Modeling of the hysteresis behavior of single-crystalline barium titanate with allowance for domain structure evolution

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

“…There are two approaches to modeling the evolution of the spatial domain structure depending on the interpretation of the domain wall: a diffuse interface [ 43 , 44 , 45 , 46 , 47 , 48 , 49 , 68 ] and a sharp interface [ 62 , 63 , 64 , 65 , 66 ]. In diffuse interface models (for example, the phase–field method), domain walls are three-dimensional objects, such as the domains themselves, and they are considered part of a continuum, whose polarization continuously changes within the domain wall.…”

“…In the general case, the total energy of the polydomain ferroelectric crystal is considered [ 17 ] an additive function of the Helmholtz thermodynamic potential (stored energy density), the domain wall energy, the free space energy, and the energetic contribution due to the applied electrical and mechanical loads. In most ferroelectric models taking into account microstructure (see, for example [ 17 , 65 , 67 , 68 ]), with the exception of phase–field models, the term of domain wall energy, depending on the polarization gradient, is not taken into account. In this study, it is also assumed that the size of the domain is much larger than the domain wall thickness used so that the domain wall energy can be ignored [ 69 ].…”

“…One of the most accurate ways to describe the behavior of ferroelectric domain structures is the direct finite-element -coupled electromechanical modeling of spatial domain structures. Attempts to take into account the evolution of real domain structures by means of finite-element (FE) modeling were undertaken in works [ 68 , 70 , 71 ].…”

“…The aim of the study is an investigation into the influence of the domain structure’s initial topology and its evolution on the hysteresis curves of ferroelectroelastic single-crystal materials based on FE homogenization for all possible rank-2 laminate-based representative volume elements of spatial domain structures. In [ 68 ], we considered the approach of direct finite-element modeling of the hysteresis behavior for polydomain crystals of the tetragonal phase. This study presents a further development of this approach related to the consideration of the rhombohedral phase.…”

“…The restricted discrete variety (relatively small number) of variants of representative volume elements (RVE) of domain structures (8 for the tetragonal and 14 for the rhombohedral phase) revealed in the work makes it possible to fully study the behavior of the rank-2 laminated domain ferroelectric structures. The material behavior at the microlevel at each point of the continuum is described by a multiphase microstructural model of a ferroelectroelastic material [ 68 ] with a diffuse interface. Resulting averaging dielectric and electromechanical hystereses for all possible domain structures are obtained based on multivariate computational experiments on crystal representative volume elements using periodicity conditions.…”