Sur l'identification de fissures planes via le concept d'écart à la réciprocité en élasticité

Overview of Identification Methods of Mechanical Parameters Based on Full-field Measurements

“…Reciprocity gap functionals are also useful for crack identification, see e.g. [1,7] for equilibrium conditions, and [11] for a variant of this approach, based on a instantaneous reciprocity gap, applicable to crack identification from elastodynamic measurements in the time domain.…”

“…Closed-form solutions for constitutive parameter identification are available in some very particular cases only (e.g., uniaxial tensile test, 3-point or 4-point bending tests), for which the strain distribution is constant or linear and can be directly determined from Equation (1). The constitutive parameters are therefore directly related to the measured strain/displacement components and the applied forces.…”

“…The constitutive parameters are therefore directly related to the measured strain/displacement components and the applied forces. Most often, however, the strain/stress fields are heterogeneous and the link between the measured quantities and the constitutive parameters is implicit, through the set of governing equations (1,2,3), and cannot easily be expressed in terms of explicit formulae. This article aims at reviewing methods recently proposed for parameter identification based on field measurements, namely:…”

Line segment cracks identification via the reciprocity gap principle and Fourier transform

“…In 2D situations and in the framework of the Laplace equation numerical investigation for a single buried line segment crack has been presented by Santosa and Vogelius [10], the case of a collection of buried cracks has been studied by Bryan and Vogelius in [6] . When complete data is available on the boundary S. Andrieux and A. Ben Abda introduced in [11] and [12] the reciprocity gap concept which turned out to be a relevent tool for recovering 3D-planar cracks in the case of Laplace equation and elastostatic system [13]. The proof of the uniqueness result is constructive and semi-explicit algorithms were built on it [14] , [2]and [1].…”

Problem of detecting inclusions by topological optimization

“…In 1993, other authors proved a Lipschitz stability result for linear cracks. An identifiability result has been developed by Andrieux and Ben Abda in [5] in 1992. In the case of a collection of cracks Bryan and Vogeluis in [10], followed by G. Alessandrini and D. Valenzuela in [3] proved uniqueness results.…”