Break of reciprocity principle induced by cracks in concrete: experimental evidence and applications to nonlinear tomography

As largely demonstrated by many authors, localized cracks in heterogeneous media act as nonlinear scatterers; consequently, when an heterogeneous medium is perturbed by a mechanical excitation, its elastic response shows nonlinear features, dependent on the amplitude. Experiments presented here will show that the presence of localized nonlinear scatterers not only breaks the proportionality of the elastic response, but also affects the reciprocity principle, which thus, in some conditions, is no longer valid. Experiments performed on a concrete beam with a significant crack have demonstrated that the reciprocity principle holds true only when the amplitude of excitation is low or when the distance between the crack and the source/receiver is comparable (i.e. source/receiver are symmetric in space with respect to the crack). Besides highlighting the break of reciprocity, experiments have proved its dependence on the amplitude of excitation and on the position of the emitting and receiving transducers with respect to the crack. By taking advantage of these features, a nonlinear tomography of a cracked fibre-reinforced concrete beam was performed, allowing to reproduce an image of the scanned surface and to locate the position of the crack. The sensitivity of the approach to locate small localised nonlinear features is being investigated.