Analytical and numerical modelling of wave scattering by a linear and nonlinear contact interface

In the aerospace or civil engineering industries, effective structural integrity management of critical assets has been improved based on preventive measures such as earlier detection and characterization of structural damages for proper actions. This explains the recent increase in the research works involving non-destructive and structural health monitoring techniques. It is rather obvious that conventional linear ultrasonic methods have reached their limit regarding the detection of small localized damage. This underpins the current research effort in the field of nonlinear ultrasonics, where the weak nonlinear behavior introduced by structural damage generates new frequency components (higher harmonics), that can be exploited for damage detection and characterization.

Generally, localized damages can be mainly grouped as fatigue cracks and delamination where the nonlinear response is due to contact acoustic nonlinearity. The mechanism involved here is well documented in literature based on various theoretical models. For example, a traction law describing the relationship between the stress and the relative displacement at the interface is widely used to model the ultrasonic response of an interface. This approach is convenient because it is amendable to analytical resolution using a perturbation analysis, contrary to other discontinuous interface models such as unilateral contact.

Recently, Australian scientists presented a novel analytical approach for modeling plane-wave scattering at a plane interface characterized by either linear or nonlinear traction law. Dr. Philippe Blanloeuil (Postdoctoral fellow) and Professor Chun Wang from the University of New South Wales in collaboration with Francis Rose from Defense Science and Technology Group and Martin Veidt from the University of Queensland decomposed the scattering field into two contributions referred to as Mode I and Mode II contributions. Consequently, the scattering problems for linear springs were also reduced to an explicit analytical solution involving two unknows. Their work is published in the Journal of Sound and Vibration.

Unlike the conventional approaches that involved the numerical solution of four unknown variables, this approach is rather simple and advantageous as the scattering decomposition reduces to determining two unknows: tangential and normal components that can be solved analytically. Furthermore, the perturbation analysis that rely majorly on the preceding decomposition led to successive approximations that could as well be solved analytically. This resulted in the formulation of first analytic formulae for nonlinear wave scattering at the nonlinear interface. The formulas were effective compared to the computational results based on the finite element method. The excellent agreement observed highlighted the practical value of the analytical formulas.

As proof of the concept, the authors used the same nonlinear traction law to describe the interface response to validate the practicability of the approach. Analytical solutions were compared to numerical data obtained from the finite element method. Interestingly, an excellent agreement was reported for both linear and nonlinear scattering responses. In a statement to Advances in Engineering, Dr. Philippe Blanloeuil, the first author observed that the analytical formulas can be applied in the evaluation of the effects of various parameters such as the compressive load, amplitude, frequency and incidence wave angle to achieve the desired optimal conditions of the particular application. Therefore, the proposed novel approach will offer practical value in parametric studies of nonlinear scattering at the contact interface.