A new inverse approach for the localization and characterization of defects based on compressive experiments

Compressive tests involving buckling are known to be defect sensitive, nevertheless, to our knowledge, no inverse approach has been proposed yet to use this property for the localization and characterization of material defects. This is due to geometric imperfections, which greatly influence and even dominate the response of defective parts under compression. In comparison with a system lacking geometric imperfections, the modified system does not present any bifurcation, showing that the non-linear progressive response is mainly governed by such imperfections. Before implementing any inverse procedures it is necessary to know whether extracting meaningful material defect information from compressive tests on specimen which also have geometric imperfections is possible. To tackle this issue, an equivalent eigenvalue problem will be extracted from the non-linear response, a problem corrected from geometric imperfections. A dedicated inverse formulation based on the modified constitutive relation error will then be constructed which will involve only well-posed linear problems. Examples illustrate the potential of the methodology to localize and identify single and multiple defects.