printed disks: it can be seen how compositions that are characterized by higher Shore hardness need a higher extrusion multiplier to achieve extrusion.By the optical microscopy images in Figure 3, it can be assumed that both the top and side views of most of the printed disks are acceptable.However, when increasing the CIP above 30 vol.% (Figure 3G), optical microscopy analysis revealed that further adjustment of the extrusion multiplier is needed to avoid printing failures at the edge of the printed samples.By increasing the filler content to 60 vol.%CIP, also the quality of the top layer is negatively affected.In this study, further adjustment of the multiplier was not investigated to a further extent because of the shielding effect of the CIP network, as discussed previously.

Cyclic Mechanical Compression and Tension Characterization
Cyclic mechanical tests under compression and tension were performed for five different 3D printed samples, namely, CB 15 vol.%CIP 15 vol.%,CB 15 vol.%CIP 30 vol.%, CB 15 vol.%,CIP 15 vol.%,CIP 30 vol.%.Among them, the first two are the selfsensing MREs we intend to showcase in this work, and the latter three are used as control samples.
Figure 4A illustrates the piezoresistive effect for all tested compositions.The sensitivity of the samples as piezoresistive sen-sors has been evaluated as the difference in resistance between the maximum and minimum strain hold times of the ninth cycle (see Figure 4B,C).The ninth cycle has been selected to minimize the effect of the stress-softening behavior of elastomers, called the Mullins effect, in good agreement with results reported in the literature. [55]Similarly, the MR effect is characterized by As shown in Figure 4A, the main result achieved by this test is not only that the proposed self-sensing MREs showcase a large piezoresistive effect, up to 42% in compression and 98% in tension, but also that the presence of the magnetic field increases the MREs' sensitivity for both CB 15% CIP 15% and CB 15% CIP 30%.In fact, both in compression and in tension the self-sensing MREs result in a greater relative piezoresistive effect when the magnetic field is present.Applying an external magnetic field results in a magnetization in the MREs, which causes an attractive force between the CIP, resulting in a contraction of the composite known as magnetostriction.This phenomenon is superimposed onto the deformation imposed by the testing machine, changing the piezoresistive behavior of the samples.As a result, all selfsensing MREs showcase a greater piezoresistive sensitivity when operating with the magnetic field, rather than without.In particular, CB 15% CIP 30% has greater sensitivity both with and without the magnetic field.Whilst the latter is easily explainable by a greater resistivity drop due to the presence of the magnetic field (see Figure 2B), the former must be caused by a combination of a higher amount of overall filler leading to a stiffer material (see Figure 4D-I) and a higher baseline resistivity of CB 15% CIP 30% (see Figure 2B).Figure 4B,C illustrate examples of singular tests, 10% tension of CB 15% CIP 30% and 10% compression of CB 15% CIP 15%, respectively.Both of them are characterized by a slight drift of the resistance signal mostly present in the first few cycles and visible relaxation both at the minimum and maximum stress point.Tensile tests also show peculiar peaks at the beginning and end of the maximum strain hold time.Such an effect has been reported for pure piezoresistive sensors under tensile testing when low conductive filler content is used. [56,57]imilarly, Figure 4K summarizes the MR effect observed in all samples, whereas Figure 4J reports the instantaneous stiffness of all CIP composites in the absence of a magnetic field.The stiffening of the composites is measured as the instantaneous stiffness increase due to the presence of the magnetic field.The rising edge of the nineth cycle is also reported for every composite (see Figure 4D-I for samples with and without CB, respectively).First, results from the single filler CIP composites are used to characterize the relationship between CIP vol.%, imposed deformation, and observed MR effect.Concerning the baseline stiffness reported in Figure 4J, it can be noticed how the CIP concentration strongly affects the sample stiffness without additional CB filler.Moreover, both compositions behave much stiffer under compression than under tension.Under compression tests, Figure 4K shows that increasing the deformation (e.g., from 10% to 20%) results in a higher MR effect.It is well known that for compression tests the MR effect is low at low deformations, and it first increases and then decreases as strain increases. [55]owever, Schubert et al. observed that above 10-15% strain the MR effect increases again. [58]At higher compression ranges, the particle-particle distance is reduced, thus making their magnetic interaction stronger in the presence of a magnetic field, resulting in a higher MR effect.Moreover, increasing the CIP vol.% leads to a higher MR effect both in the case of 10% and 20% compression tests.This can be explained by the higher magnetization of the sample due to the higher content of CIP, as it has been shown in literature. [8]In the case of tension tests, no significant change in the MR effect has been observed by increasing the CIP concentration.As already reported in the literature, isotropic MREs tend to show a similar MR effect at 10%, 20%, and 30% filler vol.