Skip to main content
Top
Published in: Archive of Applied Mechanics 1/2021

21-09-2020 | Original

Transversely isotropic magnetoactive elastomers: theory and experiments

Authors: Alireza Beheshti, Ramin Sedaghati, Subhash Rakheja

Published in: Archive of Applied Mechanics | Issue 1/2021

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

The current contribution is concerned with the development of novel constitutive equations for anisotropic magnetoactive elastomers (MAEs). A hyperelastic material model for an incompressible magnetoelastic medium representing transversely isotropic MAEs has been developed to investigate their response behavior in the presence of the applied magnetic field while undergoing finite deformation. Transversely isotropic MAE samples in circular cylindrical geometry with 15% iron particle volume fraction are then fabricated and experimentally tested to measure their permeability and torque–twist response. The experimental results have then been effectively utilized to identify the constant material parameters in the proposed material model. Finally, the accuracy and validity of the proposed constitutive equations are demonstrated through the comparison of the simulation and experimental results.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Literature
1.
go back to reference Boczkowska, A., Awietj, S.: Microstructure and properties of magnetorheological elastomers. In: Boczkowska, A. (ed.) Advanced Elastomers—Technology, Properties and Applications. InTech, New York (2012) Boczkowska, A., Awietj, S.: Microstructure and properties of magnetorheological elastomers. In: Boczkowska, A. (ed.) Advanced Elastomers—Technology, Properties and Applications. InTech, New York (2012)
2.
go back to reference Farshad, M., Benine, A.: Magnetoactive elastomer composites. Polym. Test. 23(3), 347–353 (2004) Farshad, M., Benine, A.: Magnetoactive elastomer composites. Polym. Test. 23(3), 347–353 (2004)
3.
go back to reference Coquelle, E., Bossis, G.: Mullins effect in elastomers filled with particles aligned by a magnetic field. Int. J. Solids Struct. 43(25–26), 7659–7672 (2006)MATH Coquelle, E., Bossis, G.: Mullins effect in elastomers filled with particles aligned by a magnetic field. Int. J. Solids Struct. 43(25–26), 7659–7672 (2006)MATH
4.
go back to reference Menzel, A.M.: Mesoscopic characterization of magnetoelastic hybrid materials: magnetic gels and elastomers, their particle-scale description, and scale-bridging links. Arch. Appl. Mech. 89(1), 17–45 (2018) Menzel, A.M.: Mesoscopic characterization of magnetoelastic hybrid materials: magnetic gels and elastomers, their particle-scale description, and scale-bridging links. Arch. Appl. Mech. 89(1), 17–45 (2018)
5.
go back to reference Bellan, C., Bossis, G.: Field dependence of viscoelastic properties of Mr Elastomers. Int. J. Mod. Phys. B 16(17–18), 2447–2453 (2012) Bellan, C., Bossis, G.: Field dependence of viscoelastic properties of Mr Elastomers. Int. J. Mod. Phys. B 16(17–18), 2447–2453 (2012)
6.
go back to reference Carlson, J.D., Jolly, M.R.: MR fluid, foam and elastomer devices. Mechatronics 10(4–5), 555–569 (2000) Carlson, J.D., Jolly, M.R.: MR fluid, foam and elastomer devices. Mechatronics 10(4–5), 555–569 (2000)
7.
go back to reference Kallio, M.: The Elastic and Damping Properties of Magnetorheological Elastomers. VTT Publications, New York (2005) Kallio, M.: The Elastic and Damping Properties of Magnetorheological Elastomers. VTT Publications, New York (2005)
8.
go back to reference Vicente, J.D., Bossis, G., Lacis, S., Guyot, M.: Permability measurements in cobalt ferrite and carbonyl iron powders and suspensions. J. Magn. Magn. Mater. 251(1), 9 (2002) Vicente, J.D., Bossis, G., Lacis, S., Guyot, M.: Permability measurements in cobalt ferrite and carbonyl iron powders and suspensions. J. Magn. Magn. Mater. 251(1), 9 (2002)
9.
