Abstract
We investigate the behavior of soft magnetoactive periodic laminates under remotely applied magnetic field. We derive explicit formulae for the induced deformation due to magnetic excitation of the laminates with hyperelastic magnetoactive phases. Next, we obtain the closed-form formulae for the velocities of long transverse waves. We show the dependence of the wave velocity on the applied magnetic intensity and induced strains, as well as on the wave propagation direction. Based on the long wave analysis, we derive closed-form formulae for the critical magnetic field corresponding to the loss of macroscopic stability. Finally, we analyze the transverse wave band gaps appearing in magnetoactive laminates in the direction normal to the layers. We illustrate the band gap tunability—width and position—by magnetically induced deformation.
References
1.
Ginder
, J. M.
, Clark
, S. M.
, Schlotter
, W. F.
, and Nichols
, M. E.
, 2002
, “Magnetostrictive Phenomena in Magnetorheological Elastomers
,” Int. J. Mod. Phys. B
, 16
(17n18
), pp. 2412
–2418
. 10.1142/S021797920201244X2.
Guan
, X.
, Donga
, X.
, and Ou
, J.
, 2008
, “Magnetostrictive Effect of Magnetorheological Elastomer
,” J. Magn. and Magn. Mat.
, 320
(3–4
), pp. 158
–163
. 10.1016/j.jmmm.2007.05.0433.
Varga
, Z.
, Filipcsei
, G.
, and Zrinyi
, M.
, 2005
, “Smart Composites with Controlled Anisotropy
,” Polymer
, 46
(18
), pp. 7779
–7787
. 10.1016/j.polymer.2005.03.1024.
Ginder
, J. M.
, Nichols
, M. E.
, Elie
, L. D.
, and Clark
, S. M.
, 2000
, “Controllable-Stiffness Components Based on Magnetorheological Elastomers
,” Proc. SPIE
, 3985
(1
), p. 418
. 10.1117/12.3888445.
Erb
, R. M.
, Libanori
, R.
, Rothfuchs
, N.
, and Studart
, A. R.
, 2012
, “Composites Reinforced in Three Dimensions by Using Low Magnetic Fields
,” Science
, 335
(6065
), pp. 199
–204
. 10.1126/science.12108226.
Ginder
, J. M.
, Schlotter
, W. F.
, and Nichols
, M. E.
, 2001
, “Magnetorheological Elastomers in Tunable Vibration Absorbers
,” Proc. SPIE
, 4331
(1
), pp. 103
–111
. 10.1117/12.4326947.
Deng
, H. X.
, Gong
, X. L.
, and Wang
, L. H.
, 2006
, “Development of an Adaptive Tuned Vibration Absorber with Magnetorheological Eastomer
,” Smart Mater. Struct.
, 15
(5
), pp. N111
–N116
. 10.1088/0964-1726/15/5/N028.
Wang
, Q.
, Dong
, X.
, Li
, L.
, and Ou
, J.
, 2018
, “Mechanical Modeling for Magnetorheological Elastomer Isolators Based on Constitutive Equations and Electromagnetic Analysis
,” Smart Mater. Struct.
, 27
(6
), p. 065017
. 10.1088/1361-665X/aabdb59.
Gong
, X.
, Fan
, Y.
, Xuan
, S.
, Xu
, Y.
, and Peng
, C.
, 2012
, “Control of the Damping Properties of Magnetorheological Elastomers by Using Polycaprolactone as a Temperature-Controlling Component
,” Ind. Eng. Chem. Res.
, 51
(18
), pp. 6395
–6403
. 10.1021/ie300317b10.
Yang
, J.
, Gong
, X.
, Deng
, H.
, Qin
, L.
, and Xuan
, S.
, 2012
, “Investigation on the Mechanism of Damping Behavior of Magnetorheological Elastomers
,” Smart Mater. Struct.
, 21
(12
), p. 125015
. 10.1088/0964-1726/21/12/12501511.
Farshad
, M.
