Experiments and modeling of mechanically-soft, hard magnetorheological foams with potential applications in haptic sensing

TL;DR

This work tackles sensing deformation in mechanically-soft, magnetically-hard h-MRE foams by leveraging deformation-induced changes in external magnetic flux without requiring continuous external fields. It develops a thermodynamically consistent, compressible magneto-elastic framework that couples finite-strain mechanics with magnetism via an internal remanent field, using a two-scale homogenization to express mechanical and magnetic energies in terms of porosity and particle content. The model, calibrated against oedometric data and supported by FE simulations and analytical Gou-based solutions, accurately predicts both mechanical and magnetic responses across multiple particle fractions and loading conditions, enabling inference of deformation, stiffness, and stress from magnetic signals. The results demonstrate the feasibility of multi-modal haptic sensing with 3D-printed-like isotropic foams, offering a path toward passive, embedded magnetic sensing in soft actuators and tactile devices, with future work focusing on dissipative dynamics and broader loading regimes.

Abstract

This study proposes a family of novel mechanically-soft and magnetically-hard magnetorheological foams that, upon deformation, lead to robust and measurable magnetic flux changes in their surroundings. This allows to infer qualitatively and even quantitatively the imposed deformation and, eventually from that, an estimation of the stiffness and average stress on the sample even in complex loading scenarios involving combinations of uniform or nonuniform compression/tension with superposed shearing in different directions. The work provides a complete experimental, theoretical and numerical framework on finite strain, compressible magneto-elasticity, thereby allowing to measure and predict coupled magneto-mechanical properties of such materials with different particle volume fractions and then use it to estimate and design potential haptic sensing devices.

Figures (11)

• Figure 1: Geometric dimensions of (top row) cube-in-cube and (bottom row) cube-in-sphere molds. From the cube-in-cube we obtain 8 specimens of volume $10\times 10\times 10~m m^3$. From the cube-in-sphere mold we obtain one specimen of the same dimensions. Optical microscope images of the as fabricated $h$-MRE foams show a polydisperse void distribution with sizes ranging between $50{-}200~µ m$. A sketch of the silicone matrix with the magnetic particles is shown also for completeness. The $h$-MRE foam samples are subsequently permanently magnetized using a two-coil electromagnet.
• Figure 2: High resolution optical micrographs of the $h$-MRE foam microstructure with closed porosity and $c_\texttt{p}=0.12$ (see Table \ref{['tab:microstructural_params']} for more details on the microstructural parameters). (a,c) horizontal and (b,d) vertical cross-sections of the samples. (c,d) closeup zooms revealing the NdFeB particles as white spots due to light reflections.
• Figure 3: Two experimental tests are considered. A camera tracks markers to measure the sample deformation, a force sensor (not shown) attached to the top plate measures the force applied to the sample, and a 3-axis Hall sensor measures the magnetic flux $0.5~m m$ below the center of the bottom side of the sample (see sketches in orange color). All measurements are synchronized in time. (a) Oedometric compression along the magnetization direction $2$. A PMMA casing with a square cross-section of $10\times10~m m^{2}$ constrains the lateral displacements of the sample. (b) Uniaxial compression along the magnetization direction $2$ where the lateral sides are traction-free.
• Figure 4: Oedometric compression tests for $h$-MRE foams with $c_\texttt{p}=0.12$ ($c_\texttt{v}=0.45$, $c_\texttt{pm}=0.21$). (a) Purely mechanical response of magnetized and unmagnetized cube samples (also tested in all three principal directions). (b) Magnetic flux along the magnetization direction as a function of the applied engineering compressive strain. (c) Variation in the magnetic flux along the magnetization direction as a function of the applied engineering compressive strain.
• Figure 5: Uniaxial compression tests for $h$-MRE foams with $c_\texttt{p}=0.12$ ($c_\texttt{v}=0.45$, $c_\texttt{pm}=0.21$). (a) Purely mechanical response of magnetized and unmagnetized cube samples (also tested in all three principal directions). (b) Magnetic flux along the magnetization direction as a function of the applied engineering compressive strain. (c) Variation in the magnetic flux along the magnetization direction as a function of the applied engineering compressive strain.

Theorems & Definitions (6)

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