go back to reference Lokander, M., Stenberg, B.: Improving the magnetorheological effect in isotropic magnetorheological rubber materials. Polym. Test. 22(6), 677–680 (2003) Lokander, M., Stenberg, B.: Improving the magnetorheological effect in isotropic magnetorheological rubber materials. Polym. Test. 22(6), 677–680 (2003)
10.
go back to reference Odenbach, S.: Microstructure and rheology of magnetic hybrid materials. Arch. Appl. Mech. 86(1–2), 269–279 (2016) Odenbach, S.: Microstructure and rheology of magnetic hybrid materials. Arch. Appl. Mech. 86(1–2), 269–279 (2016)
11.
go back to reference Borin, D., Stepanov, G., Dohmen, E.: Hybrid magnetoactive elastomer with a soft matrix and mixed powder. Arch. Appl. Mech. 89(1), 105–117 (2018) Borin, D., Stepanov, G., Dohmen, E.: Hybrid magnetoactive elastomer with a soft matrix and mixed powder. Arch. Appl. Mech. 89(1), 105–117 (2018)
12.
go back to reference Jolly, M.R., Carlson, J.D., Muñoz, B.C., Bullions, T.A.: The magnetoviscoelastic response of elastomer composites consisting of ferrous particles embedded in a polymer matrix. J. Intell. Mater. Syst. Struct. 7(6), 613–622 (1996) Jolly, M.R., Carlson, J.D., Muñoz, B.C., Bullions, T.A.: The magnetoviscoelastic response of elastomer composites consisting of ferrous particles embedded in a polymer matrix. J. Intell. Mater. Syst. Struct. 7(6), 613–622 (1996)
13.
go back to reference Lokander, M., Stenberg, B.: Performance of isotropic magnetorheological rubber materials. Polym. Test. 22(3), 245–251 (2003) Lokander, M., Stenberg, B.: Performance of isotropic magnetorheological rubber materials. Polym. Test. 22(3), 245–251 (2003)
14.
go back to reference Varga, Z., Filipcsei, G., Zrínyi, M.: Magnetic field sensitive functional elastomers with tuneable elastic modulus. Polymer 47(1), 227–233 (2006) Varga, Z., Filipcsei, G., Zrínyi, M.: Magnetic field sensitive functional elastomers with tuneable elastic modulus. Polymer 47(1), 227–233 (2006)
15.
go back to reference Dorfmann, A., Ogden, R.W.: Nonlinear magnetoelastic deformations. Q. J. Mech. Appl. Math. 57(4), 599–622 (2004)MathSciNetMATH Dorfmann, A., Ogden, R.W.: Nonlinear magnetoelastic deformations. Q. J. Mech. Appl. Math. 57(4), 599–622 (2004)MathSciNetMATH
16.
go back to reference Bustamante, R.: Transversely isotropic nonlinear magneto-active elastomers. Acta Mech. 210(3–4), 183–214 (2009)MATH Bustamante, R.: Transversely isotropic nonlinear magneto-active elastomers. Acta Mech. 210(3–4), 183–214 (2009)MATH
17.
go back to reference Danas, K., Kankanala, S.V., Triantafyllidis, N.: Experiments and modeling of iron-particle-filled magnetorheological elastomers. J. Mech. Phys. Solids 60(1), 120–138 (2012) Danas, K., Kankanala, S.V., Triantafyllidis, N.: Experiments and modeling of iron-particle-filled magnetorheological elastomers. J. Mech. Phys. Solids 60(1), 120–138 (2012)
18.
go back to reference Kankanala, S.V., Triantafyllidis, N.: On finitely strained magnetorheological elastomers. J. Mech. Phys. Solids 52(12), 2869–2908 (2004)MathSciNetMATH Kankanala, S.V., Triantafyllidis, N.: On finitely strained magnetorheological elastomers. J. Mech. Phys. Solids 52(12), 2869–2908 (2004)MathSciNetMATH
19.
