Electromagnetic near-field imaging of missing fibers in periodic fiber-reinforced laminates
Résumé
One focuses onto planar laminates that are involving in each of their horizontal layers periodically-arranged circular cylindrical fibers within a given polymeric matrix. Fibers can be absent in some parts, one or several of them, close-by or farther away. First, one summarizes how to model the time-harmonic electromagnetic behavior of these damaged laminates via (i) super-cell concepts such as a specific zone containing all missing fibers is repeated in the horizontal direction to both right and left infinity to yield back a planar periodically-organized laminate, (ii) contrast-source integral field formulations now involving the calculation of proper Green functions, prone to first-order approximations if as expected fiber cross-sections are small enough versus local wavelengths at the operation frequency, (iii) and in a couple of limit cases homogenizations so as defects appear unchanged yet live within homogeneous anisotropic slabs. Then, one investigates how to infer from properly generated and collected near-field scattering (anomalous field) data at least the localization of these missing fibers. MUSIC and RAP-MUSIC algorithms and joint-sparsity-constrained iterative solutions are developed in reflection mode configurations for planar, line, and coil-like sources depending upon operation frequencies, geometries and materials of concern. Examples (for single-layer laminates as a preliminary step towards multi-layer cases) going from carbon-fiber cases in the HF and VHF range and glass-fiber ones in the microwave and subTHz regime are proposed. Linkage with the testing of photonic crystals is also illustrated.