% when measured using tensile testing. [58]In tension tests, the particles are pulled further from each other, leading to a decrease in the MR effect. [9]Hernández et al. reported an effect of particle weight fraction on MR effect, where the highest MR effect was achieved at 63 wt.%.However, the deformation range used in their work is much lower. [59]The 10% deformation used in our work can be expected to be a high enough deformation to explain the insignificance of particle concentration on the MR effect in tensile tests.Overall, pure CIP composites showcase a compression modulus between 1.5 and 2 MPa and achieve an MR effect up to 84%.Dargahi et al. [60] showcase significantly higher MRE effects, up to 295%, at the same volume percentage of CIP filler.The higher MR effect in their work can be explained by the low shear modulus of 37.7 kPa they achieved using a different matrix material, which makes the resulting composite not suitable for 3D printing.It is also important to highlight that the testing conditions in terms of applied mechanical load and magnetic field are different from the ones proposed in our work, potentially further contributing to the difference in results.When computing the single cycle dissipated energy (see Figure 4L,M), it can be seen how single filler CIP composites dissipate large amounts of energy at high deformations (e.g., 20% compression).Such a characteristic, combined with a 40% reduction of their dampening properties as a result of the MR effect, makes them suitable materials for tunable vibration damping, as already demonstrated in the literature. [17,18]Moving on to the hybrid self-sensing MREs containing both CIP and CB, they differ noticeably from their single filler counterparts.First, their instantaneous stiffness at low deformations (e.g., 10%) remains stable while increasing the CIP concentration.Only at 20% compression, a jump in instantaneous stiffness by increasing the CIP concentration can be observed.In contrast to pure CIP samples, the MR Effect decreases by increasing the compression deformation.The CB has diamagnetic behavior and we can assume that the magnetic field distribution inside the samples will change.However, further investigation needs to be done to better understand this phenomenon.Under compression, the single filler composite CB 15% appears to be even stiffer than the hybrid filler composited in the absence of a magnetic field (see Figure 4D,E).Such a behavior can be caused by the characteristic shape of CB particles, with a very high surface-to-volume ratio and rough surface.Because of such characteristics, they develop high shear forces among each other when compressed, resulting in high stiffness of the composites.However, adding CIP shields the CB particles from each other.Such shielding is not only electrical, as seen in Figure 2, but also mechanical, and results in a decrease in stiffness under compression.However, by increasing the CIP content the MR effect observed in the compression tests decreases.This can be explained by the fact that, at 15 vol.%CB and 30 vol.% CIP, smaller CB particles fill the interstices of the coarse CIP. [53]This not only allows the diamagnetic CB to shield the CIP, but it also prevents compression, resulting in a significantly stiffer behavior without the magnet, thus in a lower MR effect, as shown in the literature. [42,61]Nevertheless, under tension, the carbon filler in the interstices of the coarse CIP does not block the deformation, and therefore, a higher CIP content results in a higher magnetization inside the magnetoresistive material.This leads to a higher magnetic force between the particles, which has to be overcome during tension experiments in the presence of the magnet.
Moreover, similarly to what was observed for Shore hardness in Figure 3K, the presence of CB reduces the difference in stiffness between 15 and 30 vol.% CIP (see Figure 4F), allowing the higher magnetization to play a crucial role in stiffening the composite.As a result, a slight increase in the MR effect could be observed under tension as CIP content increases.Overall, the highest MR effect of 236% could be achieved under 10% compression on the printed sample 15 vol.%CIP and 15 vol.%CB.Other stateof-the-art works on self-sensing MREs showcase an MR effect between 20% and 33% when working with carbon nanotubes, [61] and up to 49% when working with CB. [40] This last result is comparable to the MR effect observed in the 20% compression test (see Figure 4K), but is significantly lower than the MR effect observed in our hybrid MREs under 10% compression.However, such works characterize the MR effect using different materials, both as elastomeric matrix and fillers, and different experimental tests when compared to this paper.Such differences can lead to large variations in the estimation of the MR effect, as reported by Vatandoost et al. [62] Figure 4L illustrates how at large deformations, hybrid selfsensing MREs are not able to dissipate as much energy as their single filler CIP counterparts.However, the MR-induced stiffening causes them to increase their damping properties (see Figure 4M), rather than decrease them, unlike what has been observed in single filler MREs.Moreover, in the case of lower deformations (e.g., 10%), they are characterized by similar performance to the single filler CIP composites, while showcasing a greater increase in dissipated energy as a result of the presence of the magnetic field, especially in the case of 10% compression.
