Qualitative identification of cracks using 3D transient elastodynamic topological derivative: Formulation and FE implementation

► Non-iterative global qualitative crack identification approach exploiting transient elastodynamic data, based on the concept of topological derivative, is proposed. ► Topological derivative of a broad class of cost functionals established using 3D small-crack asymptotics in a transient elastodynamic framework. ► Easy implementation within a classical FEM platform: simplicity and efficiency (once the correct expression of the topological derivative, established in this article, is available). ► Computationally efficient adjoint-based formulation. ► Demonstrated on 3D numerical experiments: cracks are correctly located, and they orientation is also estimated by pointwise optimization of TD summing up: a mathematical asymptotic analysis (small-crack expansion) yielding crack identification methodology that is easy to implement and use by engineers.