Archive of Applied Mechanics

, Volume 89, Issue 1, pp 63–76 | Cite as

Magnetostriction effect in soft magnetic elastomers

  • Oleg V. Stolbov
  • Yuriy L. RaikherEmail author


We discuss the magnetostriction effect in soft magnetic elastomers: stretching/shrinking of a sample under the action of uniform magnetic field in the absence of mechanical loads. Qualitative analysis shows that the field has a twofold effect on the medium; one of those mechanisms works at the macroscopic scale whereas the other one stems from the mesoscopic processes. Essentially, the latter one is defined by the “architecture” of short-range spatial order existing in the ferromagnet particle assembly. This conclusion is illustrated with the aid of numerical modeling. First, it is done on a 2D elastic array filled with linearly magnetizable particles. It is shown that it is indeed the presence of clusters that controls both the sign and magnitude of magnetostriction in the composite. In other words, two composites with the same matrix/filler content may behave very differently depending on their mesoscale structure. Further on, to get a more realistic description, the modeling is extended to a 3D array of spherical particles randomly distributed in an elastic matrix. Although the general conclusions hold, the quantitative results differ substantially.


Magnetorheological polymers Magnetostriction effect Magntomechanics 



This work has been initiated under auspices of and carries on the line of RFBR-DFG project 16-51-12001 (PAK907). We also acknowledge funding from RFBR projects 17-42-590504 and 17-41-590160.


