Nonlinear electromechanical analysis: a constitutive theory for perovskite type ferroelectrics |
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| Authors: | Dai-Ning Fang Wei Lu Keh-Chih Hwang |
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| Institution: | 1. Faculty of Mechanical Engineering, University of Žilina, Univerzitná 1, 010 26 Žilina, Slovakia;2. Faculty of Civil Engineering, University of Žilina, Univerzitná 1, 010 26 Žilina, Slovakia;3. Faculty of Mechanical Engineering, VŠB-TU Ostrava, 17. listopadu 2172/15, 70800 Ostrava, Czech Republic;4. Institute of Experimental Physics, Slovak Academy of Sciences, Watsonova 47, 040 01 Košice, Slovakia;1. College of Mechanical Engineering and Applied Electronics Technology, Beijing University of Technology, Beijing, People’s Republic of China;2. Beijing Institute of Control Engineering, People’s Republic of China;1. School of Mechatronic Engineering, Southwest Petroleum University, Chengdu, SiChuan 610500, PR China;2. PipeChina Southwest Pipeline Company, Chengdu 610218, PR China;3. Engineering Technology Research Institute of CNPC Bohai Drilling Engineering Company Limited, Tianjin 300450, PR China;4. School of Mechanical Engineering, Chengdu Textile College Servoir Geology and Exploitation, Chengdu, SiChuan 611731, PR China |
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| Abstract: | A constitutive theory is established in this paper to describe the nonlinear electromechanical behavior of perovskite type ferroelectrics subjected to external stress and external electric field. In the proposed theory, each domain is considered as an inclusion. The Helmholtz free energy and Gibbs free energy of a constituent element, that are derived by using micromechanics approaches, are functionals of the orientation distribution function (ODF) that depicts the domain distribution patterns. By applying the internal variable theory and expanding ODF in Fourier series, the yielding condition, the evolution of ODF, and the constitutive relation are obtained. In terms of the simplification of the constitutive relation, theoretical predictions are compared with experimental results. There is an agreement between the theoretical and the experimental results, indicating that the theory is reasonable and applicable. It should be pointed out that the constitutive model proposed in this paper is restricted to ferroelectric materials exhibiting transformation from cubic to tetragonal only. |
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| Keywords: | Ferroelectric material Constitutive relation Orientation distribution function (ODF) |
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