Nonlinear constitutive behavior of ferroelectric materials |
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Authors: | HaiJun Li Feng Liu and TzuChiang Wang |
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Institution: | (1) LNM, Institute of Mechanics, Chinese Academy of Sciences, Beijing, 100190, China |
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Abstract: | The ferroelectric specimen is considered as an aggregation of many randomly oriented domains. According to this mechanism,
a multi-domain mechanical model is developed in this paper. Each domain is represented by one element. The applied stress
and electric field are taken to be the stress and electric field in the formula of the driving force of domain switching for
each element in the specimen. It means that the macroscopic switching criterion is used for calculating the volume fraction
of domain switching for each element. By using the hardening relation between the driving force of domain switching and the
volume fraction of domain switching calibrated, the volume fraction of domain switching for each element is calculated. Substituting
the stress and electric field and the volume fraction of domain switching into the constitutive equation of ferroelectric
material, one can easily get the strain and electric displacement for each element. The macroscopic behavior of the ferroelectric
specimen is then directly calculated by volume averaging. Meanwhile, the nonlinear finite element analysis for the ferroelectric
specimen is carried out. In the finite element simulation, the volume fraction of domain switching for each element is calculated
by using the same method mentioned above. The interaction between different elements is taken into account in the finite element
simulation and the local stress and electric field for each element is obtained. The macroscopic behavior of the specimen
is then calculated by volume averaging. The computation results involve the electric butterfly shaped curves of axial strain
versus the axial electric field and the hysteresis loops of electric displacement versus the electric field for ferroelectric
specimens under the uniaxial coupled stress and electric field loading. The present theoretical prediction agrees reasonably
with the experimental results.
Supported by the National Natural Science Foundation of China (Grant No. 10572138) |
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Keywords: | volume fraction of domain switching multi-domain mechanical model finite element method (FEM) domain switching |
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