The jump of the normal component of the
electric displacement vector D is equal to the surface density a of electric charges.
The
electric displacement components must satisfy Equation (2) (Ruan et al.
The nominal electric field is [??] = [PHI]/[L.sub.3] and the nominal
electric displacement is defined by [??] = Q/[L.sub.1][L.sub.2], the true electric field by E = [PHI]/[l.sub.3], and the true
electric displacement by D = Q/([l.sub.1][l.sub.2]).
where T is the stress tensor, D is the
electric displacement vector, C is the elastic modulus tensor measured in a constant electric field, [??] is the piezoelectric tensor, and [??] is the dielectric tensor measured at constant strains.
Find a displacement field u : [OMEGA] x [0, T] [right arrow] [R.sup.d], a stress field [sigma] : [OMEGA] x [0, T] [right arrow] [S.sub.d], an electric potential field [phi] : [OMEGA] x [0, T] [right arrow] R, an
electric displacement field D : [OMEGA] x [0, T] [right arrow] [R.sup.d], a bonding field [beta] : [[GAMMA].sub.3] x [0, T] [right arrow] R and an internal state variable field k : [OMEGA] x [0, T] [right arrow] [R.sup.m] such that
[bar.S], [bar.T], [bar.E], [bar.H], [bar.D] and [bar.B] are the strain, stress, electric, magnetic,
electric displacement and magnetic induction fields.
with D being the
electric displacement vector, [f.sub.v] the volume force, [f.sub.A] the surface force, and [[sigma].sub.q] the electric surface stress.
where [c.sub.ijkl], [e.sub.ikl], and [k.sub.ij] are, respectively, the elastic, piezoelectric, and dielectric permittivity constants and [D.sub.i] denotes
electric displacement.
The lower
electric displacement observed in some composite films could be attributed to the lower film quality, which makes the applied electric field strength on the films to its breakdown strength.