Effect of elastic modulus on the nonlinear ultrasonic Lamb waves in cortical bone: A numerical study

Ultrasonic Lamb wave has attracted considerable interest to characterize the human cortical bone. Especially, the nonlinear ultrasonic Lamb wave shows great potential to evaluate the micro-damage of cortical bone. However, the quantitatively analysis about the effect of the bone material mechanical properties on the nonlinear Lamb wave are very limited. In this study, a finite-difference time-domain (FDTD) method was used to simulate the propagation of phase velocity matching mode pair S1 mode and its corresponding double frequency Lamb wave mode S2 (DFLW-S2) in cortical bone plate. The simulations were carried out under various values of the elastic modulus and the amplitude of DFLW-S2 at different propagation distance was calculated from the data. The results show that the deduction of elastic modulus would lead to phase velocity mismatch of S1 and DFLW-S2. The wave filed of DFLW-S2 would thus present a distinct periodical distribution with the propagation distance. The spatial period decreased exponentially with the reducing elastic modulus. The amplitude of DFLW-S2 dropped rapidly when second order elastic modulus decreased from 100% to 92% and then remained roughly unchanged. The present results may provide a deep understanding of the behavior of nonlinear Lamb wave in the material damage assessment.