  1. 1.
    Alekseev, A.G., Kornev, A.E.: Elastic Magnetic Materials. Khimiya, Moscow (1976)Google Scholar
  2. 2.
    Alekseev, A.G., Kornev, A.E.: Magnetic Elastomers. Khimiya, Moscow (1987)Google Scholar
  3. 3.
    Bohlius, S., Brand, H.R., Pleiner, H.: Macroscopic dynamics of uniaxial magnetic gels. Phys. Rev. E 70, 061,411 (2004)CrossRefGoogle Scholar
  4. 4.
    Borcea, L., Bruno, O.: On the magneto-elastic properties of elastomer-ferromagnet composites. J. Mech. Phys. Solids 49, 2877–2919 (2001)MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    Davies, L.C.: Model of magnetorheological elastomers. J. Appl. Phys. 85, 3348–3351 (1999)CrossRefGoogle Scholar
  6. 6.
    Dorfmann, A., Ogden, R.W.: Nonlinear magnetoelastic deformations. Q. J. Mech. Appl. Math. 57, 599–622 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  7. 7.
    Dosoudil, R., Us̆áková, M., Franek, J., Sláma, J., Olah, V.: RF electromagnetic wave absorbing properties of ferrite polymer composite materials. J. Magn. Magn. Mater. 304, 755–757 (2006)CrossRefGoogle Scholar
  8. 8.
    Farshad, M., Benine, A.: Magnetoactive elastomer composites. Polym. Test. 23, 347–353 (2004)CrossRefGoogle Scholar
  9. 9.
    Farshad, M., Le Roux, M.: Compression properties of magnetostrictive polymer composite gels. Polym. Test. 24, 163–168 (2005)CrossRefGoogle Scholar
  10. 10.
    Ginder, J.M., Clark, S.M., Schlotter, W.F., Nichols, M.E.: Magnetostrictive phenomena in magnetorheological elastomers. Int. J. Mod. Phys. B 16, 2412–2418 (2002)CrossRefGoogle Scholar
  11. 11.
    Gollwitzer, C., Turanov, A., Krekhova, M., Lattermann, G.: Measuring the deformation of a ferrogel sphere in a homogeneous magnetic field. J. Chem. Phys. 128, 164,709 (2008)CrossRefGoogle Scholar
  12. 12.
    Gong, X., Liao, G., Xuan, S.: Full-field deformation of magnetorheological elastomer under uniform magnetic field. Appl. Phys. Lett. 100, 211,909 (2012)CrossRefGoogle Scholar
  13. 13.
    Günther, D., Borin, D. Yu., Günther, S., Odenbach, S.: X-ray micro-tomographic characterization of field-structured magnetorheological elastomers. Smart Mater. Struct. 21, 015,005 (2012)Google Scholar
  14. 14.
  15. 15.
    Ivaneyko, D., Toshchevikov, V., Saphiannikova, M., Heinrich, G.: Mechanical properties of magneto-sensitive elastomers: unification of the continuum-mechanics and microscopic theoretical approaches. Soft Matter 10, 2213–2225 (2014)CrossRefGoogle Scholar
  16. 16.
    Jarkova, E., Pleiner, H., Mller, H.W., Brand, H.R.: Hydrodynamics of isotropic ferrogels. Phys. Rev. E 68, 041,706 (2003)CrossRefGoogle Scholar
  17. 17.
    Jolly, M.R., Carlson, J.D., Muñoz, B.C.: A model of the behaviour of magnetorheological materials. Smart Mater. Struct. 5, 607–614 (1996)CrossRefGoogle Scholar
  18. 18.
    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, 613–622 (1996)CrossRefGoogle Scholar
  19. 19.
    Kankanala, S.V., Triantafyllidis, N.: On finitely strained magnetorheological elastomers. J. Mech. Phys. Solids 52, 2869–2908 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  20. 20.
    Laskar, J.M., Philip, J., Baldev, R.: Experimental evidence for reversible zippering of chains in magnetic nanofluids under external magnetic fields. Phys. Rev. E 80, 041,401 (2009)CrossRefGoogle Scholar
  21. 21.
    Lattermann, G., Krekhova, M.: Thermoreversible ferrogels. Macromol. Rapid Commun. 27, 1373–1379 (2006)CrossRefGoogle Scholar
  22. 22.
    Lazarus, N., Meyer, C.D., Bedair, S.S., Slipher, G.A., Kierzewski, I.M.: Magnetic elastomers for stretchable inductors. ACS Appl. Mater. Interfaces 7, 10080–10084 (2015)CrossRefGoogle Scholar
  23. 23.
    Liu, J., Walmer, M.: Process and Magnetic Properties of Rare-Earth Bonded Magnets, Chap. 2, pp. 27–68. Springer, New York (2006)Google Scholar
  24. 24.
    Mitsumata, T., Ikeda, K., Gong, J.P., Osada, Y., Szabo, D., Zrínyi, M.: Magnetism and compressive modulus of magnetic fluid containing gels. J. Appl. Phys. 85, 8451–8455 (1999)CrossRefGoogle Scholar
  25. 25.
    Morozov, K., Shliomis, M., Yamaguchi, H.: Magnetic deformation of ferrogel bodies: Procrustes effect. Phys. Rev. E 79, 040,801 (2009)CrossRefGoogle Scholar
  26. 26.
    Najgebauer, M., Szczygowski, J., Ślusarek, B., Przybylski, M., Kapłon, A., Rolek, J.: Magnetic Composites in Electric Motors, vol. 452. Lecture Notes in Electrical Engineering, chap. 2, pp. 15–28. Springer, Cham (2018)Google Scholar
  27. 27.
    Nikitin, L.V., Mironova, L.S., Stepanov, G.V., Samus, A.N.: The influence of a magnetic field on the elastic and viscous properties of magnetoelastics. Polym. Sci. Ser. A 43, 443–450 (2001)Google Scholar
  28. 28.
    Raikher, Yu.L., Stolbov, O.V.: Magnetodeformational effect in a ferroelastic material. Tech. Phys. Lett. 26, 156–158 (2000)CrossRefGoogle Scholar
  29. 29.
    Raikher, Yu.L., Stolbov, O.V.: Magnetodeformational effect in ferrogel samples. J. Magn. Magn. Mater. 258-259, 477–479 (2003)CrossRefGoogle Scholar
  30. 30.
    Raikher, Yu.L., Stolbov, O.V.: Deformation behavior of an ellipsoidal ferrogel in a uniform magnetic field. J. Appl. Mech. Tech. Phys. 46, 434–443 (2005)CrossRefGoogle Scholar
  31. 31.
    Raikher, Yu.L., Stolbov, O.V.: Numerical modeling of large field-induced strains in ferroelastic bodies: a continuum approach. J. Phys. Condens. Matter 20, 204,126 (2008)Google Scholar
  32. 32.
    Raikher, Yu.L., Stolbov, O.V., Balasoiu, M.: Modelling of magnetodipolar striction in soft magnetic elastomers. Soft Matter 7, 8484–8487 (2011)CrossRefGoogle Scholar
  33. 33.
    Shen, Y., Golnaraghi, M.F., Heppler, G.R.: Experimental research and modeling of magnetorheological elastomers. J. Intell. Mater. Syst. Struct. 15, 27–35 (2004)CrossRefGoogle Scholar
  34. 34.
    Zhou, G.Y.: Shear properties of a magnetorheological elastomer. Smart Mater. Struct. 12, 139–146 (2003)CrossRefGoogle Scholar
  35. 35.
    Zrínyi, M., Barsi, L., Büki, A.: Deformation of ferrogels induced by nonuniform magnetic fields. J. Chem. Phys. 104, 8750–8756 (1996)CrossRefGoogle Scholar
  36. 36.
    Zubarev, AYu., Borin, D. Yu.: Effect of particle concentration on ferrogel magnetodeformation. J. Magn. Magn. Mater. 377, 373–377 (2012)CrossRefGoogle Scholar

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Authors and Affiliations

  1. 1.Laboratory of Physics and Mechanics of Soft MatterInstitute of Continuous Media Mechanics, Russian Academy of Sciences, Ural BranchPermRussia

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