Journal
INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS
Volume 106, Issue -, Pages 60-69Publisher
PERGAMON-ELSEVIER SCIENCE LTD
DOI: 10.1016/j.ijnonlinmec.2018.09.001
Keywords
Nonlinear electroelasticity; Dielectric membranes; Euler-Lagrange equations; Stability; Bifurcation
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Funding
- National Natural Science Foundation of China [11372212, 11172201]
- China Scholarship Council
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We derive a reduced theory describing the incremental deformation of an electrodes-coated dielectric plate that takes the leading-order thickness effect into account. By focusing on deformations that are symmetric with respect to the mid-plane, a power series expansion of the incremental deformation and electric field in the thickness direction is used to reduce the second variation of the total energy to an optimal form. The associated Euler-Lagrange equations are then the governing equations for the reduced model. The validity of this reduced model is verified by comparing the bifurcation condition derived from it with the two-term expansion of the exact bifurcation condition in two special cases. We compare our model with another approximate theory that recently appeared in the literature.
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