Continuum Mechanics and Thermodynamics

, Volume 31, Issue 3, pp 741–750 | Cite as

A non-isothermal phase-field model for piezo–ferroelectric materials

  • A. Borrelli
  • D. GrandiEmail author
  • M. Fabrizio
  • M. C. Patria
Original Article


We propose a model for the study of piezo–ferroelectric materials, based on the Ginzburg–Landau approach to the ferroelectric transition, in which the inelastic deformation is a direct function of the ferroelectric polarization. The non-isothermal effects related to the phase change and other dissipative phenomena are considered by a suitable energy balance equation, according to the restrictions of the second principle. The hysteresis phenomena for polarization and inelastic strain are considered from both the energetic perspective of the vector Ginzburg–Landau equation and the dissipation-dominated perspective of the rate-independent evolutionary equations.


Ferroelectric Ferroelastic Hysteresis Phase field Non-isothermal model 


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  • A. Borrelli
    • 1
  • D. Grandi
    • 1
    Email author
  • M. Fabrizio
    • 2
  • M. C. Patria
    • 1
  1. 1.Dipartimento di Matematica e InformaticaUniversità degli Studi di FerraraFerraraItaly
  2. 2.Dipartimento di MatematicaUniversità di BolognaBolognaItaly

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