Finite-Element Modeling of the Hysteresis Behavior of Tetragonal and Rhombohedral Polydomain Ferroelectroelastic Structures

Abstract

The influence of the domain structure's initial topology and its evolution on the hysteresis curves of tetragonal and rhombohedral polydomain structures of ferroelectroelastic materials is studied. Based on the analysis of electrical and mechanical compatibility conditions, all possible variants of representative volume elements of tetragonal and rhombohedral second-rank-domain laminate structures were obtained and used in simulations. Considerable local inhomogeneity of stress and electric fields within the representative volume, as well as domain interaction, necessitates the use of numerical methods. Hysteresis curves for laminated domain patterns of the second rank were obtained using finite-element homogenization. The vector-potential finite-element formulation as the most effective method was used for solving nonlinear coupled boundary value problems of ferroelectroelasticity. A significant anisotropy of the hysteresis properties of domain structures was established both within individual phases and when comparing the tetragonal and rhombohedral phases. The proposed approach describes the effects of domain hardening and unloading nonlinearity.

Keywords: domain; domain hardening; domain structure evolution; ferroelectric/ferroelastic; finite-element homogenization; hysteresis; modeling; rhombohedral phase; single crystal; tetragonal phase.

Figure 1

A 90-degree domain wall as an example of a non-180-degree rank-1 domain wall and its characteristic vectors.

Figure 2

Boundary conditions on the RVE of ferroelectroelastic material under electric loading in the [001] direction for the electric vector-potential formulation.

Figure 3

RVEs of compatible topologies for rhombohedral domain structures.

Figure 4

(a) Dielectric hysteresis and (b) electromechanical hysteresis for three loading directions for topology {1221} of the tetragonal phase and residual field distributions of (c) micro-stress intensity, (d) remanent polarization, and (e) plastic strain intensity under loading in the [100] direction and subsequent unloading.

Figure 5

(a) Dielectric hysteresis and (b) electromechanical hysteresis for three loading directions for topology {1458} of the rhombohedral phase and residual field distributions of (c) micro-stress intensity, (d) remanent polarization and (e) plastic strain intensity under loading in the [100] direction and subsequent unloading.

Figure 6

Comparison of (a) dielectric hysteresis and (b) electromechanical hysteresis for RVEs of tetragonal T{1324} and rhombohedral R{1342} topologies under loading in directions [100], [010], and [001], and the residual field distribution of remanent polarization magnitude for (c) T{1324} and (d) R{1342} topologies under electric loading in the [010] direction and subsequent unloading.