On implicit constitutive relations in elastic ferroelectrics



A considerable effort is being made to foster the use of implicit constitutive relations in mechanics of the continuous medium. From this point of view, the class of elastic bodies extends to a much larger category than the classical Cauchy and Green elastic bodies. In this work, a subclass of the recently proposed classes of electro-elastic bodies is taken into consideration to propose models for elastic ferroelectrics. These models, even though they are not based on thermodynamical arguments, seem capable enough to provide the hysteretic behavior of ferroelectric materials.


Implicit constitutive equations Electro-elastic bodies Ferroelectrics 

Mathematics Subject Classification

74A20 82D45 


  1. 1.
    Arvanitakis, A.I., Kalpakides, V.K., Hadjigeorgiou, E.P.: Electric field gradients and spontaneous quadrupoles in elastic ferroelectrics. Acta Mech. 218, 269–294 (2011)CrossRefMATHGoogle Scholar
  2. 2.
    Bustamante, R., Rajagopal, K.R.: On a new class of electro-elastic bodies I. In: Proc. R. Soc. A 469, 20120521 (2013)Google Scholar
  3. 3.
    Bustamante R., Rajagopal K.R.: On a new class of electro-elastic bodies II. Boundary value problems. In: Proc. R. Soc. A 469, 20130106 (2013)Google Scholar
  4. 4.
    Bustamante, R., Rajagopal, K.R.: Implicit constitutive relations for nonlinear magnetoelastic bodies. In: Proc. R. Soc. A 471, 20140959 (2015)Google Scholar
  5. 5.
    Bustamante, R., Dorfmann, A., Ogden, R.W.: On electric body forces and Maxwell stresses in an electroelastic solid. Int. J. Eng. Sci. 47, 1131–1141 (2009)MathSciNetCrossRefMATHGoogle Scholar
  6. 6.
    Dorfmann, A., Ogden, R.W.: Nonlinear electroelasticity. Acta Mech. 174, 167–183 (2005)CrossRefMATHGoogle Scholar
  7. 7.
    Kafadar, C.B.: Theory of multipoles in classical electromagnetism. Int. J. Eng. Sci. 9, 831–853 (1971)CrossRefMATHGoogle Scholar
  8. 8.
    Mindlin, R.D.: Polarization gradient in elastic dielectrics. Int. J. Solids Struct. 4, 637–642 (1968)CrossRefMATHGoogle Scholar
  9. 9.
    Müller, R., Gross, D., Schrade, D., Xu, B.X.: Phase field simulation of domain structures in ferroelectric materials within the context of inhomogeneity evolution. Int. J. Fract. 147, 173–180 (2007)CrossRefMATHGoogle Scholar
  10. 10.
    Rajagopal, K.R.: On implicit constitutive theories. Appl. Math. 48, 279–319 (2003)MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Rajagopal, K.R.: The elasticity of elasticity. Z. Agew. Math. Phys. 58, 309–317 (2007)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Rabe, K., Ahn, C.H., Triscone, J.-M. (eds.): Physics of Ferroelectrics. A Modern Approach, Topics Appl. Physics, pp. 1–30. Springer–Verlag, Berlin (2007)Google Scholar
  13. 13.
    Tiersten, H.F.: On the nonlinear equations of thermo-electroelasticity. Int. J. Eng. Sci. 9, 587–604 (1971)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Toupin, R.A.: The elastic dielectric. J. Rat. Mech. Anal. 5, 849–915 (1956)MathSciNetMATHGoogle Scholar
  15. 15.
    Zhang, W., Bhattacharya, K.: A computational model of ferroelectric domains. Part I: model formulation and domain switching. Acta Mater. 53(1), 185–198 (2005)CrossRefGoogle Scholar
  16. 16.
    Wolfram Mathematica v.9.0, Wolfram Research Inc. (2012)Google Scholar
  17. 17.
    Grindlay, I.: An Introduction to the Phenomenological Theory of Ferroelectricity. Pergamon, Oxford (1970)Google Scholar
  18. 18.
    Lines, M.E., Glass, A.M.: Principles and Applications of Ferroelectrics and Related Materials. Oxford university Press, Oxford (1977)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Department of Materials Science and EngineeringUniversity of IoanninaIoanninaGreece

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