Qualitative identification of the interfacial condition in cracks via the method of topological sensitivity
Fatemeh Pourahmadian (University of Minneosta), Bojan Guzina (University of Minnesota)
Characterization and Imaging of Structural and Material Imperfections
Mon 4:20 - 5:40
Barus-Holley 191
The method of Topological Sensitivity (TS) has been shown to provide a simple non-iterative approach to the wave-based imaging of defects in elastic media. Its strength lies in providing a computationally efficient and robust way of identifying and geometrically reconstructing distinct inner heterogeneities without the need for prior information in the form of initial guess. In this study, the capability of TS in determining the contact condition between the surfaces of a crack embedded in an elastic solid is investigated. To this end, the TS-based approach is formulated in the frequency domain for imaging partially closed cracks. The crack contact condition is modeled in the average sense via a set of residual interfacial stiffnesses. The corresponding elastic polarization tensor is derived and computed. With such result, the new TS formula is obtained, showing that the location and normal vector to the surface of a finite hidden crack (with residual stiffness) are identifiable via the TS irrespective of the contact condition. Having this initial information about the hidden crack, it is shown mathematically that useful information about the crack interfacial condition can further be extracted non-iteratively from the two independent terms (one affiliated with the normal crack stiffness, the other with its tangential counterpart) featured in the newly obtained TS formula. A computational platform based on the regularized boundary integral equation method for 3D elastodynamics is developed to simulate the experimental data and calculate the TS field over a range of testing frequencies. The results of numerical experiments for a canonical testing configuration verify the effectiveness of the proposed crack identification approach.