go back to reference Saxena, P., Hossain, M., Steinmann, P.: Nonlinear magneto-viscoelasticity of transversally isotropic magneto-active polymers. Proc. Math. Phys. Eng. Sci. 470(2166), 20140082 (2014) Saxena, P., Hossain, M., Steinmann, P.: Nonlinear magneto-viscoelasticity of transversally isotropic magneto-active polymers. Proc. Math. Phys. Eng. Sci. 470(2166), 20140082 (2014)
20.
go back to reference Weiss, J.A., Maker, B.N., Govindjee, S.: Finite element implementation of incompressible, transversely isotropic hyperelasticity. Comput. Methods Appl. Mech. Eng. 135(1–2), 107–128 (1996)MATH Weiss, J.A., Maker, B.N., Govindjee, S.: Finite element implementation of incompressible, transversely isotropic hyperelasticity. Comput. Methods Appl. Mech. Eng. 135(1–2), 107–128 (1996)MATH
21.
go back to reference Qiu, G.Y., Pence, T.J.: Remarks on the behavior of simple directionally reinforced incompressible nonlinearly elastic solids. J. Elast. 49(1), 1–30 (1997)MathSciNetMATH Qiu, G.Y., Pence, T.J.: Remarks on the behavior of simple directionally reinforced incompressible nonlinearly elastic solids. J. Elast. 49(1), 1–30 (1997)MathSciNetMATH
22.
go back to reference Merodio, J., Ogden, R.W.: Material instabilities in fiber-reinforced nonlinearly elastic solids under plane deformation. Arch. Mech. 54(5–6), 525–552 (2002)MathSciNetMATH Merodio, J., Ogden, R.W.: Material instabilities in fiber-reinforced nonlinearly elastic solids under plane deformation. Arch. Mech. 54(5–6), 525–552 (2002)MathSciNetMATH
23.
go back to reference Merodio, J., Ogden, R.W.: Instabilities and loss of ellipticity in fiber-reinforced compressible non-linearly elastic solids under plane deformation. Int. J. Solids Struct. 40(18), 4707–4727 (2003)MathSciNetMATH Merodio, J., Ogden, R.W.: Instabilities and loss of ellipticity in fiber-reinforced compressible non-linearly elastic solids under plane deformation. Int. J. Solids Struct. 40(18), 4707–4727 (2003)MathSciNetMATH
24.
go back to reference Merodio, J., Ogden, R.W.: Mechanical response of fiber-reinforced incompressible non-linearly elastic solids. Int. J. Nonlinear Mech. 40(2–3), 213–227 (2005)MATH Merodio, J., Ogden, R.W.: Mechanical response of fiber-reinforced incompressible non-linearly elastic solids. Int. J. Nonlinear Mech. 40(2–3), 213–227 (2005)MATH
25.
go back to reference Horgan, C.O., Saccomandi, G.: A new constitutive theory for fiber-reinforced incompressible nonlinearly elastic solids. J. Mech. Phys. Solids 53(9), 1985–2015 (2005)MathSciNetMATH Horgan, C.O., Saccomandi, G.: A new constitutive theory for fiber-reinforced incompressible nonlinearly elastic solids. J. Mech. Phys. Solids 53(9), 1985–2015 (2005)MathSciNetMATH
26.
go back to reference Kassianidis, F., Ogden, R.W., Merodio, J., Pence, T.J.: Azimuthal shear of a transversely isotropic elastic solid. Math. Mech. Solids 13(8), 690–724 (2008)MathSciNetMATH Kassianidis, F., Ogden, R.W., Merodio, J., Pence, T.J.: Azimuthal shear of a transversely isotropic elastic solid. Math. Mech. Solids 13(8), 690–724 (2008)MathSciNetMATH
27.
go back to reference Horgan, C.O., Murphy, J.G.: Torsion of incompressible fiber-reinforced nonlinearly elastic circular cylinders. J. Elast. 103(2), 235–246 (2010)MathSciNetMATH Horgan, C.O., Murphy, J.G.: Torsion of incompressible fiber-reinforced nonlinearly elastic circular cylinders. J. Elast. 103(2), 235–246 (2010)MathSciNetMATH
28.
