By Jiashi Yang
This quantity is meant to supply researchers and graduate scholars with the fundamental 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 important in equipment functions instead of answer concepts of mathematical difficulties. the maths utilized in this booklet is minimum. This quantity is acceptable for a one-semester graduate direction on electroelasticity. it may possibly even be used as a reference for graduate scholars and researchers in mechanics and acoustics.
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7. 7-1. 7-6). 8. TOTAL STRESS FORMULATION A more compact formulation will result if we introduce the following total energy density: Then the constitutive relations take the following form: where we have introduced a total stress tensor in material form. 7-1) becomes The following expressions will be useful in Chapter 6. 29 Chapter 2 LINEAR PIEZOELECTRICITY FOR INFINITESIMAL FIELDS In this chapter we specialize the nonlinear equations in Chapter 1 to the case of infinitesimal deformations and fields, which results in the linear theory of piezoelectricity.
2-1. For linear piezoelectricity we use x as the independent spatial coordinates. Let the unit outward normal of S be n. 2-1. A piezoelectric body and partitions of its surface. For boundary conditions we consider the following partitions of S: where is the part of S on which the mechanical displacement is prescribed, and is the part of S where the traction vector is prescribed. represents the part of S which is electroded where the electric potential is no more than a function of time, and is the unelectroded part.
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. 6-4) can be written as four equations for the four unknowns and 25 Consider an interface between medium 1 and medium 2.
An introduction to the theory of piezoelectricity by Jiashi Yang