Skip to main content
Log in

Anisotropic multiferroic ellipsoidal particulate composites

  • Original
  • Published:
Archive of Applied Mechanics Aims and scope Submit manuscript

Abstract

The objective of this work is to investigate the magnetoelectricity (ME) of an ellipsoidal particulate composite made of piezoelectric and piezomagnetic phases. We employ a micromechanical model, the Mori–Tanaka mean-field method, to evaluate the effects of crystallographic orientations of the constituents, and the aspect ratio, volume fraction, and orientations of the ellipsoids. We compare this micromechanical solution with those predicted by the finite element analysis, which provides the benchmark results for a periodic array of inclusions. Based on this model, we find the optimal aspect ratio and volume fractions of the inclusion when the ellipsoids are poled along the normal direction. Further, we show that, for the case of \(\hbox {CoFe} _{2}\hbox {O}_{4}\)\(\hbox {BaTiO}_{{3}}\) ellipsoidal particulate composite, the ME voltage coefficient can be enhanced at the optimal orientation as compared to those at normal cut.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

References

  1. Aboudi, J.: Micromechanical analysis of fully coupled electro-magneto-thermo-elastic multiphase composites. Smart Mater. Struct. 10, 867–877 (2001)

    Google Scholar 

  2. Alshits, V.I., Darinskii, A.N., Lothe, J.: On the existence of surface waves in half-infnite anisotropic elastic media with piezoelectric and piezomagnetic properties. Wave Motions 16, 265–284 (1992)

    MATH  Google Scholar 

  3. Arfken, G.B., Weber, H.J.: Mathematical Methods for Physicists, p. 199. Academic Press, San Diago (2001)

    MATH  Google Scholar 

  4. Avakian, A., Gellmann, R., Ricoeur, A.: Nonlinear modeling and finite element simulation of magnetoelectric coupling and residual stress in multiferroic composites. Acta Mech. 226, 2789–2806 (2015)

    MathSciNet  MATH  Google Scholar 

  5. Avakian, A., Ricoeur, A.: Constitutive modeling of nonlinear reversible and irreversible ferromagnetic behaviors and application to multiferroic composites. J. Intell. Mater. Syst. Struct. 27, 2536–2554 (2016)

    Google Scholar 

  6. Bayrashev, A., Robbins, W.P., Ziaie, B.: Low frequency wireless powering of microsystems using piezoelectric–magnetostrictive laminate composites. Sens. Actuators 114, 244–249 (2004)

    Google Scholar 

  7. Benveniste, Y.: Magnetoelectric effect in fibrous composites with piezoelectric and piezomagnetic phases. Phys. Rev. B 51, 16424–16427 (1995)

    Google Scholar 

  8. Bichurin, M.I., Petrov, V.M., Averkin, S.V., Liverts, E.: Present status of theoretical modeling the magnetoelectric effect in magnetostrictive-piezoelectric nanostructures. Part I: low frequency electromechanical resonance ranges. J. Appl. Phys. 107, 053904 (2010)

    Google Scholar 

  9. Camacho-Montes, H., Sabina, F.J., Bravo-Castillero, J., Guinovart-Díaz, R., Rodríguez-Ramos, R.: Magnetoelectric coupling and cross-property connections in a square array of a binary composite. Int. J. Eng. Sci. 47, 294–312 (2009)

    Google Scholar 

  10. Eerenstein, W., Mathur, N.D., Scott, J.F.: Multiferroic and magnetoelectric materials. Nature 442, 759–765 (2006)

    Google Scholar 

  11. Fiebig, M.: Revival of the magnetoelectric effect. J. Phys. D Appl. Phys. 38, R123–R152 (2005)

    Google Scholar 

  12. Huang, J.H., Kuo, W.-S.: The analysis of piezoelectric/piezomagnetic composite materials containing ellipsoidal inclusions. J. Appl. Phys. 81, 1378–1386 (1997)

    Google Scholar 

  13. Kim, J.-Y.: Micromechanical analysis of effective properties of magneto-electro-thermo-elastic multilayer composites. Int. J. Eng. Sci. 49, 1001–1018 (2011)