go back to reference Horgan, C.O., Murphy, J.G.: Finite extension and torsion of fiber-reinforced non-linearly elastic circular cylinders. Int. J. Nonlinear Mech. 47(2), 97–104 (2012) Horgan, C.O., Murphy, J.G.: Finite extension and torsion of fiber-reinforced non-linearly elastic circular cylinders. Int. J. Nonlinear Mech. 47(2), 97–104 (2012)
29.
go back to reference Destrade, M., Donald, B.M., Murphy, J.G., Saccomandi, G.: At least three invariants are necessary to model the mechanical response of incompressible, transversely isotropic materials. Comput. Mech. 52(4), 959–969 (2013)MathSciNetMATH Destrade, M., Donald, B.M., Murphy, J.G., Saccomandi, G.: At least three invariants are necessary to model the mechanical response of incompressible, transversely isotropic materials. Comput. Mech. 52(4), 959–969 (2013)MathSciNetMATH
30.
go back to reference Destrade, M., Horgan, C.O., Murphy, J.G.: Dominant negative Poynting effect in simple shearing of soft tissues. J. Eng. Math. 95(1), 87–98 (2014)MathSciNetMATH Destrade, M., Horgan, C.O., Murphy, J.G.: Dominant negative Poynting effect in simple shearing of soft tissues. J. Eng. Math. 95(1), 87–98 (2014)MathSciNetMATH
31.
go back to reference Hamdaoui, M.E., Merodio, J., Ogden, R.W., Rodríguez, J.: Finite elastic deformations of transversely isotropic circular cylindrical tubes. Int. J. Solids Struct. 51(5), 1188–1196 (2014) Hamdaoui, M.E., Merodio, J., Ogden, R.W., Rodríguez, J.: Finite elastic deformations of transversely isotropic circular cylindrical tubes. Int. J. Solids Struct. 51(5), 1188–1196 (2014)
32.
go back to reference Polignone, D.A., Horgan, C.O.: Cavitation for incompressible anisotropic nonlinearly elastic spheres. J. Elast. 33(1), 27–65 (1993)MATH Polignone, D.A., Horgan, C.O.: Cavitation for incompressible anisotropic nonlinearly elastic spheres. J. Elast. 33(1), 27–65 (1993)MATH
33.
go back to reference Lu, J., Zhang, L.: Physically motivated invariant formulation for transversely isotropic hyperelasticity. Int. J. Solids Struct. 42(23), 6015–6031 (2005)MATH Lu, J., Zhang, L.: Physically motivated invariant formulation for transversely isotropic hyperelasticity. Int. J. Solids Struct. 42(23), 6015–6031 (2005)MATH
34.
go back to reference Feng, Y., Okamoto, R.J., Namani, R., Genin, G.M., Bayly, P.V.: Measurements of mechanical anisotropy in brain tissue and implications for transversely isotropic material models of white matter. J. Mech. Behav. Biomed. Mater. 23, 117–32 (2013) Feng, Y., Okamoto, R.J., Namani, R., Genin, G.M., Bayly, P.V.: Measurements of mechanical anisotropy in brain tissue and implications for transversely isotropic material models of white matter. J. Mech. Behav. Biomed. Mater. 23, 117–32 (2013)
35.
go back to reference Murphy, J.G.: Transversely isotropic biological, soft tissue must be modelled using both anisotropic invariants. Eur. J. Mech. A Solids 42, 90–96 (2013)MathSciNetMATH Murphy, J.G.: Transversely isotropic biological, soft tissue must be modelled using both anisotropic invariants. Eur. J. Mech. A Solids 42, 90–96 (2013)MathSciNetMATH
36.
go back to reference Horgan, C.O., Murphy, J.G.: Reverse poynting effects in the torsion of soft biomaterials. J. Elast. 118(2), 127–140 (2014)MathSciNetMATH Horgan, C.O., Murphy, J.G.: Reverse poynting effects in the torsion of soft biomaterials. J. Elast. 118(2), 127–140 (2014)MathSciNetMATH
37.
