An Introduction to the Theory of Piezoelectricity by Jiashi Yang

By Jiashi Yang

This quantity is meant to supply researchers and graduate scholars with the fundamental features 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 on formula and knowing of difficulties priceless in gadget purposes instead of answer recommendations of mathematical difficulties. the maths utilized in this ebook is minimal.


This quantity is acceptable for a one-semester graduate path on electroelasticity. it may well even be used as a reference for graduate scholars and researchers in mechanics and acoustics.

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1-56) have been used. Hence 21 In summary, the balance laws in material form are CONSTITUTIVE RELATIONS 5. 1-38). Then 22 where we have introduced In terms of the displacement vector, we have which, in the unabbreviated notation, takes the following form: From we have 23 where has been used. The free energy that determines the constitutive relations of nonlinear electroelastic materials may be written as [6] 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.

Integrity bases for constructing a scalar function of a symmetric tensor and a vector for all crystal classes are known [7]. 6. INITIAL-BOUNDARY-VALUE PROBLEM Since the curl-free equation is automatically satisfied. The angular momentum equation is satisfied because is symmetric. The present mass density appears in the equation of conservation of mass only, and therefore can be calculated from the equation after the deformation and the electric field have been found. The energy equation is satisfied by the forms of the constitutive relations.

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. 4-6). 4-5) to it. The initial energy and the external work for the difference are zero. 4-5) implies that, for the difference, at any Since both T and U are nonnegative, From the positive-definiteness of T and U, Hence the two solutions are identical to within a static rigid body displacement and a constant potential.

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