    MATH  Google Scholar 

  14. Kuo, H.-Y.: Multicoated elliptic fibrous composites of piezoelectric and piezomagnetic phases. Int. J. Eng. Sci. 49, 561–575 (2011)

    MATH  Google Scholar 

  15. Kuo, H.-Y.: Fibrous composites of piezoelectric and piezomagnetic phases: generalized plane strain with transverse electromagnetic fields. Mech. Mater. 75, 103–110 (2014)

    Google Scholar 

  16. Kuo, H.-Y., Bhattacharya, K.: Fibrous composites of piezoelectric and piezomagnetic phases. Mech. Mater. 60, 159–170 (2013)

    Google Scholar 

  17. Kuo, H.-Y., Chen, C.-Y.: Decoupling transformation for piezoelectric–piezomagnetic fibrous composites with imperfect interfaces. Int. J. Solids Struct. 54, 111–120 (2015)

    Google Scholar 

  18. Kuo, H.-Y., Hsin, K.-H.: Functionally graded piezoelectric–piezomagnetic fibrous composites. Acta Mech. 229, 1503–1516 (2018)

    MathSciNet  Google Scholar 

  19. Kuo, H.-Y., Huang, T.-Y.: Effective moduli of multiferroic fibrous composites with spring-type imperfect interfaces under generalized plane strain with transverse electromagnetic fields. Int. J. Solids Struct. 80, 456–464 (2016)

    Google Scholar 

  20. Kuo, H.-Y., Kuo, Y.-M.: Magnetoelectricity in multiferroic particulate composites with arbitrary crystallographic orientation. Smart Mater. Struct. 21, 105038 (2012)

    Google Scholar 

  21. Kuo, H.-Y., Pan, E.: Effective magnetoelectric effect in multicoated circular fibrous multiferroic composites. J. Appl. Phys. 109, 104901 (2011)

    Google Scholar 

  22. Kuo, H.-Y., Wang, Y.-L.: Optimization of magnetoelectricity in multiferroic fibrous composites. Mech. Mater. 50, 88–99 (2012)

    Google Scholar 

  23. Kuo, H.-Y., Wang, K.-H.: Size-dependent effective behaviors of multiferroic fibrous composites with interface stress. Int. J. Solids Struct. 106–107, 164–173 (2017)

    Google Scholar 

  24. Kuo, H.-Y., Slinger, A., Bhattacharya, K.: Optimization of magnetoelectricity in piezoelectric–magnetostrictive bilayers. Smart Mater. Struct. 19, 125010 (2010)

    Google Scholar 

  25. Kumar, A., Sharma, G.L., Katiyar, R.S., Pirc, R., Blinc, R., Scott, J.F.: Magnetic control of large room-temperature polarization. J. Phys. Condens. Matter 21, 382204 (2009)

    Google Scholar 

  26. Labusch, M., Etier, M., Lupascu, D.C., Schröder, J., Keip, M.-A.: Product properties of a two-phase magneto-electric composite: synthesis and numerical modeling. Comput. Mech. 54, 71–83 (2014)

    MathSciNet  MATH  Google Scholar 

  27. Labusch, M., Schröder, J., Lupascu, D.C.: A two-scale homogenization analysis of porous magneto-electric two-phase composites. Arch. Appl. Mech. 89, 1123–1140 (2019)

    Google Scholar 

  28. Lee, J., Boyd IV, J.G., Lagoudas, D.C.: Effective properties of three-phase electro-magneto-elastic composites. Int. J. Eng. Sci. 43, 790–825 (2005)

    MathSciNet  MATH  Google Scholar 

  29. Li, J.Y.: Magnetoelectroelastic multi-inclusion and inhomogeneity problems and their applications in composite materials. Int. J. Eng. Sci. 38, 1993–2001 (2000)

    Google Scholar 

  30. Li, J.Y., Dunn, M.L.: Micromechanics of magnetoelectroelastic composite materials: average fields and effective behaviour. J. Intell. Mater. Syst. Struct. 9, 404–416 (1998a)