Finally, 20% tension cyclic tests have been attempted on the hybrid self-sensing MREs, resulting in delamination and mechanical failure of the 3D printed samples.The complete 20% tension cyclic tests are reported in the Supporting Information (see Figure S8, Supporting Information).
To further study how the mechanical and electrical properties are affected by particles' distribution, Figure 5 shows SEM images taken from the 3D printed samples, illustrating the distribution of CIP and CB both in the self-sensing MREs and the single filler composites.
It can be seen that in 15 vol.%CB and 15 vol.%CIP (Figure 5A), the CIP are isolated from each other and fully surrounded by CB, with several portions on the images in which there are no CIP, but only CB.This is due to the difference in size between the particles and their equal volume concentration.Conversely, in 15 vol.%CB and 30 vol.% CIP (Figure 5B), the CIP volume concentration is doubled, resulting in a much lower distance between magnetic particles and fewer areas populated solely by CB.As Mcgeary [53] reported, in the 15 vol.%CB and 30 vol.% CIP, the CB is able to fully fill the interstices between the coarser CIP.As previously discussed, this produces a stiffer material under compression, when compared with the single filler CIP composite, but has a limited effect under tension.At lower CIP vol.%, the higher relative number of CB particles creates CB clusters, responsible for the mechanical and electrical behavior aforementioned when describing Figure 4.For reference, Figure 5C-D show how CB and CIP are distributed within the matrix when they are used as single fillers, in the case of 15 vol.%CB and 0 vol.%CIP, 0 vol.%CB and 15 vol.%CIP, 0 vol.%CB and 30 vol.% CIP, respectively.

Magnetoresistive Characterization of the Printed Disks
This analysis aims to expand the results shown in Figure 2.However, instead of fibers, 3D-printed disks were used to investigate the effect of different external magnetic fields on the electrical conductivity along the thickness of the samples (Figure 6C-H).For the study, printed parts based on TPS with CB 15 vol.%,CB 15 vol.%CIP 15 vol.%, and CB 15 vol.%CIP 30 vol.% have been selected.The applied magnetic field was adjusted by the size and numbers of the magnets and the results are shown in Figure 6.
The absolute resistances at 0 mT highlight that adding a small volume fraction of CIP (15 vol.%) decreases the resistance and at a higher filler content (30 vol.%) the resistance ends up increasing it over the starting values without CIP filler.This result supports the findings in Figure 2, and confirms that CB 15 vol.%CIP 15 vol.% is beneath the threshold where the CIP content increases the resistivity of the self-sensing MREs significantly, and CB 15 vol.%CIP 30 vol.% is above it.Overall, both CB 15 vol.%CIP 15 vol.% and CB 15 vol.%CIP 30 vol.% showcase a linear decrease of the samples' resistance as a function of the magnetic field until 496 mT, followed by an even steeper drop.We assume that such a drop can be explained by the mechanical properties of the elastomeric matrix and the reconfiguration of the conductive CB network.On one hand, as the magnetic pulling force increases, the magnitude of the resulting magnetostriction depends on the mechanical characteristics of the matrix itself: the nonlinear properties of the stress-strain characteristic of elastomers (e.g., hyperelastic behavior) affect the magnetoresistive sensitivity of the composite materials.On the other hand, as the magnetostriction increases, the CB network is compressed, and jamming of the CB particles occurs, potentially resulting in nonlinear resistivity drops, thus increasing the composite sensitivity at high magnetic fields (e.g., 496 mT).
