Rate-dependent electro-mechanical coupling response of ferroelectric materials: A finite element formulation
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This paper presents a three-dimensional (3D) constitutive model for predicting nonlinear polarization and electro-mechanical strain responses of ferroelectric materials subject to various histories of electric fields and mechanical stresses. The electro-mechanical coupling constants are expressed as functions of a polarization state and it is assumed that in absence of the polarization, the material does not exhibit electro-mechanical coupling response. The polarization model due to an electric field input is additively decomposed into time-dependent reversible and irreversible parts. The model also incorporates the effect of compressive stresses on the polarization response. Thus, the constitutive model is capable of incorporating the effect of loading rates, mechanical stresses, and electric fields on the overall hysteretic electro-mechanical and polarization switching response of ferroelectric materials. The constitutive model is implemented in a continuum 3D finite element in order to perform rate-dependent electro-mechanical coupling analyses of smart structures. The experimental data on the polarization switching and hysteretic butterfly strain responses of lead zirconate titanate (PZT) reported by Fang and Li (1999) are used to validate the constitutive model. Parametric studies are also conducted to examine the effect of loading rates and coupled electro-mechanical boundary conditions on the overall performance of PZT. Finally, FE analyses are performed to simulate shape changing in smart composite structures. 2013 Elsevier Ltd. All rights reserved.
