A constitutive model for ferroelectric polycrystals

A rate-dependent two-dimensional free energy model for ferroelectric single crystals

“…First, we simulate a quasistatic polarization hysteresis loop of a BaTiO 3 single crystal recently observed by Burcsu et al [8], see Figure 5. The material parameters in (14) are chosen to fit the experimental observation. The applied electric field is sinusoidal, and its amplitude and frequency are E amp = 1.1 MV/m and f E = 0.05 Hz, respectively.…”

“…However, their model showed a deficiency in a comparison with measurements of uniaxial material response [22]. In order to solve the inconsistency, Hwang et al [17], Chen and Lynch [11,12], Huber et al [14] incorporated the local interaction between adjacent regions of material with differing polarization states, which was neglected in the original work of Hwang et al Kim and Jiang [20] also proposed a similar constitutive and finite element model adopting a Reuss type micromechanics assumption. Their model consists of Helmholtz free energy, switching criterion and switching kinetics; the rate of switching is assumed to be proportional to the thermodynamic driving force.…”

Continuum thermodynamics of ferroelectric domain evolution: Theory, finite element implementation, and application to domain wall pinning

“…As for the electric potential drop, this feature of the solutions has interesting implications for sharp interface and other larger scale phenomenological constitutive theories for domain switching in ferroelectrics. Sharp interface theory Kessler and Balke (2001), single crystal continuum slip theory Huber et. al (1999), and polycrystalline flow theory Landis (2002b) have each identified the contribution to the driving force for switching associated with the changes in material properties due to switching.…”

“…We have included the caveat of "approximate normality" due to the previous results shown in Figure 7, illustrating the dependence of G c on the axial stress parallel to the domain wall. It may be possible (and valuable) to construct a rigorous normality framework, but such a theory will differ from that already established in other phenomenological theories (Kessler and Balke, 2001;Huber et al, 1999;Landis, 2002).…”

Comparison of phenomenological and laminate‐based models for rate‐dependent switching in ferroelectric continua

“…Models for switching behavior of ferroelectrics include phase-field models [3][4][5][6][7], phenomenological models [1,[8][9][10][11][12], and micromechanical models [13][14][15][16][17][18][19]. Of particular interest in the latter class are so-called laminate-based approaches [2,[20][21][22][23][24].…”