Two models to simulate rate-dependent domain switching effects—application to ferroelastic polycrystalline ceramics

Abstract

The aim of this paper is to study rate-dependent switching in ferroelastic materials. More specifically, a micro-mechanically motivated model is embedded into an iterative three-dimensional and electromechanically coupled finite-element framework. An established energy-based criterion serves for the initiation of domain switching processes as based on reduction in (local) Gibbs free energy. Subsequent nucleation and propagation of domain walls is captured via a linear kinetics theory with rate-dependent effects being incorporated in terms of a deformation-dependent limit-time parameter. With this basic model in hand, two different switching formulations are elaborated in this work: on the one hand, a straightforward volume-fraction ansatz is applied with the volume-fraction value depending on the limit-time parameter; on the other hand, a reorientation-transformation formulation is proposed, whereby the orientation tensor itself is assumed to depend on the limit-time parameter. Macroscopic behaviour such as stress versus strain curves or stress versus electrical displacement graphs are obtained by applying straightforward volume-averaging techniques to the three-dimensional finite-element-based simulation results which provides important insights into the rate-dependent response of the investigated ferroelastic materials.

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.…”

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

“…In the current thermodynamic formulation, the basic energetic constitutive quantity is the electromechanical stored energy density f = ψ + h from (19). For example, in the case of a classic rigid dielectric solid,…”

“…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].…”

Micromechanical modelling of switching phenomena in polycrystalline piezoceramics: application of a polygonal finite element approach

“…Alternative modelling concepts, however, incorporated such interactions present in crystalline materials by means of the so-called Eshelby inclusion method in order to provide a mean field estimate of the effective response [15][16][17][18]. Intergranular effects are explicitly considered in several models in terms of related finite element formulations [19][20][21][22][23][24][25]. The local and average energy release during domain switching in ferroelectrics are rigorously derived in [26] with application to advanced polarisation switching models.…”