Computational modeling of rate-dependent domain switching in piezoelectric materials

Abstract

In this contribution a micromechanically motivated model for rate-dependent switching effects in piezoelectric materials is developed. The proposed framework is embedded into a three-dimensional finite element setting whereby each element is assumed to represent an individual grain. Related dipole (polarization) directions are thereby initially randomly oriented at the element level to realistically capture the originally un-poled state of grains in the bulk ceramics. The onset of domain switching processes is based on a representative energy criterion and combined with a linear kinetics theory accounting for time-dependent propagation of domain walls during switching processes. In addition, grain boundary effects are incorporated by making use of a macromechanically motivated probabilistic approach. Standard volume-averaging techniques with respect to the response on individual grains in the bulk ceramics are later on applied to obtain representative hysteresis and butterfly curves under macroscopically uniaxial loading conditions at different loading frequencies. It turns out that the simulations based on the developed finite element formulation nicely match experimental data reported in the literature.

Computational modelling of microcracking effects in polycrystalline piezoelectric ceramics

“…Nevertheless, it is obvious that realistic grain boundaries inhere various additional and more complex phenomena under fatigue loading than those accounted for in this contribution, wherein only permittivities and stiffnesses were included. However, based on this first attempt towards an integral modelling of a micro-cracked piezoelectric mesostructure, it is of particular interest to incorporate nonlinear effects in the bulk such as phase transformations; see [16,2,18] and references cited in the these works.…”

“…Under loading conditions within the fatigue range, amorphous structures occur in these intergranular zones [15], which suggests to account solely for reduced coupling effects. Different thermodynamically motivated constitutive models for the grain behaviour have been proposed, see for example [10,11,29,30,12,17], most of them additionally incorporating switching phenomena; in view of numerical applications based on an energy-related switching criterion, the reader is also referred to [2,18] and references cited in these works.…”

Constitutive modelling of rate-dependent domain switching effects in ferroelectric and ferroelastic materials

“…In order to account for an un-poled virgin state within the subsequently elaborated finite element examples, the underlying orientation-vector m will-for each individual finite element-be randomly initiated by means of Eulerian angles from which P s | t 0 and ε s | t 0 can be computed. For details of implementation and further background information the reader is refer to our previous works, Arockiarajan et al [12][13][14].…”

“…In view of such time-dependent phase-transformation, a linear kinetics theory is applied in this work; see Delibas et al [15] and Arockiarajan et al [14,16] for detail elaborations. In this regard, a duration time value ( t l ) is introduced characterising the time interval needed to complete a switching process after its initiation.…”

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].…”