The slope of the self-sensing MRE with 30 vol.% CIP is steeper because the magnetic interaction with the magnetic field will be stronger, and based on literature a higher magnetization can be assumed. [55]The relative resistance is a much clearer indication of the self-sensing properties of the proposed MREs.CB 15% CIP 30% showcases a larger relative resistance drop for all tested values, up to 68% at 544 mT, and has higher self-sensing capabilities when compared with 15% CIP 15%.As expected, CB 15% does not show any magnetoresistive effect because of the low diamagnetic behavior of CB.Taking into account that the two MRE disks display substantial magnetostriction, that causes a piezoresistive sensor signal, we computed the macroscopic deformation, see Figure 6E-G.As shown by Mondal et al., [55] in the presence of an unpaired permanent magnet configuration, a magnetic force between the magnetic particles is still present.Therefore, the macroscopic geometry of the self-sensing MRE disks based on hybrid filler CIP and CB is affected by applying the magnetic field.By compressing the disks the distance between the top and bottom electrodes gets shorter and the resistance of the self-sensing MREs decreases.To further investigate the role of magnetostriction, the deformation induced by the presence of a 302 mT magnetic field has been measured as shown in Figure 6F-H.Then, under the hypothesis of the magnetostriction being the sole cause of resistance drop, the piezoresistive and deformation data (see Figure 4A,D-F, respectively) have been used to compute the required magnetostrictive deformation needed to produce the resistance drop observed in Figure 6B.Results show that the measured macroscopic deformation is significantly smaller than the one estimated by the model, both using 20% and 10% compression data.As a conclusion, we can infer that the total observed deformation cannot be the sole cause of the observed magnetoresistivity, and we hypothesize that a partial relative rearrangement of the CB and CIP networks contributes to the high magnetoresistivity of the self-sensing MREs.We believe that the same characteristic CIP local clustering observed in single filler MREs [63] happens in self-sensing MREs, promoting a rearrangement of the CB network, thus reducing the resistance of the composite.

Hall Effect
The Hall effect of the two selected self-sensing MREs, as well as three single filler composites, has been investigated with and without the magnetic field and is presented in Figure 7.To do so, a 12 V input voltage V 0 and a 302 mT magnetic field H have been applied to samples, and the Hall voltage V hall has been measured.For the TPS samples with 15 and 30 vol.% CIP no Hall effect could be observed, because of the insulating SiO 2 coating on top of the carbonyl iron particles.Conversely, a measurable Hall effect has been observed in all conductive samples containing CB. Increasing the volume fraction of CIP results in an increase of the Hall effect, with the self-sensing MRE disk with 15 vol.%CB and 30 vol.% CIP showing the highest Hall effect.This can be explained by the higher magnetization of the self-sensing MRE with higher CIP content causing the greater relative resistance drop (see Figure 6B)).

Conclusion
In this paper, we propose the first reported case of 3D printable self-sensing magnetorheological material (MRE).MREs are materials that change their mechanical properties (e.g., stiffness) when an external magnetic field is applied.If a conductive filler is added to a standard MRE, the resulting material showcases a magnetoresistive effect.The material hereby showcased, consisting of SEBS-based TPS as the elastomeric matrix, and CIP and CB as the magnetic and conductive filler, respectively, is the first reported case of FDM of self-sensing MREs using a single screwbased printing head.
Starting from a baseline of a 15% CB, we investigated increasing volume fractions of CIP and how they would affect the electrical resistivity and the magnetostrictive and magnetoresistive effect.Noticeably, increasing the CIP volume fraction decreases the resistivity of the hybrid composite up until a given threshold, between 25% and 30% volume of CIP.This phenomenon is caused by the relative particle size of CB and CIP.At the threshold value of CIP, CB just fills all the gaps between the coarse CIP.If more CIP is added, the now segmented CB network results in higher electrical resistance.
A pellet printer is used to showcase how the proposed material can be 3D printed, allowing for much larger design freedom with respect to other elastomers' manufacturing techniques.By tuning the extrusion multiplier, composites containing 15 and 30 vol.% CIP have been printed successfully, both with and without 15 vol.%CB.A higher CIP vol.% was not further investigated due to the aforementioned shielding effect observed at high vol.%CIP.
The 3D-printed disks are used to investigate the magnetostrictive, the MR effect, and both piezoresistive and magnetoresistive properties.On one hand, both CB 15 vol.%CIP 15 vol.% and CB 15 vol.%CIP 30 vol.% showcase a great piezoresistive effect, up to 42% and 98% in compression and tension, respectively.On the other, the tests under a 302 mT magnetic field showcase enhanced sensitivity, due to the superimposition of magnetostriction to the externally imposed deformation.When characterizing the magnetoresistive response, both CB 15% CIP 15% and CB 15% CIP 30% showcase a linear resistance decrease as the magnetic field increases, with a steeper final drop above 496 mT.Finally, both the magnetostriction and the Hall effect have been investigated to fully characterize the samples.
