1. P. Von Lockette, S. Lofland, J. Roche, J. Mineroff, M. Babcock
Rowan University, Glassboro, NJ
Investigating new symmetry classes in magnetorheological elastomers (MREs)
Magnetorheological elastomers (MREs) are composite materials made from rubber mixed with magnetic particles whose mechanical behavior changes in a magnetic field. Theories on MRE behavior assign this change to restoring magnetic torques developed within the bulk material that stem from particle-field interactions. This work, however, addresses the fundamental difference in behavior between MREs formed from soft-magnetic (magnetically isotropic) particles such as iron (termed S-MREs) which can not develop internal torques and those formed using hard-magnetic (magnetically anisotropic) particles such as barium hexaferrite (termed H-MREs) that do generate magnetic torques at the particle level. These torques are governed by T = m x H. Historically, experimentation and theory in the field have focused solely on S-MREs. This work is the first study of H-MRE behavior.
Conclusions
Four classifications show distinct magnetic properties with respect to remanent magnetizations supporting claims of material classifications.
Particle magnetization (S-MRE vs.H-MRE) dictates nature of internal distributed magnetic bending moment, mH, in cantilever bending configuration;
H-MREs show mH proportional to field strength (magnitude and sign) yielding active behavior
S-MRE’s show mH proportional to field strength (magnitude only) and deflection yielding reactive behavior
Phenomenological model allows quantitative determination of shear stiffness-field sensitivity parameter , b, and quantitatively shows:
H-MREs, aligned and unaligned, are insensitive to field strength for low fields
Aligned H-MREs transition to S-MRE type behavior at higher field strengths; combined behavior may result from existing remanent magnetizations parallel and perpendicular to field direction
Elastic-magnetic coupling factors defined in cantilever bending mode, f, KH, and Ke
Demagnetization energy captures S-MRE response well in magneto-elastic energy minimization model
Motivation
Soft-magnetic, particles will align magnetically with the external field, m = cH, yielding no magnetic torque,
T = (cH) x H = 0.
Results: Static Bending
Results: Dynamic Shear
0.18
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02 H
The MRE Effect, which is the change in relative shear modulus found from
has been the standard measure of MRE performance. Aligned Fe and Unaligned Fe S-MREs outperform Aligned BaM and Unaligned BaM H-MREs in this regard.
Integrating magnetically induced force vs. deflection curves in cantilever bending yields work done by magnetic actuation vs. field strength.
Aligned barium shows highest magnetic work while unaligned barium shows very little due to disorder in magnetic domains. T
Hard-magnetic, particles maintain internal magnetization, m, allowing torque production, T = m x H. H
Research Question
Hypothesis: The fundamentally different magnetic torque generation mechanisms in H-MREs and S-MREs will provide fundamentally different magnetorheological responses in static bending and dynamic shear.
Objectives:
Develop proxies for four classifications of MRE materials based on magnetization and particle alignment pairs.
Develop models that predict material behavior using appropriate physics.
Quantitatively determine elastic-magnetic coupling factors for each material class.
Fe (Soft)
BaM (Hard)
Unaligned
Aligned
Particle Alignment
Magnetization
Aligned & Unaligned Fe
Relatively constant response
show relatively constant field sensitivity.
The magnetic moment’s relationship to field strength varies by material type. Shown at moH = 90mT.
becomes sensitive to field at higher fields.
Aligned BaM
Linear response
Aligned &
Unaligned BaM
have little sensitivity at low fields. Unaligned BaM may show transitional behavior.
No response
Material Fabrication
325 mesh iron (Fe)
powder
(Soft-magnetic )
~40 mm M-type barium
Hexferrite (BaM)
(Hard
magnetic) or
moH H
Given experimentally determined elastic bending compliance, K*=1/Ke, and internal magnetic moment, mH(H), load vs. deflection vs. field strength is predicted.
where
Cure with (above, aligned) or without (below, unaligned) a magnetic field of moH ~ 1-2T.
Given experimentally determined elastic and magnetic bending stiffnesses, Ke and KH, load vs. deflection vs. field strength is predicted.
Dow Corning HS II, silicone elastomer compound
References
Borcea L and Bruno O 2001 On the magneto-elastic properties of elastomer–ferromagnet composites J. Mech. Phys. Solids 49, 2877
Dorfmann A. and Ogden R W 2003 Magnetoelastic modeling of elastomers, Eur. J. Mech. A/Solids 22, 497
Zhou G Y 2003 Shear properties of a magnetorheological elastomer Smart Mater. Struct. 12:1 139
Lanotte L, Ausiano G, Hison C, Iannotti V, Luponio C, and Luponio, Jr. C 2004 State of the art and development trends of novel nanostructured elastomagnetic composites J. Optoelectronics Adv. Materi., 6, 523
Kankanala S V and Triantafyllidis N 2004 On finitely strained magnetorheological elastomers J. Mech. Phys. Solids 52, 2869
Shen Y, Golnaraghi M F, and Heppler G 2004 R Experimental research and modeling of magnetorheological elastomers J. Intell. Mater. Syst. Struct. 15, 27
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H-MREs exhibit remanent magnetization (internal magnetization exists without external field present which is characteristic of hard magnets) while S-MRE do not. Remanent magnetizations increase parallel vs. perpendicular to poling direction.
Experimental Methods and Modeling
Natural frequency shifts with field strength yielding field dependent shear stiffness through
where is the combined effective elastic-magnetic shear stiffness.
Dynamic Shear
H, wn
Representative Dynamic Response of System
Free Bending Test
Phenomenological model ke
Input, F(t) m c
Output,
Magnetic behavior
a term yields S-MRE behavior while b term yields H-MRE behavior.
Natural frequency
Damping ratio
System Gain
Measurable magnetic field sensitivity parameter
Elastic-magnetic coupling
Magnetic stiffness
Static Bending
Minimization of bending strain energy density combined with the particles’ demagnetization tensor (D) are used to model vmax plus elasto-magnetic couplings, kH & KE.
Bernoulli-Euler beam theory is used to calculate internal magnetic moments, mH, and predict tip deflections, vmax, for S- and H-MREs.
Magnetic coil
Force transducer (P, vmax)
MRE sample
Clamps
Magnetic flux
Forced Bending Test x
v(x) H
aligned BaM bends freely,
aligned and unaligned Fe will only return to their undeformed state,
and unaligned BaM shows no response.
Aligned BaM for moH = T shown. Tick marks are ¼ in.
Elastic stiffness
Tip Deflection
magnetic flux direction
aluminum box frame
magnetic coil
MRE busing, mass, and output accelerometer
input accelerometer
shaker