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Electromechanical Interactions
The following is a brief qualitative description of the most important dielectric, electromechanical and
piezoelectric relationships, including parameter definitions. For detailed mathematical formulas, solid state
physics relationships, methods of parameter determination, etc., please consult the appropriate specialist
literature (see recommendations on page 38).
Basic electromechanical equations
The following relationships apply only to small electrical and mechanical
amplitudes, i.e. small-signal values
Only in this region is it possible
for polarized piezoelectric ceramics to be described by linear relationships
between the mechanical strain (S) or mechanical stress (T) components and
the components of the electric field E or the dielectric displacement D.
These linear relationships are derived using dielectric, piezoelectric and
elasticity “constants”. Because they depend on the anisotropy of the
piezoelectric material, these physical quantities can only be defined in
terms of tensors which reflect the directionality of the electric field, the
mechanical stresses, etc.
In simplified form, the basic relationships between the electrical and elastic properties (for a static or
quasistatic application) can be represented as follows
where:
D dielectric displacement
T mechanical stress
E electric field
S mechanical strain
d piezoelectric charge constant
T permittivity (for T = constant)
sE elasticity constant ( E = constant)
The piezoelectric constants relating the electric field E, the dielectric displacement D, the mechanical
stress T and the strain S require directionality indexing. Analogous to crystallographic descriptions for
piezo-ferroelectric ceramics, the polarization vector is usually set parallel to the z or 3rd axis of a
righthanded Cartesian coordinate system.
The directional parameters are given the subscripts 1,2 and 3 corresponding to the directions of x, y and z,respectively. Mechanical shear stresses (couples) about x, y and z, and the corresponding shear strains, are designated with the subscripts 4, 5 and 6, respectively.
Orthogonal system
to describe
piezoelectric materials
