By Jiashi Yang
This quantity is meant to supply researchers and graduate scholars with the elemental elements of the continuum modeling of electroelastic interactions in solids. A concise therapy of linear, nonlinear, static and dynamic theories and difficulties is gifted. The emphasis is on formula and figuring out of difficulties priceless in machine purposes instead of answer recommendations of mathematical difficulties. the math utilized in this ebook is minimum. This quantity is appropriate for a one-semester graduate direction on electroelasticity. it could even be used as a reference for graduate scholars and researchers in mechanics and acoustics.
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Extra info for An introduction to the theory of piezoelectricity
They can be transformed to path-independent integrals by the divergence theorem. 3-1. 3-4). 3-2. 3-3. Study the conservation laws for linear, static piezoelectricity . 4. 2-1) has been used. Therefore, 43 where is the kinetic energy density, and is the quasistatic Poynting vector. 4-2) may be considered as a generalized version of Poynting’s theorem in electromagnetics. 2-9) have been used. 4-5) is called the energy integral which states that the energy at time t is the energy at time plus the work done to the body from to t.
Also define the second-rank four-tensor and the fourth-rank four-tensor and all other components of where Then and Therefore, yields the homogeneous equation of motion and the charge equation. 2 Vector Potential Formulation Consider the case when there is no body charge. Since the divergence of D vanishes, we can introduce a vector potential by 46 which satisfies the divergence-free condition on D. 5-8), yields Similarly, for the electric field E, we introduce an anti-symmetric tensor by Then the curl-free condition on E takes the following form: In summary, the equations for this formulation are Note that in this formulation the internal energy U is used, which is positive definite.
The free energy that determines the constitutive relations of nonlinear electroelastic materials may be written as  where the material constants are called the second-order elastic, piezoelectric, electric susceptibility, third-order elastic, first odd electroelastic, electrostrictive, third-order electric susceptibility, fourth-order elastic, second odd electroelastic, first even electroelastic, third odd electroelastic, and fourth-order electric susceptibility, respectively. These material constants are called the fundamental material constants.