go back to reference Moreira, C.S., Nunes, L.C.S.: Effects of fiber orientation in a soft unidirectional fiber-reinforced material under simple shear deformation. Int. J. Nonlinear Mech. 111, 72–81 (2019) Moreira, C.S., Nunes, L.C.S.: Effects of fiber orientation in a soft unidirectional fiber-reinforced material under simple shear deformation. Int. J. Nonlinear Mech. 111, 72–81 (2019)
38.
go back to reference Bonet, J., Burton, A.J.: A simple orthotropic, transversely isotropic hyperelastic constitutive equation for large strain computations. Comput. Methods Appl. Mech. Eng. 162(1–4), 151–164 (1998)MATH Bonet, J., Burton, A.J.: A simple orthotropic, transversely isotropic hyperelastic constitutive equation for large strain computations. Comput. Methods Appl. Mech. Eng. 162(1–4), 151–164 (1998)MATH
39.
go back to reference Itskov, M., Aksel, N.: A class of orthotropic and transversely isotropic hyperelastic constitutive models based on a polyconvex strain energy function. Int. J. Solids Struct. 41(14), 3833–3848 (2004)MathSciNetMATH Itskov, M., Aksel, N.: A class of orthotropic and transversely isotropic hyperelastic constitutive models based on a polyconvex strain energy function. Int. J. Solids Struct. 41(14), 3833–3848 (2004)MathSciNetMATH
40.
go back to reference Itskov, M., Ehret, A.E., Mavrilas, D.: A polyconvex anisotropic strain-energy function for soft collagenous tissues. Biomech. Model. Mechanobiol. 5(1), 17–26 (2006) Itskov, M., Ehret, A.E., Mavrilas, D.: A polyconvex anisotropic strain-energy function for soft collagenous tissues. Biomech. Model. Mechanobiol. 5(1), 17–26 (2006)
41.
go back to reference Gasser, T.C., Ogden, R.W., Holzapfel, G.A.: Hyperelastic modelling of arterial layers with distributed collagen fibre orientations. J. R. Soc. Interface 3(6), 15–35 (2006) Gasser, T.C., Ogden, R.W., Holzapfel, G.A.: Hyperelastic modelling of arterial layers with distributed collagen fibre orientations. J. R. Soc. Interface 3(6), 15–35 (2006)
42.
go back to reference Guo, Z.Y., Peng, X.Q., Moran, B.: A composites-based hyperelastic constitutive model for soft tissue with application to the human annulus fibrosus. J. Mech. Phys. Solids 54(9), 1952–1971 (2006)MATH Guo, Z.Y., Peng, X.Q., Moran, B.: A composites-based hyperelastic constitutive model for soft tissue with application to the human annulus fibrosus. J. Mech. Phys. Solids 54(9), 1952–1971 (2006)MATH
43.
go back to reference Pao, Y.-H.: Electromagnetic forces in deformable continua. In: Nevat-Nasser, S. (ed.) Mechanics Today, pp. 209–305. Pergamon Press Inc., New York (1978) Pao, Y.-H.: Electromagnetic forces in deformable continua. In: Nevat-Nasser, S. (ed.) Mechanics Today, pp. 209–305. Pergamon Press Inc., New York (1978)
44.
go back to reference Kovetz, A.: Electromagnet Theory. Oxford University Press, New York (2000)MATH Kovetz, A.: Electromagnet Theory. Oxford University Press, New York (2000)MATH
45.
go back to reference Batra, R.C: Elements of continuum mechanics. AIAA Education Series (2006) Batra, R.C: Elements of continuum mechanics. AIAA Education Series (2006)
46.
go back to reference Beheshti, A., Sedaghati, R., Rakheja, S.: Finite deformation analysis of isotropic magnetoactive elastomers. Contin. Mech. Thermodyn. 2020, 1–16 (2020)MATH Beheshti, A., Sedaghati, R., Rakheja, S.: Finite deformation analysis of isotropic magnetoactive elastomers. Contin. Mech. Thermodyn. 2020, 1–16 (2020)MATH
47.
