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| The modelling of interactions between ultrasonic waves and cracks is of great interest in many fields of applied mechanics. When the wavelengths are much larger than the width of the cracks, the latter are usually replaced by zero-thickness interfaces and appropriate jump conditions. A realistic non-linear hyperbolic model accounting for the finite compressibility of crack faces under normal loading conditions has been presented for applications in mechanical engineering.
Numerical experiments and the derivation of differential equations from the Partial Differential equations model will be first presented before the mathematical study. For N cracks, the model becomes a Neutral Delay Differential System with many mathematical challenges: non-linear stability, small divisors, homogenization. |
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