Stochastic modeling of nonlinear, anisotropic and inhomogenous magnetic material using Karhunen-Loeve Expansion


Temperature evolution of dielectric constant showing the characteristic temperatures in RFE.

In material science, the enthusiasm of  discovering new materials and
enhancing properties of existing materials never melts. Ferroelectric ceramics belong a group of dielectric materials which have a spontaneous polarization that can be reversed by the application of an external field. Since the pioneering research results
by Curie brothers, ferroelectric materials have been used widely in industrial
applications. For many applications, it is necessary to enhance some
properties of ferroelectrics, e.g., higher permittivity, lower temperature sensitivity, and better piezoelectric constants.

Relaxor ferroelectrics (Relaxors) are a group of ferroelectrics with
distinctive properties such as large field induced strains and high dielectric permittivity comparing with normal ferroelectric materials. The outstanding electro-mechanical coupling constants of relaxors make them useful as  core parts in sensors (mechanical to electrical) and actuators (electrical to mechanical). Since the first  relaxor-behaved material, lead magnesium niobate (PMN), was reported in 1961, both significant theoretical and experimental results have been discovered, as described by Prof. Kleemann "The enigma of relaxor ferroelectrics seems to come close to be deciphered". Apart from experimental and theoretical studies, numerical simulation has emerged as a new tool to study the behavior of functional materials, owing to the rapid development of computer technology. Phase field method is one of the most advanced  tool for material modeling.

Domain configuration of relaxor ferrroelectrics with different random field strength. a)0 kV/mm, b)1 kV/mm, c)5 kV/mm, d)10 kV/mm.

Recent Results

  1. The random field has been successfully implemented into the model. The Box-Muller method is chosen as a generator for the random field. A parameter study for different values for the variance of the Gaussian distribution has been carried out.
  2. The validity of the model has been checked for several cases including pure electric loading, pure mechanical loading and electro-mechanical coupling loading. The ferroelectric/relaxor (FE/RE) core-shell structure have been simulated by this model, and the results showed good consistency with piezoresponse force microscopy observations.
  3. The FE/RE bilayer structure has been simulated by this model and hysteresis loops have been obtained.

Research interest

finite element method; relaxor ferroelectric modelling; phase-field


M.Eng. Shuai Wang


Dolivostr. 15

D-64293 Darmstadt



+49 6151 16 - 24390


+49 6151 16 - 24404




wangshuai1212 (at) gmail...

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