Identification of planar cracks by complete overdetermined data: inversion formulae

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Abstract
The problem of determining a crack by overspecified boundary data is considered. When complete data are available on the external boundary, a reciprocity gap concept is introduced. This concept formalizes the comparison of the response of the safe body to the response of the cracked one of the same physical characteristics. If the crack is known (or assumed) to be planar, explicit inversion formulae are derived determining the host plane equation and the length of an emerging crack in two-dimensional (2D) situations. A reciprocity gap functional is designed and exploited to establish a complete identification result. Numerical trials of the identification methods proposed show very good accuracies and insignificant computational costs.