Overall, as mentioned previously, this work showcases a 3Dprintable TPS-CIP-CB-based self-sensing MRE and thoroughly investigates its mechanical and electrical properties.By combining the magnetostrictive effect and the MR effect due to the CIP filler with the piezoresistive effect granted by the CB filler, the proposed composites showcase a relative magnetoresistive drop of up to 68%.Moreover, this work analyzes in-depth the effects that different CIP volume fractions have on the magnetostrictive effect, the MR effect, and the piezoresistive effect, both in tension and compression, up to 20% deformation.Additionally, we show how the proposed material can be 3D printed using a pellet printer, reporting the first case in the literature of a 3D-printed self-sensing MRE.However, we acknowledge that a deep understanding of the physical phenomena at the base of the interaction between CIP and CB is still missing and we endorse future work on the characterization of such interaction both at a macro and micro scale.Finally, future work should also include extensive mechanical and magneto-mechanical testing, to further explore the potential, the limitations, and the possible applications of the proposed family of self-sensing MREs.All in all, the developed material can be simultaneously used as a structure, actuator, and sensor and this, on top of the design freedom allowed by 3D printing, paves the way for a multitude of applications.

Experimental Section
For each tested composition, the three desired volume fractions were mixed together and then extruded so as to obtain 1.75 mm diameter fibers.Those fibers were then used to investigate the effect of different volume fractions on the conductivity of the material.Then, a few selected compositions are manually cut into pellets and a single-head pellet printer was used to 3D print standardized cylindrical samples.Based on the obtained quality of the prints, some compositions were tested both in a varying magnetic field and cyclic mechanical loads, whilst recording their resistance with a multimeter.
Materials and Processing-Materials: The SEBS-based TPS used for the elastomeric matrix was a styrene-based tri-block copolymer with Shore hardness 75 VLRH (KRAIBURG TPE GmbH and Co KG, Waldkraiburg, Germany).The carbon black is Ensaco 260G (Imerys, Paris, France).Two commercial carbonyl iron particles (BASF, Ludwigshafen, Germany) were used: the HS type was a CIP without surface treatment and the CC type includes a SiO 2 coating.
Materials and Processing-Mixing: The mixing of the self-sensing MRE was performed using a torque rheometer (HAAKE PolyLab OS, Thermofisher, Durlach, Germany).First, the torque rheometer was heated up to 180 °C.Then, the SEBS was added and a mixing speed of 30 rpm was set.CIP and CB are added after 30 and 60 min, respectively.Finally, the MRE was left to mix for 60 min at 30 rpm and 180 °C.The volume fraction of the individual components changes accordingly to the specific mixture, and the total volume of material inside the mixing rheometer was always 48.3 cm 3 .In this work, it investigated several CIP/CB compositions: 15% CB, 15% CIP, 30% CIP, 45% CIP, 60% CIP, 15% CB 10% CIP, 15% CB 15% CIP, 15% CB 20% CIP, 15% CB 25 % CIP, 15% CB 30% CIP, and 15% CB 35% CIP.All the percentages were given in volume fractions.
Materials and Processing-Extrusion: All the compositions created by mixing were then extruded in the form of a filament with a 1.75 mm diameter, using a capillary rheometer (RH7, Netzsch-Gerätebau, Selb, Germany).First, the MRE was placed inside the capillary rheometer and the machine was heated up to 180 °C.Once such an extrusion temperature was reached, the MRE was extruded at a constant speed of 10 mms −1 .
Materials and Processing-3D Printing: Out of the six different extruded hybrid MRE fibers (see Figure 2C-I), CB 15% CIP 15%, and CB 15% CIP 30% had been selected for 3D printing.On one hand, such a choice allows us to further study one self-sensing MRE below and one above the CIP conductivity threshold.On the other hand, those two MREs could then be compared with their non-conductive MRE counterparts, containing solely CIP 15% and CIP 30% volume fractions, respectively.Moreover, the MRE control sample with CIP 30% had been chosen because it had previously been proven that a CIP volume fraction of 30% corresponds to the highest energy density achievable in MREs. [64]The compositions selected for 3D printing were manually cut into pellets of roughly 3 − 5 mm in length and printed using a single-screw extruder pellet printer (TU-maker Voladora NX+, International Technology 3D Printers S.L., Valencia, Spain).This process was carried out on the following compositions: 15% CB, 15% CIP, 30% CIP, 45% CIP, 60% CIP, 15% CB 15% CIP, and 15% CB 30% CIP.All the percentages were given in volume fractions.The main parameters for the printer were the following: nozzle diameter of 0.6 mm, layer height of 0.2 mm, printing speed of 14 mms −1 , infill of 100%, and the lowest extrusion multiplier that ensures continuous extrusion, for every printed composition.First, all composites had been printed as 20 mm diameter and 3 mm height disks.This particular shape was required in order to perform magnetic and mechanical characterization (e.g., cyclic compression and tension tests).Then, in order to test the 3D printing performance on more complex shapes and geometries, the two selected self-sensing MREs (CB 15% CIP 15% and CB 15% CIP 30%) were used to 3D print custom-drawn (Solidworks2021) logos of 'EMPA' and 'University of Cambridge'.Such a choice allowed u to showcase a wide range of features on two vastly different geometries: one bulkier and more topologically complex, the other more planar but far richer in small and precise details.The Shore hardness A of six different samples for each composition had been measured using a durometer (HBA 100.0,Sauter AG, Basel, Switzerland).

