Page 239 - Mechanics of Microelectromechanical Systems

226 Chapter 4
that have been introduced in the same Chapter 1 as and The shear
stress for instance, produces rotation about the direction 6 of Fig. 4.42,
and similarly, generates the rotation 4 whereas gives rotation about
direction 5. The subscripts 4, 5 and 6 are used to denote these directions.
The deformation of a piezoelectric body in the presence of both external
mechanical loading and electric field is calculated in the linear domain as the
sum of a mechanically-produced deformation and an electrically-generated
displacement, according to the matrix equation:

where is the total strain vector (the subscript m means mechanical and
is used to distinguish this vector from the permittivity vector, which has the
same notation) defined as:

is the stress vector, similarly defined as:

and {E} is the electric field vector, having three components:

The two matrices that enter Eq. (4.99) are the compliance matrix which
is calculated for constant field (the electrodes of the piezoelectric component
are shortcut) and is a 6 x 6 symmetric matrix defined as:

and the charge constant matrix, defined as: