Abstract
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.
Highlights
Piezoelectric materials have widespread applications in modern technical areas such as mechatronics, electromechanical devices, microelectromechanical systems or smart structures, serving as sensors, actuators or transducers [1, 2, 3]
Piezoelectric materials produce electric charges when mechanically deformed and an electric potential causes a mechanical deformation. This property makes them suitable for sensor and transducer applications [6].The aim of the paper is to determine the electro-stressed state of an elastic-piezoelectric material under mechanical and electric loads
Yünlü are very small and electrical interactions are non-linear; the constitutive equations of polarization field and symmetric stress have been linearized to a degree
Summary
Piezoelectric materials have widespread applications in modern technical areas such as mechatronics, electromechanical devices, microelectromechanical systems or smart structures, serving as sensors, actuators or transducers [1, 2, 3]. Piezoelectric materials produce electric charges when mechanically deformed and an electric potential causes a mechanical deformation This property makes them suitable for sensor and transducer applications [6].The aim of the paper is to determine the electro-stressed state of an elastic-piezoelectric material under mechanical and electric loads. It has been assumed that both mechanic and electrical interactions are non-linear. Yünlü (or displacement gradients) are very small and electrical interactions are non-linear; the constitutive equations of polarization field and symmetric stress have been linearized to a degree. In our study [15], the constitutive equations determining the linear electro-thermomechanical behavior of a thermoelastic-piezoelectric medium have been obtained. The constitutive equations have been obtained that determine the non-linear electrothermomechanical behavior of elastic-piezoelectric medium. Since the temperature has been assumed to be constant, no temperature change has been considered leading to the omission of the heat flux vector formulation
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