go back to reference Beheshti, A., Sedaghati, R., Rakheja, S.: Development of a small-deformation material model for an isotropic magneto-active elastomer. Acta Mech. 231(6), 2287–2301 (2020)MathSciNetMATH Beheshti, A., Sedaghati, R., Rakheja, S.: Development of a small-deformation material model for an isotropic magneto-active elastomer. Acta Mech. 231(6), 2287–2301 (2020)MathSciNetMATH
48.
go back to reference Spencer, A.J.M.: Continuum Theory of the Mechanics of Fibre-Reinforced Composites. Springer, Wien (1984)MATH Spencer, A.J.M.: Continuum Theory of the Mechanics of Fibre-Reinforced Composites. Springer, Wien (1984)MATH
49.
go back to reference Krupka, J.: Measurement of the complex permittivity, initial permeability, permeability tensor and ferromagnetic linewidth of gyromagnetic materials. Meas. Sci. Technol. 29(9), 092001 (2018) Krupka, J.: Measurement of the complex permittivity, initial permeability, permeability tensor and ferromagnetic linewidth of gyromagnetic materials. Meas. Sci. Technol. 29(9), 092001 (2018)
50.
go back to reference Schubert, G., Harrison, P.: Magnetic induction measurements and identification of the permeability of magneto-rheological elastomers using finite element simulations. J. Magn. Magn. Mater. 404, 205–214 (2016) Schubert, G., Harrison, P.: Magnetic induction measurements and identification of the permeability of magneto-rheological elastomers using finite element simulations. J. Magn. Magn. Mater. 404, 205–214 (2016)
51.
go back to reference Lopez-Pamies, O.: A new I-1-based hyperelastic model for rubber elastic materials. C. R. Méc. 338(1), 3–11 (2010)MathSciNetMATH Lopez-Pamies, O.: A new I-1-based hyperelastic model for rubber elastic materials. C. R. Méc. 338(1), 3–11 (2010)MathSciNetMATH
52.
go back to reference Johlitz, M., Diebels, S.: Characterisation of a polymer using biaxial tension tests. Part I: hyperelasticity. Arch. Appl. Mech. 81(10), 1333–1349 (2010)MATH Johlitz, M., Diebels, S.: Characterisation of a polymer using biaxial tension tests. Part I: hyperelasticity. Arch. Appl. Mech. 81(10), 1333–1349 (2010)MATH
53.
go back to reference van den Bogert, P.A.J., de Borst, R.: On the behaviour of rubberlike materials in compression and shear. Arch. Appl. Mech. 64(2), 136–146 (1994)MATH van den Bogert, P.A.J., de Borst, R.: On the behaviour of rubberlike materials in compression and shear. Arch. Appl. Mech. 64(2), 136–146 (1994)MATH
54.
go back to reference Frollo, I., Krafčík, A., Andris, P., Přibil, J., Dermek, T.: Circular samples as objects for magnetic resonance imaging—mathematical simulation, experimental results. Meas. Sci. Rev. 15(6), 313–318 (2015) Frollo, I., Krafčík, A., Andris, P., Přibil, J., Dermek, T.: Circular samples as objects for magnetic resonance imaging—mathematical simulation, experimental results. Meas. Sci. Rev. 15(6), 313–318 (2015)
55.
go back to reference Stolbov, O.V., Raikher, Y.L.: Magnetostriction effect in soft magnetic elastomers. Arch. Appl. Mech. 89(1), 63–76 (2018) Stolbov, O.V., Raikher, Y.L.: Magnetostriction effect in soft magnetic elastomers. Arch. Appl. Mech. 89(1), 63–76 (2018)
Metadata
Title
Transversely isotropic magnetoactive elastomers: theory and experiments
Authors
Alireza Beheshti
Ramin Sedaghati
Subhash Rakheja
Publication date
21-09-2020
Publisher
Springer Berlin Heidelberg
Published in
Archive of Applied Mechanics / Issue 1/2021
Print ISSN: 0939-1533
Electronic ISSN: 1432-0681
DOI
https://doi.org/10.1007/s00419-020-01778-0

Other articles of this Issue 1/2021

Archive of Applied Mechanics 1/2021 Go to the issue

Premium Partners