Topological derivative methods for damage detection

Abstract

This paper deals with the use of the topological derivative as a structural health monitoringmethod, for locating the presence of flaws in an aluminium plate. By minimizing a scalar ob-jective function that measures the least squares difference between the measured and calculatedsignals, flaws can be detected. The topological derivative somehow describes the sensitivity ofthe objective function to localized perturbations of the material properties due to the defectspresence. Here, we reconstruct small defects via the topological derivative by using multi-frequency synthetic data, for several representative configurations of the actuators and sensors,and several defect locations. Among these, some fairly demanding configurations are consideredthat are not accessible to conventional methods, such as actuators and sensors located very closeto the plate boundary and defects located beyond both elongated through-slits and elongatedinclusions of a different material.