TY - JOUR U1 - Zeitschriftenartikel, wissenschaftlich - begutachtet (reviewed) A1 - Rjelka, Marek A1 - Köhler, Bernd A1 - Mayer, Andreas T1 - Nonlinear effects of micro-cracks on long-wavelength symmetric Lamb waves JF - Ultrasonics N2 - For an elastic medium containing a homogeneous distribution of micro-cracks, an effective one-dimensional stress-strain relation has been determined with finite element simulations. In addition to flat micro-cracks, voids were considered that contain a Hertzian contact, which represents an example for micro-cracks with internal structure. The orientation of both types of micro-cracks was fully aligned or, for flat micro-cracks, totally random. For micro-cracks with Hertzian contacts, the case of random orientation was treated in an approximate way. The two types of defects were found to give rise to different degrees of non-analytic behavior of the effective stress-strain relation, which governs the nonlinear propagation of symmetric (S0) Lamb waves in the long-wavelength limit. The presence of flat micro-cracks causes even harmonics to grow linearly with propagation distance with amplitudes proportional to the amplitude of the fundamental wave, and gives rise to a static strain. The presence of the second type of defects leads to a linear growth of all harmonics with amplitudes proportional to the power 3/2 of the fundamental amplitude, and to a strain-dependent velocity shift. Simple expressions are given for the growth rates of higher harmonics of S0 Lamb waves in terms of the parameters occurring in the effective stress-strain relation. They have partly been determined quantitatively with the help of the FEM results for different micro-crack concentrations. Y1 - 2018 SN - 0041-624x SS - 0041-624x U6 - https://doi.org/10.1016/j.ultras.2018.06.001 DO - https://doi.org/10.1016/j.ultras.2018.06.001 VL - 90 SP - 98 EP - 108 PB - Elsevier CY - Amsterdam [u.a.] ER -