The purpose of the paper is to establish vector-valued rate-type models for the hysteretic properties in deformable ferroelectrics within the framework of continuum thermodynamics. Unlike electroelasticity and piezoelectricity, in ferroelectricity both the polarization and the electric field are simultaneously independent variables so that the constitutive functions depend on both. This viewpoint is naturally related to the fact that an hysteresis loop is a closed curve in the polarization–electric field plane. For the sake of generality, the deformation of the material and the dependence on the temperature are allowed to occur. The constitutive functions are required to be consistent with the principle of objectivity and the second law of thermodynamics. Objectivity implies that the constitutive equations are form invariant within the set of Euclidean frames. Among other results, the second law requires a general property on the relation between the polarization and the electric field via a differential equation. This equation shows a dependence fully characterized by two quantities: the free energy and a function which is related to the dissipative character of the hysteresis. As a consequence, different hysteresis models may have the same free energy. Models compatible with thermodynamics are then determined by appropriate selections of the free energy and of the dissipative part. Correspondingly, major and minor hysteretic loops are plotted.

A thermodynamic approach to rate-type models in deformable ferroelectrics

Giorgi C.
;
2021-01-01

Abstract

The purpose of the paper is to establish vector-valued rate-type models for the hysteretic properties in deformable ferroelectrics within the framework of continuum thermodynamics. Unlike electroelasticity and piezoelectricity, in ferroelectricity both the polarization and the electric field are simultaneously independent variables so that the constitutive functions depend on both. This viewpoint is naturally related to the fact that an hysteresis loop is a closed curve in the polarization–electric field plane. For the sake of generality, the deformation of the material and the dependence on the temperature are allowed to occur. The constitutive functions are required to be consistent with the principle of objectivity and the second law of thermodynamics. Objectivity implies that the constitutive equations are form invariant within the set of Euclidean frames. Among other results, the second law requires a general property on the relation between the polarization and the electric field via a differential equation. This equation shows a dependence fully characterized by two quantities: the free energy and a function which is related to the dissipative character of the hysteresis. As a consequence, different hysteresis models may have the same free energy. Models compatible with thermodynamics are then determined by appropriate selections of the free energy and of the dissipative part. Correspondingly, major and minor hysteretic loops are plotted.
File in questo prodotto:
File Dimensione Formato  
10.1007_s00161-020-00953-6.pdf

accesso aperto

Descrizione: Articolo principale
Tipologia: Full Text
Licenza: DRM non definito
Dimensione 923.16 kB
Formato Adobe PDF
923.16 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11379/550257
 Attenzione

Attenzione! I dati visualizzati non sono stati sottoposti a validazione da parte dell'ateneo

Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 10
  • ???jsp.display-item.citation.isi??? 9
social impact