Investigation of the Higher Harmonic Lamb Wave Generation in Hyperelastic Isotropic Material

Micro-structural damages, such as micro-cracks and voids, give locally rise to stresses and may initiate subsequent failure of structural components. Therefore, the development of methods for the detection of microstructural damage and the observation of their growth is an important and ongoing area of research, especially for thin-walled structures.The proposed method for the detection is based on the nonlinearity caused by the micro-structural damages. Lamb waves are generated which induce simultaneously higher harmonic modes due the inherent nonlinearity. For detailed investigations, numerical simulations are essential. In this work, the nonlinearity is modeled by the material law, which is based on the Neo- Hookean and Mooney-Rivlin material models. In contrast to previous studies, which used third order elastic coefficients, these hyperelastic material models are widely accepted, frequently used, and implemented in commonly available FEM software.In the numerical investigations, Lamb waves are generated in a thin-walled aluminum plate with windowed sine burst signals. Due to the nonlinearity in the material law, the waves are not only observed at the excitation frequency, but also at higher harmonic frequencies. Excitation at especially selected frequencies evoke the cumulative effect, and thus gives rise to the amplitudes of the higher harmonics. Comparing the S1–S2 and S2–S4 mode pairs clearly show the higher sensitivity of the latter to the material nonlinearity. This matches with previous published experimental results. Finally, it is shown that the results obtained agree qualitatively well with numerical analyses, in which the micro-structural damages are modeled directly by a respective finite element discretization.