    Google Scholar 

  31. Li, J.Y., Dunn, M.L.: Anisotropic coupled-field inclusion and inhomogeneity problems. Philos. Mag. A 77, 1341–1350 (1998b)

    Google Scholar 

  32. Liu, G., Nan, C.-W., Cai, N., Lin, Y.: Calculations of giant magnetoelectric effect in multiferroic composites of rare-earth-iron alloys and PZT by finite element method. Int. J. Solids Struct. 41, 4423–4434 (2004)

    MATH  Google Scholar 

  33. Michel, J., Moulinec, H., Suquet, P.: Effective properties of composite materials with periodic microstructure: a computational approach. Comput. Meth. Appl. Mech. Eng. 172, 109–143 (1999)

    MathSciNet  MATH  Google Scholar 

  34. Nan, C.-W.: Magnetoelectric effect in composites of piezoelectric and piezomagnetic phases. Phys. Rev. B 50, 6082–6088 (1994)

    Google Scholar 

  35. Nan, C.-W., Bichurin, M.I., Dong, S., Viehland, D., Srinivasan, G.: Multiferroic magnetoelectric composites: historical perspective, status, and future directions. J. Appl. Phys. 103, 031101 (2008)

    Google Scholar 

  36. Nye, J.F.: Physical Properties of Crystals. Oxford University Press, Oxford (1985)

    Google Scholar 

  37. Ricoeur, A., Lange, S.: Constitutive modeling of polycrystalline multiconstituent and multiphase ferroic materials based on a condensed approach. Arch. Appl. Mech. 89, 973–994 (2019)

    Google Scholar 

  38. Schröder, J., Keip, M.-A.: Two-scale homogenization of electromechanically coupled boundary value problems. Comput. Mech. 50, 229–244 (2012)

    MathSciNet  MATH  Google Scholar 

  39. Srinivas, S., Li, J.Y., Zhou, Y.C., Soh, A.K.: The effective magnetoelectroelastic moduli of matrix-based multiferroic composites. J. Appl. Phys. 99, 043905 (2006)

    Google Scholar 

  40. Tang, T., Yu, W.: Variational asymptotic homogenization of heterogeneous electromagnetoelastic materials. Int. J. Eng. Sci. 46, 741–757 (2008)

    MathSciNet  MATH  Google Scholar 

  41. Tang, T., Yu, W.: Micromechanical modeling of the multiphysical behavior of smart materials using the variational asymptotic method. Smart Mater. Struct. 18, 125026 (2009)

    Google Scholar 

  42. Terada, K., Saiki, I., Matsui, K., Yamakawa, Y.: Two-scale kinematics and linearization for simultaneous two-scale analysis of periodic heterogeneous solids at finite strain. Comput. Methods Appl. Mech. Eng. 192, 3531–3563 (2003)

    MathSciNet  MATH  Google Scholar 

  43. Wang, Y., Or, S.W., Chan, H.L.W., Zhao, X., Luo, H.: Enhanced magnetoelectric effect in longitudinal-transverse mode Terfenol-D/Pb(\(\text{ Mg }_{1/3}\)Nb\(_{2/3}\))\(\text{ O }_{{3}}\)-\(\text{ PbTiO }_{{3}}\) laminate composites with optimal crystal cut. J. Appl. Phys. 103, 124511 (2008)

    Google Scholar 

  44. Yang, P., Zhao, K., Yin, Y., Wan, H.G., Shu, J.S.: Magnetoelectric effect in magnetostrictive/piezoelectric laminate composite Terfenol-D/ \(\text{ LiNbO }_{{3}}\)[(zxtw)129\(^{\circ }\)/30\(^{\circ }\)]. Appl. Phys. Lett. 88, 172903 (2006)

    Google Scholar 

Download references

Acknowledgements

We are grateful to the financial support of National Science Council, Taiwan, under Contract No. NSC 100-2628-E-009-022-MY2.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Hsin-Yi Kuo.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Kuo, HY., Ling, YH. Anisotropic multiferroic ellipsoidal particulate composites. Arch Appl Mech 90, 369–383 (2020). https://doi.org/10.1007/s00419-019-01614-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00419-019-01614-0

Keywords

Navigation