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Mathematical and Computational Applications is published by MDPI from Volume 21 Issue 1 (2016). Articles in this Issue were published by another publisher in Open Access under a CC-BY (or CC-BY-NC-ND) licence. Articles are hosted by MDPI on as a courtesy and upon agreement with the previous journal publisher.
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Math. Comput. Appl. 2011, 16(4), 839-848;

On Constitutive Equations for Anisotropic Nonlinearly Piezoelectric Materials

Department of Manufacturing Engineering, Technology Faculty, Süleyman Demirel University, 32260, Isparta, Turkey
Author to whom correspondence should be addressed.
Published: 1 December 2011
PDF [200 KB, uploaded 1 April 2016]


In this paper, the elastic-piezoelectric continuum has been investigated theoretically and its non-linear constitutive equations have been defined. The theory is formulated in the context of continuum electrodynamics. The solid medium is assumed to be non-linear, homogeneous, compressible and isothermal, has elastic and piezoelectric anisotropy. Basic principles of modern continuum mechanics and balance equations of electrostatic have provided guidance and have been determining in the process of this study. From the formulation belonging to the constitutive equations, it has been observed that the symmetric stress and polarization have been derived from a scalar-valued thermodynamic potential defined in calculations. As a result of thermodynamic constraints, it has been determined that the free energy function is dependent on a symmetric tensor and a vector. The free energy function has been represented by a power series expansion and the type and number of terms taken into consideration in this series expansion has determined the non-linearity of the medium. Finally, the quasi-linear constitutive equations are substituted in the balance equations to obtain the field equations.
Keywords: Piezoelectric; Continuum electrodynamics; Constitutive equations; Anisotropy Piezoelectric; Continuum electrodynamics; Constitutive equations; Anisotropy
This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).

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Usal, M.; Yünlü, L. On Constitutive Equations for Anisotropic Nonlinearly Piezoelectric Materials. Math. Comput. Appl. 2011, 16, 839-848.

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