Polygonal finite element method for nonlinear constitutive modeling of polycrystalline ferroelectrics

• Published in: Finite elements in analysis and design Vol. 42; no. 2; pp. 107 - 129
• Main Authors: Sze, K.Y., Sheng, N.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01-11-2005; Elsevier
• Subjects: Computational techniques; Condensed matter: electronic structure, electrical, magnetic, and optical properties; Domain switching; Electric saturation; Exact sciences and technology; Ferroelectrics; Finite-element and galerkin methods; Fundamental areas of phenomenology (including applications); Grain; Hybrid element; Magnetic properties and materials; Magnetomechanical and magnetoelectric effects, magnetostriction; Mathematical methods in physics; Physics; Polygonal finite element; Electric saturation; Hybrid element; Ferroelectrics; Polygonal finite element; Grain; Domain switching; Constitutive equation; Stiffness matrix; Energy method; Electric potential; Electric stress; Polycrystals; Finite element method; Microcracking; Ferroelectricity; Variational calculus; Ferroelectric switching; Hybrid finite element; Hybrid model; Modelling; Non linear effect; Domain decomposition; Electromechanical properties; Crystal structure
• ISSN: 0168-874X; 1872-6925
• DOI: 10.1016/j.finel.2005.04.004

In meso-mechanistic analyses, crystal grains are often idealized as polygons. Presuming that each grain possesses its own unique and uniform crystallographic structure, it is highly desirable to model a grain by only one basic computational sub-domain. To this end, polygonal finite element models are developed for constitutive modeling of polycrystalline ferroelectrics. The success of these models relies on a hybrid electromechanical variational principle with equilibrating assumed electromechanical stress (
stress
+
electric
displacement
). To construct the element electromechanical stiffness matrix, only piecewise boundary interpolations of the electromechanical displacement (
displacement
+
nodal
electric
potential
) are required. Higher-order elements are made available by inserting side-nodes along the element edges and enriching the electromechanical stress. By incorporating an energy-based nonlinear constitutive model, characteristic features in electric saturation and domain switching are successfully reproduced in the finite element simulation. The effect of microcracking on the macroscropic response of ferroelectrics is also studied.