Transient elastography
The approach studied here is to be linked to the so-called hybrid inverse problems. Having been made available internally as the solution of a preliminary wave based inverse problem, the full-field measurements considered are used to construct by local algebraic manipulations a system, possibly redundant, of PDE whose solutions are the unknown coefficients that can now be recovered as a second step. ...
Topological sensitivity and Time-reversal approaches with piezoelectric sensors
The focus of this work is the transient wave-based detection and identification of defects embedded in elastic solids using piezoelectric transducers. It addresses this problem within a comprehensive framework encompassing description of elastic wave propagation within the probed media as well as consideration of the coupling phenomena induced by the transducers. Modeling of piezoelectric transducers is discussed and application of a proven reciprocity theorem enables the proposition of an iterative construction procedure of electric inputs generating waves expected to focus on the sought defects. Next, the identification problem is investigated by way of an adjoint field-based topological sensitivity approach that permits the construction of a defect indicator function based on the derived reciprocity identity.