Most of the nonlinear ultrasonic studies to date have been experimental, but few theoretical predictive studies exist,
especially for Lamb wave ultrasonic. Compared with nonlinear bulk waves and Rayleigh waves, nonlinear Lamb waves
for structural health monitoring become more challenging due to their multi-mode dispersive features. In this paper,
predictive study of nonlinear Lamb waves is done with finite element simulation. A pitch-catch method is used to
interrogate a plate with a "breathing crack" which opens and closes under tension and compression. Piezoelectric wafer
active sensors (PWAS) used as transmitter and receiver are modeled with coupled field elements. The "breathing crack"
is simulated via "element birth and death" technique. The ultrasonic waves generated by the transmitter PWAS
propagate into the structure, interact with the "breathing crack", acquire nonlinear features, and are picked up by the
receiver PWAS. The features of the wave packets at the receiver PWAS are studied and discussed. The received signal is
processed with Fast Fourier Transform to show the higher harmonics nonlinear characteristics. A baseline free damage
index is introduced to assess the presence and the severity of the crack. The paper finishes with summary, conclusions,
and suggestions for future work.