Identifying cracks in homogeneous and bimaterial bodies using 3D elastodynamic topological sensitivity

The concept of topological sensitivity (TS), originally proposed for topological optimization, quantifies the perturbation induced to a given cost functional by the nucleation of an infinitesimal flaw in a reference defect-free body. The TS field has since been found to permit qualitative imaging of buried flaws from wave-based data. In this article, the TS is derived for three-dimensional crack identification exploiting over-determined transient elastodynamic boundary data. Simple and efficient adjoint-state based formulations are proposed in elasticity, enhanced by the recourse to closed-form expressions of the polarization tensor arising in the featured asymptotic analysis when the trial small crack is circular or elliptic. This approach, which allows a qualitative reconstruction of cracks in terms of their location and orientation, is implemented within a conventional FEM platform. Extensive 3D time-domain numerical experiments highlight its usefulness and performance.