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In the field of guided waves for non-destructive testing, the interaction of these waves with damages or other discontinuities in a structure is critical. When a guided wave mode travels and hits a defect, it scatters in all directions, converting to other modes and reflecting the existing one. These interactions are captured in scattered far field complex amplitudes. The amplitudes are stored in scattering matrices, which characterise the elastodynamic behaviour of a defect completely. Scattering matrices are also useful to simulate backpropagation from a defect using ray-tracing methods.
Simulating these interactions is challenging, and analytical solutions only exist for simple geometries. Still, using general tools like the finite element method results in large, usually costly models. Recently, researchers proposed a method based on a numerical implementation of the Kirchhoff–Helmholtz integral that allows the computation of the scattering matrices using a model containing only the damaged region. However, classical methods to resolve the far field and low-order elements were used, leading to large models yet more efficient than using other techniques.
We propose using the SBFEM as an alternative to enhance the computation of the far field scattering. The damaged region is discretised using high-order polyhedral elements, while the far field is constructed using a modified version of the SBFEM. Examples compared to the literature demonstrate the validity of the approach.
Modeling wave propagation in large structures using the Scaled Boundarx Finite Element Method
(2015)