, and Le Roux
, M.
, 2004
, “A New Active Noise Abatement Barrier System
,” Polym. Test.
, 23
(7
), pp. 855
–860
. 10.1016/j.polymertesting.2004.02.00312.
Yu
, K.
, Fang
, N. X.
, Huang
, G.
, and Wang
, Q.
, 2018
, “Magnetoactive Acoustic Metamaterials
,” Adv. Mater.
, 30
(21
), pp. 1
–10
. 10.1002/adma.20170634813.
Tian
, T. F.
, Li
, W. H.
, and Deng
, Y. M.
, 2011
, “Sensing Capabilities of Graphite Based MR Elastomers
,” Smart Mater. Struct.
, 20
(2
), p. 025022
. 10.1088/0964-1726/20/2/02502214.
Lanotte
, L.
, Ausanio
, G.
, Hison
, C.
, Iannotti
, V.
, and Luponio
, C.
, 2003
, “The Potentiality of Composite Elastic Magnets as Novel Materials for Sensors and Actuators
,” Sens. Actuat.
, 106
(1–3
), pp. 56
–60
. 10.1016/S0924-4247(03)00133-X15.
Kim
, Y.
, Yuk
, H.
, Zhao
, R.
, Chester
, S. A.
, and Zhao
, X.
, 2018
, “Printing Ferromagnetic Domains for Untethered Fast-Transforming Soft Materials
,” Nature
, 558
(7709
), pp. 274
–279
. 10.1038/s41586-018-0185-016.
Tang
, S. Y.
, Zhang
, X.
, Sun
, S.
, Yuan
, D.
, Zhao
, Q.
, Yan
, S.
, Deng
, L.
, Yun
, G.
, Zhang
, J.
, Zhang
, S.
, and Li
, W.
, 2018
, “Versatile Microfluidic Platforms Enabled by Novel Magnetorheological Elastomer Microactuators
,” Adv. Funct. Mater.
, 28
(8
), p. 1705484
. 10.1002/adfm.v28.817.
Stanier
, D. C.
, Ciambella
, J.
, and Rahatekar
, S. S.
, 2016
, “Fabrication and Characterisation of Short Fibre Reinforced Elastomer Composites for Bending and Twisting Magnetic Actuation
,” Compos. Part A
, 91
(1
), pp. 168
–176
. 10.1016/j.compositesa.2016.10.00118.
Makarova
, L. A.
, Alekhina
, Y. A.
, Rusakova
, T. S.
, and Perov
, N. S.
, 2016
, “Tunable Properties of Magnetoactive Elastomers for Biomedical Applications
,” Phys. Procedia
, 82
(1
), pp. 38
–45
. 10.1016/j.phpro.2016.05.00819.
Luo
, Z.
, Evans
, B. A.
, and Chang
, C. H.
, 2019
, “Magnetically Actuated Dynamic Iridescence Inspired by the Neon Tetra
,” ACS Nano
, 13
(4
), pp. 4657
–4666
. 10.1021/acsnano.9b0082220.
Tang
, J.
, Qiao
, Y.
, Chu
, Y.
, Tong
, Z.
, Zhou
, Y.
, Zhang
, W.
, Xie
, S.
, Hu
, J.
, and Wang
, T.
, 2019
, “Magnetic Double-Network Hydrogels for Tissue Hyperthermia and Drug Release
,” J. Mater. Chem. B
, 7
(8
), pp. 1311
–1321
. 10.1039/C8TB03301C21.
Maugin
, G. A.
, 1981
, “Wave Motion in Magnetizable Deformable Solids
,” Int. J. Eng. Sci.
, 19
(3
), pp. 321
–388
. 10.1016/0020-7225(81)90059-822.
Abd-Alla
, A. E. N.
, and Maugin
, G. A.
, 1987
, “Nonlinear Magnetoacoustic Equations
,” J. Acoust. Soc. Am.
, 82
(5
), pp. 1746
–1752
. 10.1121/1.39516723.
Hefni
, I. A. Z.
, Ghaleb
, A. F.
, and Maugin
, G. A.
, 1995
, “Surface Waves in a Nonlinear Magnetoelastic Conductor of Finite Electric Conductivity
,” Int. J. Eng. Sci.
, 33
(14
), pp. 2085
–2102
. 10.1016/0020-7225(95)00054-224.
Boulanger
, P.
, 1989
, “Inhomogeneous Magnetoelastic Planewaves
,” North-Holland Ser. Appl. Math. Mech.
, 35
(C
), pp. 601
–606
. 10.1016/B978-0-444-87272-2.50095-625.
Destrade
, M.
, and Ogden
, R. W.
, 2011
, “On Magneto-acoustic Waves in Finitely Deformed Elastic Solids
,” Math. Mech. Solids
, 16
(6
), pp. 594
–604
. 10.1177/108128651038769526.
Saxena
, P.
, and Ogden
, R. W.
, 2011
, “On Surface Waves in a Finitely Deformed Magnetoelastic Half-Space
,” Int. J. Appl. Mech.
, 3
(4
), pp. 633
–665
. 10.1142/S175882511100117227.
Saxena
, P.
, and Ogden
, R. W.
, 2012
, “On Love-Type Waves in a Finitely Deformed Magnetoelastic Layered Half-Space
,” Z. Angew. Math. Phys.
, 63
(6
), pp. 1177
–1200
. 10.1007/s00033-012-0204-128.
Galich
, P. I.
, Fang
, N. X.
, Boyce
, M. C.
, and Rudykh
, S.
, 2017
, “Elastic Wave Propagation in Finitely Deformed Layered Materials
,” J. Mech. Phys. Solids
, 98
(1
), pp. 390
–410
. 10.1016/j.jmps.2016.10.00229.
Galich
, P. I.
, and Rudykh
, S.
, 2017
, “Shear Wave Propagation and Band Gaps in Finitely Deformed Dielectric Elastomer Laminates: Long Wave Estimates and Exact Solution
,” ASME J. Appl. Mech.
, 84
(9
), p. 091002
. 10.1115/1.403715930.
Rudykh
, S.
, and Bertoldi
, K.
, 2013
, “Stability of Anisotropic Magnetorheological Elastomers in Finite Deformations: A Micromechanical Approach.
,” J. Mech. Phys. Solids
, 61
(4
), pp. 949
–967
. 10.1016/j.jmps.2012.12.00831.
Danas
, K.
, Kankanala
, S. V.
, and Triantafyllidis
, N.
, 2012
, “Experiments and Modeling of Iron-Particle-Filled Magnetorheological Elastomers
,” J. Mech. Phys. Solids
, 60
(1
), pp. 120
–138
. 10.1016/j.jmps.2011.09.00632.
Galipeau
, E.
, Rudykh
, S.
, deBotton
, G.
, and Castañeda
, P. P.
, 2014
, “Magnetoactive Elastomers with Periodic and Random Microstructures
,” Int. J. Solids Struct.
, 51
(18
), pp. 3012
–3024
. 10.1016/j.ijsolstr.2014.04.01333.
Metsch
, P.
, Kalina
, K. A.
, Spieler
, C.
, and Kästner
, M.
, 2016
, “A Numerical Study on Magnetostrictive Phenomena in Magnetorheological Elastomers
,” Comput. Mater. Sci.
, 124
(1
), pp. 364
–374
. 10.1016/j.commatsci.2016.08.01234.
Vu
, D. K.
, and Steinmann
, P.
, 2007
, “Nonlinear Electro-and Magneto-Elastostatics: Material and Spatial Settings
,” Int. J. Solids Struct.
, 44
(24
), pp. 7891
–7905
. 10.1016/j.ijsolstr.2007.05.01735.
Keip
, M. A.
, and Rambausek
, M.
