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What are the basic equations for piezoelectric materials?
What are the constitutive relations in piezoelecticity?
Are thermoelectric and piezoelectric materials adequate constitutive equations reversible?
What are the relations between electro-elastic material constants appearing in different piezoelectric equations?
Three axes are defined, termed 1, 2, and 3, analogous to X, Y, and Z of the classical three-dimensional orthogonal set of axes. These are the topics covered by this page: Piezoelectric coefficients and directions. Basic piezoelectric equations. Limitations of the linear constitutive equations.
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- Nature of Piezoelectricity
- Basic Equations of Piezoelectric Materials
- 4.1 Basic equations
- 4.1.1 Piezoelectric equations
- hs
Abstract In this chapter, we introduce the basic equations of piezoelectric materials. These equations include four types of the piezoelectric equations that describe the electromechanical coupling, gradient equations and equilibrium equation. The relations between the electro-elastic material constants appearing in different piezoelectric equation...
The basic equations for piezoelectric materials include balance laws, gradient and constitutive relations. The constitutive relations are usually called piezoelectric equations in the theory of piezoelecticity, which describe the interaction effect among stress, strain, electric displacement; and electric field.
The piezoelectric equations are established based on experiments. Due to the D. Fang et al., Fracture Mechanics of Piezoelectric and Ferroelectric Solids Tsinghua University Press, Beijing and Springer-Verlag Berlin Heidelberg 2013 finiteness of the experiments, they are thus not so strict. In fact, the piezoelectric equations can be obtained by st...
D T h T es E g g , hs D d h gc , e D e dc h , & E & where, I is a unit matrix.
- Daining Fang, Jinxi Liu
- 2013
In physics and engineering, a constitutive equation or constitutive relation is a relation between two or more physical quantities (especially kinetic quantities as related to kinematic quantities) that is specific to a material or substance or field, and approximates its response to external stimuli, usually as applied fields or forces.
2.4 Piezoelectric Constitutive Equations In this section we introduce the equations which describe electromechanical properties of piezoelectric materials. The presentation is based on the IEEE standard for piezoelectricity [154] which is widely accepted as being a good representation of piezoelectric material properties. The IEEE standard as-
There are 4 mathematically-equivalent forms of piezoelectric constitutive rela- tions , each one involves one of 4 different third-order tensors of piezoelectric coupling coefficients – see Table2and equations below.
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Feb 3, 2023 · A system is described by governing equations and we obtain them by starting axiomatically with the balance equations and then use (under many assumptions) adequate “constitutive equations.” These constitutive equations are material equations.
The subscripts in piezoelectric constitutive equations have very important meanings. They describe the conditions under which the material property data was measured. For example, the subscript E on the compliance matrix s E means that the compliance data was measured under at least a constant, and preferably a zero, electric field.
