Flexoelectricity, Strain Gradients, and Singularities in Ferroelectric Materials
Publication Type:
Journal
Authors:
Year Published:
2017
Abstract:
The effect of flexoelectricity on the formation and evolution of domain structures in ferroelectric materials is developed by integrating strain gradient theory into a finite element phase field model. Length scales associated with elastic strain gradients and the corresponding polarization gradient across a domain wall are integrated into the time-dependent Ginzburg–Landau theory and numerical simulated. Theoretical relations of a shear strain gradient along an electrode/dielectric interface are first solved and verified numerically using the finite element model. A singularity in the strain gradient–induced polarization is shown to occur as the elastic strain gradient length scale approaches a flexoelectric length scale. The theory and finite element modeling is then extended to quantify strain gradient electromechanics near 180° and 90° tetragonal phase domain structures. It is shown that the strain gradient length scale (𝑙1) strongly influences changes in strain across the domain walls but has a negligible effect on the polarization. Strain gradient effects become negligible when 𝑙1≈0.1𝑙𝑃, where 𝑙𝑃 is the polarization domain wall length scale.
Journal:
Journal of Intelligent Material Systems and Structures
Volume:
28
Issue:
20
Pagination:
3091-3105
ISSN:
Short Title:
Date Published:
3/25/2017