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Published on: April 27, 2016
Variational principles for polar piezoelectric media in elastic range
Gülay Altay1, M Cengiz Dökmeci
1Faculty of Engineering & Kandilli Observatory and Earthquake Research Institute, Boğazici University, Istanbul, Turkey. askarg@boun.edu.tr
Summary
Researchers developed new variational principles for polar piezoelectric media, offering a unified approach to describe complex material behaviors. These principles simplify the derivation of fundamental equations, including interface conditions in laminated structures.
Area of Science:
- Solid Mechanics
- Materials Science
- Electromagnetism
Background:
- Polar piezoelectric media exhibit complex behaviors governed by fundamental differential equations.
- Existing variational principles often require specific constraint conditions or are limited in scope.
- Deriving equations for discontinuous or laminated media presents significant challenges.
Purpose of the Study:
- To establish alternative variational formulations for the fundamental equations of polar piezoelectric media.
- To develop a unified variational principle applicable to regions with internal surfaces of discontinuity.
- To generalize this principle for laminated polar media, encompassing interface conditions.
Main Methods:
- Deduction of a 3-field variational principle from a general physics principle.
- Modification using an involutory transformation to derive a 9-field variational principle.
- Extension and generalization of the principle for discontinuous and laminated regions.
Main Results:
- A unified variational principle was obtained for regions with internal surfaces of discontinuity.
- A generalized variational principle was derived for laminated polar media.
- This generalized principle yields all equations, including interface conditions, as Euler-Lagrange equations.
Conclusions:
- The derived variational principles offer a unified and generalized framework for polar piezoelectric media.
- These principles simplify the recovery of fundamental equations and interface conditions.
- The work recovers previously established variational principles as special cases.
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