Materials and Processing-Sample Preparation:
The 3D-printed cylindrical samples were used for both the mechanical and magnetoresistive tests.On the basis of the quality of the 3D printed samples, the compositions selected for testing were the following: 15% CB, 15% CIP, 30% CIP, 15% CB 15% CIP, and 15% CB 30% CIP.In the case of conductive samples containing CB, metallic grids were used as electrodes and glued to each flat side of the samples using commercial glue (Pattex Ultra Gel, Henkel, Düsseldorf, Germany).During the tests, the electrical resistance of the sample was recorded using a multimeter (Keithley 2450, Keithley Instruments, Solon, USA), sampling at 10 Hz.The glue was left to cure for 30 min before each test.Further specifications on the selected grid, its composition, and the mechanical properties of the interface are provided in the Figures S6 and S7 (Supporting Information).All the data processing was performed using MatLab 2020b.
Characterization-Fiber's Electrical Resistivity: For each of the extruded compositions, 10 30 mm long sections of the fiber were manually obtained using scissors and a caliper.Then, 20 resistance measurements were performed: each section was measured both in the presence and absence of an external magnetic field.To create such a magnetic field, a cylindrical neodymium magnet with a diameter of 30 mm and a height of 15 mm was used.Using a magnetometer (Extech Instruments, Nashua, New Hampshire, USA) a magnetic field of 302 mT could be observed above the permanent magnet.The magnet was placed so that the fiber rests along the diameter of one of the flat faces, as shown in Figure 2B.Conversely to most studies in literature, permanent magnets had been selected over electromagnets, in order to avoid temperature gradients.When using electromagnets, the Joule effect caused by the current in the coils could heat up the magnet significantly.Because of the proximity of the MRE to the heat source, it was impossible to separate the magneto-induced effect from the temperature-induced effect on the MRE's mechanical and electrical properties.On the other hand, permanent magnets did not generate any heat and therefore represent the best choice to isolate and investigate solely the magneto-induced effect on conductivity.The fibers' electrical resistance had been measured with a digital multimeter with maximum measurable resistance of 200 MΩ (89A, Keysight, Santa Rosa, California, USA), and the fibers' dimensions had been verified using optical microscopy.
Characterization-Optical Microscopy: An optical microscope (Carl Zeiss AG, Jena, Germany) had been used to inspect both the extruded fibers and the 3D-printed samples.In the case of the fibers, it had been used to measure the length and diameter of the tested fibers in order to compute their resistivity, as well as the qualitative images shown in Figure 2C-I.In the case of the 3D-printed samples, it had been used to capture the samples' images shown in Figure 3A-I.The light compensation had been kept constant throughout the fibers (see Figure 2C-I), and the disks (see Figure 3C-I).However, Figure 3A,B are skewed toward darker tones, to compensate for the larger amount of light coming through the wider field of view.
Characterization-Scanning Electron Microscopy: An SEM (JSM-6510 LV, JEOL Ltd., Akishima, Japan) had been used to inspect the 3D printed samples (see Figure 5).The samples had been manually cut to achieve a small enough size to fit on the sample holder, and then coated with platinum using a sputter coater (108 Auto Sputter Coater, Cressington Scientific Instruments) for 45 s at 40 mA.Images had been taken at a magnification of 100, 1000, and 10000.
