Crack detection

Health monitoring techniques are crucial in detecting defects early in industrial pipelines to avoid those problems. Among others, ultrasound acoustic measurements can help check the pipe status and locate potential cracks on its structure. In this project (see [1]), we have focused on the numerical simulation of wave propagation of Loves waves in bi-layered materials using a modal-based #PUFEM technique (a joint-project with my colleagues Philippe Destuynder, Luis María Hervella Nieto, Paula María López Pérez, and José María Orellana)

Figure 1: Lamb mode computed in a bi-layered structure.

The time-harmonic propagation of elastic waves in layered media is simulated numerically by means of a modal-based Partition of Unity Finite Element Method (PUFEM). Instead of using the standard plane waves or the Bessel solutions of the Helmholtz equation to design the discretization basis, the proposed modal-based PUFEM explicitly uses the tensor-product expressions of the eigenmodes, the so-called Love and interior modes (see Figure 1), of a spectral elastic transverse problem, which fulfil the coupling conditions among layers. This modal-based PUFEM approach does not introduce quadrature errors since the coefficients of the discrete matrices are computed in closed-form. A preliminary analysis of the high condition number suffered by the proposed method is also analyzed in terms of the mesh size and the number of eigenmodes involved in the discretization. The numerical methodology is validated through a number of test scenarios, where the reliability of the proposed PUFEM method is discussed by considering different modal basis and source terms. Finally, some indicators are introduced to select a convenient discrete PUFEM basis taking into account the observability of cracks located on a coupling boundary between two adjacent layers.

References

[1] P. Destuynder, L. Hervella-Nieto, P.M. López-Pérez, J. Orellana, A. Prieto.
A modal-based Partition of Unity Finite Element Method for elastic wave propagation problems in layered media.
Computer and Structures, 265 (2022), 106759. (pre-print)