Three-dimensional nonlocal models of deformable ferroelectrics: a thermodynamically consistent approach

What is it about?

Within the framework of continuum thermodynamics, the paper develops a scheme for the study of piezo-ferroelectric materials undergoing large deformations. The ferroelectric polarization is decomposed into the sum of a reversible and a residual part which is considered as an independent variable. The modeling of the constitutive properties is made simpler by using referential, Euclidean invariant quantities. Constitutive functions depend on a set of variables that includes their time derivatives and gradients, and therefore must be consistent with a nonlocal statement of the second law of thermodynamics where the entropy production is represented as the sum of a non-negative supply and a flux. Both terms are also assigned by means of constitutive functions. A new and quite general model relating the residual-polarization rate and the `electric Gibbs free entropy' is established. This thermodynamic potential is modeled according to the Landau-Devonshire approach and appropriate explicit expressions are proposed for anisotropic materials. Consequently, a new explicit evolution equation for the polarization vector is obtained for both high and low temperatures. In particular, the Landau-Devonshire scalar model is recovered in the isotropic case. Under the assumption of small strains and small polarization gradients, hysteresis and electromechanical coupling are described for a simple one-dimensional model. The advantage of our original approach is that a few constitutive parameters provide a good fit of material behavior.

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Why is it important?

The advantages of our model are twofold. On the one hand it shows that the thermodynamic consistency, in addition to ascertaining the physical admissibility of the constitutive functions, is also a guideline to the setting of the material model. On the other it provides a simple scheme for the selection of the parameters characterizing the material behavior.

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