Constitutive Modeling of Ferroelectrics Including Nonlinear Electrocaloric and Thermomechanical Effects

Wingen, Marius; Ricoeur, Andreas

doi:10.1016/j.matpr.2016.01.104

Cited by 1 publication

(1 citation statement)

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“…The dissipative work rateẊ feeds the irreversible processes of the inelastic zone which, compared to the whole crystal, represents just a very small area being overswept during domain wall motion. The control volume, on the other hand, is reversible and loses this energy, which must therefore be considered by a negative sign [1]: After all, the domain wall is nothing but an interface needing energy for a phase transition, being supplied by the adjacent phases which are thus cooling down. The term in braces in Eq.…”

Section: Balance Of Energymentioning

confidence: 99%

The electrocaloric effect in ferroelectrics: nonlinear modeling and simulation

Wingen

Ricoeur

2015

Proc Appl Math and Mech

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In this paper, the theoretical background of a physically based constitutive model is presented. In addition to the nonlinear ferroelectric behavior, the model considers the nonlinear coupling of thermal and electromechanical fields. Results are presented in terms of a simple analytical solution for a single domain configuration. with the material tensors Cijkl, κ il , γ, e lij , β ij and k l denoting the elasticity tensor, the dielectric tensor, the thermal coefficient, the piezoelectric tensor, the thermal stress and the pyroelectric coefficients, the constitutive equations of a nonlinear thermo-ferroelectric material are obtained aṡwhere σ ij and ij are stresses and strains, D i and E i the electric displacement and electric field and θ andS the temperature and specific entropy. The superscript "rev" refers to reversible quantities and "irr" indicates irreversible changes of state. Balance of energyFor describing a thermoelectromechanical three-field problem, a third field equation is required, which is obtained from the 1 st law of thermodynamics. In the quasistatic case it readṡpostulating that the change of internal energyU is equal to the sum of of the electromechanical work ratėthe specific heat flow ratėwhereq v is an internal heat source andq A j,j a heat flux across the boundary, and the dissipationẊ due to ferroelectric domain switching. The latter requires some considerations concerning its interpretation. The dissipative work rateẊ feeds the irreversible processes of the inelastic zone which, compared to the whole crystal, represents just a very small area being overswept during domain wall motion. The control volume, on the other hand, is reversible and loses this energy, which must therefore be considered by a negative sign [1]:

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Section: Balance Of Energymentioning

confidence: 99%