Author details

Advantages and disadvantages of each of the considered models were presented earlier. Each of the models has a number of parameters that influence on the shape of the hysteresis loops. To determine these parameters, it is necessary to compare the calculated and experimental data. However, in the mathematical plan, this model belongs to the class of inverse problems

To sum up, it can be noted that the one-dimensional models allow describing hysteresis dependences of irreversible polarization processes. The more accurate the model is based on the physics of the phenomenon, the more accurate the results of its work. For example, those models that include lot of domains are more accurate in describing quantitative dependencies. However, analysis shows that at the present moment a universal mathematical model of the polarization and deformation of polycrystalline ferroelectric materials has not yet been developed, which would accurately reflect the data of the experimental dependences. Many problems that are importance remain unresolved. Unresolved problems

• existing models do not reflect functional dependencies on the effects of any loading components with simultaneous exposure to electric fields and mechanical loads;

• the question of the validity of the application of the developed models to thin films

• there are no studies of how the anisotropy of the material changes with the simultaneous

• very poorly represented models, which take into account the effect of neighboring

• there are practically no studies related to the analysis of the similarity and differences in the existing models of Preisach, Rayleigh, Giles-Atherton, plasticity materials, except for [70, 71];

• in fact there is no mathematical analysis of the effect of model parameters on the final

• very poorly represented models, which use the functions of the density of the distribution

One-dimensional models that reflect the hysteretic properties of polycrystalline ferroelectric media on the external effects of high-intensity electric and mechanical fields are considered. The bases of construction of each model are disassembled. The fundamentals of the construction of each of the well-known Rayleigh models, evolution models, models of plasticity theory, Preisach models, models of orientation switching, energy switching models, the Giles-Atherton model are analyzed and the results of their work in the form of hysteresis loops are presented. The main

• small loops of dielectric and strain hysteresis have been poorly investigated;

action of an electric field and mechanical stresses;

result, there is no formulation of a minimum set of parameters;

domains on current switching;

and has a number of specific difficulties.

include the following:

64 Ferroelectrics and Their Applications

remains open;

of domains.

5. Conclusions

Alexander Skaliukh

Address all correspondence to: a.s.skaliukh@gmail.com

Southern Federal University, Rostov on Don, Russia
