Numerical model for the characterization of Maxwell-Wagner relaxation in piezoelectric and flexoelectric composite material. (1st October 2018)

• Record Type: Journal Article
• Authors: Nguyen, B.H.; Zhuang, X.; Rabczuk, T.
• Is Part Of: Computers & structures. Volume 208(2018)
• Page Start: 75
• Page End: 91
• Publication Date: 2018-10-01
• Subjects: Maxwell-Wagner polarization -- Piezoelectric -- Flexoelectric -- Colossal dielectric constant; Structural engineering -- Data processing -- Periodicals; Electronic data processing -- Structures, Theory of -- Periodicals; 624.171
• DOI: 10.1016/j.compstruc.2018.05.006
• Languages: English
• ISSNs: 0045-7949

Abstract

Graphical abstract: The Maxwell-Wagner polarization effect is studied for the bi-layer piezoelectric or flexoelectric material. The free charge, which characterizes the interfacial polarization, is introduced by using the complex form of dielectric permittivity via the conductivity. Under appropriate boundary conditions, the effective material coefficients, i.e. piezoelectric or flexoelectric coefficients and dielectric permittivity, can be extracted by solving a boundary value problem, and are shown to be frequency-dependent. Highlights: Numerical model of the Maxwell-Wagner polarization in a bi-layer piezoelectric or flexoelectric material is presented. Isogeometric analysis is utilized to solve the boundary value problem in order to extract the effective material coefficients. Numerical examples are performed to validate the proposed model and study the frequency-dependent behavior of the effective piezoelectric and flexoelectric coefficients as well as the giant enhancement of the dielectric permittivity. The static (at low frequency) and the instantaneous (at high frequency) effective coefficients are dictated by those of the thin and thick layer, respectively. Conductivity and the volume ratio play essential roles in the enhancement of dielectric constant. Abstract: Bi-layer structures can be engineered to investigate the interfacial polarization (Maxwell-Wagner polarization) of heterogeneous dielectric material, which shows the frequency-dependent property of the effective dielectric permittivity. However, in piezoelectric or flexoelectric heterostructures, behaviors of the effective piezoelectric or flexoelectric coefficients are remained unclear. Therefore, in this work, we present a numerical model of the Maxwell-Wagner polarization effect in a bi-layer structure made of piezoelectric or flexoelectric material. In this model, the conductivity, which qualitatively represents the free charge in a real dielectric material, is introduced to the complex dielectric permittivity. Several numerical examples are performed to validate the model and investigate the frequency dependence of the effective dielectric permittivity, piezoelectric and flexoelectric coefficients as well as the giant enhancement of dielectric constants. It is found that the static (at low frequency) and the instantaneous (at high frequency) effective coefficients are governed by those of the thin and thick layer, respectively. Moreover, both conductivity and volume ratio play essential roles in the enhancement of the dielectric constant that is underpinned by the Maxwell-Wagner effect.