Characterization-Cyclic Compression and Tensile Testing: Cyclic mechanical tests were performed using a universal testing machine with a load cell of 200N (Zwick Roell Z005, Zwick Roell Group, Ulm, Germany).Each composition was tested at 10% compression, 20% compression, and 10% tension.Attempts at 20% tension tests had shown sample delamination (see Figure S8, Supporting Information).For each test, a virgin sample undergoes ten cycles of either compression or tension, at a speed of 2 mms −1 and with a hold time at the minimum and maximum strain points of 20 s.Then, a cylindrical neodymium magnet (30 mm diameter and 15 mm height) was placed between the sample and the base of the machine, and the same cyclic test was performed a second time, so to quantify the MR effect.The same cylindrical samples had been selected both for compression and tension tests.Such geometry was commonly selected for compression tests but never before had been adopted for tension ones in previous literature.However, this choice allows us to achieve two important requirements of the analysis, whilst using permanent magnets: on one hand, it could place the sample in close contact with the magnet and achieve a higher and more uniform magnetic field, and on the other it performed both compression and tensile tests using the exact same sample geometry and experimental setup, thus achieving the same magnetic field inside the sample.This procedure ensures that the observed MR effect in tension and compression is generated by the same magnetic field.The base of the machine was ferromagnetic, so to ensure a fixed placement of the magnet, whilst the moving head was made of aluminum, so to avoid interaction forces with the magnet.On one hand, in compression tests, a pre-load of 10 N was applied before the beginning of the test.On the other hand, in tensile tests, the sample was not only glued to the electrodes but also to the machine itself.To avoid any damage to the probe due to the removal of the glue after the experiments, a PLA shield was printed (Raise3D Pro2, Raise3D, Irvine, California, USA) and placed on the probe before gluing the tensile samples to it.Following the methodology of Mondal et al., [55] the piezoresistive effect was characterized using the resistance values corresponding to the hold times of the ninth cycle, in order to minimize the drift and avoid the Mullins effect.The complete resistance/stress and resistance/strain characteristics for every single sample were reported in the Supporting Information (Figures S3-S5, Supporting Information).The relative resistance change due to the piezoresistive effect r is computed as follows: where R 0 is the average resistance over the 20 s hold time at no strain and R 0 + ΔR is the average resistance over the 20 s hold time at maximum strain of the 9 th cycle.
The relative MR effect s had been characterized using the ratio between instantaneous stiffness in the presence and absence of the magnet, as follows: where d d  is the derivative of the stress with respect to the deformation,  max is the maximum deformation, the indices 0 and 1 represent the conditions without and with the magnet, respectively.Numerically, the derivative had been obtained using the last 100 points of the rising edge of the ninth cycle.Using the instantaneous stiffness at the maximum deformation point instead of computing an average based on minimum and maximum values of deformation and force allows us to better characterize the mechanical properties of the composites.On one hand, it better captured the behavior at high strains of the tested composites, whereas an average estimation would have been strongly affected by the nonlinear behavior of elastomers.On the other, in the case of compression tests, it minimized artifacts due to the different values of pre-strain imposed on the samples.As previously discussed, a pre-load of 10 N was applied to every sample.However, every sample was characterized by a different stress/strain curve, thus resulting in different pre-strain conditions.
Similarly, the relative energy dissipated had been characterized by the ratio of the energy dissipated during the ninth cycle in the presence and in the absence of the magnet, as follows: where ∮ is the circular integral over the ninth cycle over the deformation , V is the volume of the sample,  is the recorded stress, and the indices 0 and 1 represent the conditions without and with the magnet, respectively.

Characterization-Magnetoresistive
Experiments: Magnetoresistive tests were performed using a set of permanent magnets and placing a combination of them beneath the sample, then measuring the electrical resistance of the sample itself.As previously discussed, permanent magnets were preferred to electromagnets to avoid heat generation and the resulting temperature-induced material properties' changes superimposed to the magnetic-induced ones.All the selected magnets were cylindrical neodymium magnets with a 30 mm diameter.Changing the magnets' height and number, different magnetic fields could be achieved: 0, 125, 220, 336, 496, and 544 mT.The reported values of the magnetic field had been recorded using a magnetometer (Extech Instruments, Nashua, New Hampshire, USA) in contact with the magnets themselves.For each composition and each field value, the sample was put in position and then the electrical resistance was measured continuously for 50 s.
Characterization-Magnetostrictive Experiments: The magnetostriction of disks had been investigated using five disks for each tested composition, a micrometer (RS PRO External Micrometer, RS Group plc) and a 30 mm diameter and 15 mm height cylindrical neodymium magnet.Using a magnetometer (Extech Instruments, Nashua, New Hampshire, USA) the magnetic field was measured to be 302 mT.The deformation was computed by measuring the thickness of the samples both in the presence and absence of the magnet.Then, the theoretical deformation  T M is computed as follows: where  is the deformation (see Figure 4D,E), r is the relative resistance of the sample in the specified condition (see Figure 4A), and M and C specify the test conditions, magnetoresistive tests, and cyclic compression tests without magnet, respectively.