, 2016
, “A Multiscale Approach to the Computational Characterization of Magnetorheological Elastomers
,” Int. J. Numer. Methods Eng.
, 107
(4
), pp. 338
–360
. 10.1002/nme.v107.436.
Keip
, M. A.
, and Rambausek
, M.
, 2017
, “Computational and Analytical Investigations of Shape Effects in the Experimental Characterization of Magnetorheological Elastomers
,” Int. J. Solids Struct.
, 121
(1
), pp. 1
–20
. 10.1016/j.ijsolstr.2017.04.01237.
Dorfmann
, L.
, and Ogden
, R. W.
, 2014
, Nonlinear Theory of Electroelastic and Magnetoelastic Interactions
, vol. 1
, Springer
, Boston, MA
. 10.1007/978-1-4614-9596-338.
Kankanala
, S. V.
, and Triantafyllidis
, N.
, 2008
, “Magnetoelastic Buckling of a Rectangular Block in Plane Strain
,” J. Mech. Phys. Solids
, 56
(4
), pp. 1147
–1169
. 10.1016/j.jmps.2007.10.00839.
Arruda
, E. M.
, and Boyce
, M. C.
, 1993
, “A Three-Dimensional Constitutive Model for the Large Stretch Behavior of Rubber Elastic Materials
,” J. Mech. Phys. Solids
, 41
(2
), pp. 389
–412
. 10.1016/0022-5096(93)90013-640.
Gent
, A. N.
, 1996
, “A New Constitutive Relation for Rubber
,” Rubber Chem. Technol.
, 69
(1
), pp. 59
–61
. 10.5254/1.353835741.
Goshkoderia
, A.
, and Rudykh
, S.
, 2017
, “Stability of Magnetoactive Composites with Periodic Microstructures Undergoing Finite Strains in the Presence of a Magnetic Field
,” Compos. Part B: Eng.
, 128
(1
), pp. 19
–29
. 10.1016/j.compositesb.2017.06.01442.
Yuan
, B.
, Humphrey
, V. F.
, Wen
, J.
, and Wen
, X.
, 2013
, “On the Coupling of Resonance and Bragg Scattering Effects in Three-Dimensional Locally Resonant Sonic Materials
,” Ultrasonics
, 53
(7
), pp. 1332
–1343
. 10.1016/j.ultras.2013.03.01943.
Krushynska
, A.
, Miniaci
, M.
, Bosia
, F.
, and Pugno
, N.
, 2017
, “Coupling Local Resonance with Bragg Band Gaps in Single-Phase Mechanical Metamaterials
,” Extreme Mech. Lett.
, 12
(1
), pp. 30
–36
. 10.1016/j.eml.2016.10.00444.
Rytov
, S.
, 1956
, “Acoustical Properties of a Thinly Laminated Medium
,” Soviet Phys. Acoustics
, 2
(1
), pp. 68
–80
.45.
Jandron
, M.
, and Henann
, D. L.
, 2018
, “A Numerical Simulation Capability for Electroelastic Wave Propagation in Dielectric Elastomer Composites: Application to Tunable Soft Phononic Crystals
,” Int. J. Solids. Struct.
, 150
(1
), pp. 1
–21
. 10.1016/j.ijsolstr.2018.04.02346.
Li
, J.
, Slesarenko
, V.
, Galich
, P. I.
, and Rudykh
, S.
, 2018
, “Oblique Shear Wave Propagation in Finitely Deformed Layered Composites
,” Mech. Res. Commun.
, 87
(1
), pp. 21
–28
. 10.1016/j.mechrescom.2017.12.00247.
Slesarenko
, V.
, Galich
, P. I.
, Li
, J.
, Fang
, N. X.
, and Rudykh
, S.
, 2018
, “Foreshadowing Elastic Instabilities by Negative Group Velocity in Soft Composites
,” Appl. Phys. Lett.
, 113
(3
), p. 031901
. 10.1063/1.5042077Copyright © 2019 by ASME
You do not currently have access to this content.
