COMPLAS 2025

Nonlinear behaviour of guided ultrasonic waves in fibre metal laminates using hyperelastic material properties

  • NIKIEMA, Wendwoga Fulgence (Helmut Schmidt University)
  • Rauter, Natalie (Helmut Schmidt University)

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The nonlinear behaviour of guided ultrasonic wave propagation in Fibre Metal Laminates (FMLs) is a topic of great interest due to its relevance in structural health monitoring and damage detection in structures. Some nonlinear effects, like the generation of higher harmonic modes in particular, provide valuable insights regarding the damage states of the structure. Further, the cumulative effect of higher harmonic modes, that describe their increasing amplitude with the propagation distance, is of particular interest. Theoretical considerations require two conditions to be satisfied to observe this phenomenon: Firstly, the non-zero power flow condition, which ensures energy transfer from the primary wave mode to its higher harmonics, and secondly a phase velocity matching between the primary and the higher harmonic modes [1, 2]. To analyse properly the local nonlinearity due to damage, it is important to investigate the global nonlinear behaviour of this type of hybrid material. An effective approach to investigate the global nonlinear wave propagation is the use of hyperelastic material models, which induce material nonlinearity in the structure. In order to validate these results, a simple geometric nonlinear model using the nonlinear GREEN-LAGRANGE strain tensor is used as a comparative reference. To evaluate nonlinear effects the relative nonlinearity parameter is commonly used. Based on isotropic materials such as aluminium and orthotropic materials such as carbon fibre reinforced plastics (CFRP), which are often studied in the literature [1], similar results are assumed for hybrid materials like GLARE or FML made of steel and CFRP. In this work, the cumulativ or quasi-cumulativ behaviour (the equality of the phase velocity is only approximately given) is studied numerically using COMSOL Multiphysics. An FML consisting of sixteen layers (four steel layers and three packs of four CFRP layers) is modelled and the wave propagation simulated. The Fast-FOURRIER-Transform (FFT) is used to transform the time-signal into the frequency spectrum. Subsequently the amplitude of the second harmonic mode is plotted over the propagation distance. The relative nonlinear parameter is also calculated as the ratio of the second harmonic amplitude to the amplitude of the primary wave mode. The curves presented show the cumulative response of the wave propagation, which is consistent with the theoretical framework.