Characterization-Hall Effect: The Hall effect had been characterized using five 1 mm thick and 10 × 10 mm 2 3D printed samples for every composition, as shown in Figure 7.As done in the cyclic tests, metallic grids as electrodes and glued to each side of the samples using commercial glue (Pattex Ultra Gel, Henkel, Düsseldorf, Germany).They were glued to all four sides, and one pair was used to provide a 12 V input voltage V 0 (RS PRO Digital Bench Power Supply, RS Group plc), whereas the other was used to measure the induced voltage using a multimeter (89A, Keysight, Santa Rosa, California, USA).In order to avoid bias due to the not perfectly symmetric placement of the grids, the Hall voltage V hall had been computed as follows: V hall = V(H) − V(0) (5)   where V(0) and V(H) are the measured induced voltage in the absence and presence of the magnetic field H. H is obtained using a cylindrical neodymium magnet (30 mm diameter and 15 mm height).Using a magnetometer (Extech Instruments, Nashua, New Hampshire, USA) the magnetic field is measured to be 302 mT.

Figure 3 .
Figure 3. 3D printed samples both for further testing and demonstrative purposes.A) CB 15% CIP 15% and B) CB 15% CIP 30% demonstrative prints showcasing the 'EMPA' and 'University of Cambridge' logos.Top and side view of C) CB 15% CIP 15% and D) CB 15% CIP 30% samples for further mechanical and magnetoresistive testing.Top and side view of E) CB 15% sample for further mechanical and magnetoresistive testing.F) CIP 15%, G) CIP 30%, H) CIP 45%, I) CIP 60% samples for further mechanical testing.All percentages are given as volume fractions.

Figure 4 .
Figure 4. Cyclic mechanical load tests to evaluate the piezoresistive property and MR effect of the tested samples.A) Relative resistance change as a function of the imposed strain, and examples of individual trials: B) CB 15% CIP 15% under 10% compression and C) CB 15% CIP 30% under 10% tension.The piezoresistive response is computed as the difference in resistance between the maximum and minimum strain hold times of the nineth cycle.The rising edge of the nineth cycle of the stress/strain characteristics of E) 20% compression, F) 10% compression, and D) 10% tension cyclic tests on CB 15% CIP 15% and CB 15% CIP 30% with and without the 302 mT magnetic field, and CB 15% CIP 0% only without.Rising edge of the nineth cycle of the stress/strain characteristics of G) 20% compression, H) 10% compression, and I) 10% tension cyclic tests on CIP 15% and CIP 30% with and without the magnetic field.J) Instantaneous stiffness of the different CIP composites in the absence of the magnetic field and K) MR effect.L) The energy dissipated in the absence of a magnetic field and M) magnetic-induced change in dissipated energy by the CIP composites during the nineth cycle of the stress/strain characteristics.All percentages are given in volume fractions.Solid lines represent the tests without the magnet, whereas dotted ones the tests with the magnet.

Figure 5 .
Figure 5. SEM images of the 3D printed samples: A) 15 vol.%CB and 15 vol.%CIP, B) 15 vol.%CB and 30 vol.% CIP, C) 15 vol.%CB and 0 vol.%CIP, D) 0 vol.%CB and 15 vol.%CIP, E) 0 vol.%CB and 30 vol.% CIP.All samples have been imaged with a magnitude of 100 and 1000, and the hybrid filler composited have also been imaged with a magnitude of 10000 to further characterize the interaction between CIP and CB.

Figure 6 .
Figure 6.A) Absolute and B) relative resistance change as a function of the generated magnetic field.Different magnet combinations to achieve the tested fields: C) 0 mT, D) 125 mT, E) 220 mT, F) 336 mT, G) 496 mT, and H) 544 mT.All percentages are given in volume fractions.I) Measured and predicted compression achieved by using a magnetic field H of 302 mT.J) Schematic of the experimental setup to measure samples' compression.Pictures of the compression measuring setup K) without and L) with the magnetic field.

Figure 7 .
Figure 7. A) Measured Hall effect voltage with an imposed voltage V 0 of 12 V and magnetic field H of 302 mT.B) Schematic of the experimental setup to measure the Hall effect.Pictures of the setup both C) without and D) with the magnetic field applied.