This paper presents an eddy current approach for testing, estimating, and classifying CFRP plate sub-surface defects, mainly due to delamination, through specific 2D magnetic induction field amplitude maps. These maps, showing marked fuzziness content, require the development of a procedure based on a fuzzy approach being efficiently classified. Since similar defects produce similar maps, we propose a method based on innovative fuzzy similarity formulations. This procedure can collect maps similar to each other in particular defect classes. In addition, a low-cost analysis system, including the probe, has been implemented in hardware. The developed tool can detect and evaluate the extent of surface defects with the same performance as a hardware tool of higher specifications, and it could be fruitfully employed by airline companies to maintain aircraft in compliance with safety standards.

In this work, a known Eddy Current (EC) model is adapted to characterize subsurface defects in carbon fiber-reinforced polymer (CFRP) plates intended for the civil aerospace industry. The considered defects include delaminations, microcracks, porosity, fiber breakage, and the simultaneous presence of these defects. Each defect is modeled as an additive variation in the material’s electrical conductivity tensor, allowing for a detailed mathematical representation of the defect’s influence on the CFRP’s electromagnetic behavior. The additivity of the variations in the conductivity tensor is justified by the assumption that the defects are not visible to the naked eye, implying that the material does not require non-destructive testing. The adapted EC model admits a unique and stable solution by verifying that all analytical steps are satisfied. To reconstruct 2D maps of the magnetic flux density amplitude, a FEM formulation is adopted, based on the energy functional because it ensures a stable and consistent numerical formulation given its coercivity. Moreover, the numerical approach allows precise and reliable numerical solutions, enhancing the capability to detect and quantify defects. The numerical results show that the obtained 2D maps are entirely superimposable on those highlighting the distribution of mechanical stress states known in the literature, offering a clear advantage in terms of detection costs. This approach provides an effective and economical solution for the non-destructive inspection of CFRP, ensuring accurate and timely defect diagnosis for maintaining structural integrity.

Nowadays, the automotive industry is oriented toward the production of new generation devices, such as magnetorheological fluid (MR fluid) dampers, which have a proven simplicity of design combined with reduced maintenance. Being devices powered by steady-state electric current, MR fluid dampers develop steady-state magnetic induction fields with associated steady-state thermal stresses and a consequent constant yield stress. In this work, a asymmetric MR damper has been studied using the finite element method. Specifically, since steady-state electric current circulates in the coil of the device, a magneto-static analysis of the device and particularly of the strip of MR fluid contained therein is performed using the finite element method. Furthermore, as the device is subject to heating during operation, a thermo-static analysis was also carried out using finite elements when different external temperatures were taken into account. Both analyses, performed by ANSYS® ToolbBox, highlighted the areas of the device most subject to magnetic stress providing useful indications on the influence of temperature both on the magnetization of the magnetic particles and on the MR fluid as a whole.

An innovative non-homogeneous dynamic model is presented for the recovery of temperature during the industrial laser welding process of Al-Si $5\%$ alloy plates. It considers that, metallurgically, during welding, the alloy melts with the presence of solid/liquid phases until total melt is achieved, and afterwards it resolidifies with the reverse process. Further, a polynomial substitute thermal capacity of the alloy is chosen based on experimental evidence so that the volumetric solid-state fraction is identifiable. Moreover, to the usual radiative/convective boundary conditions, the contribution due to the positioning of the plates on the workbench is considered (endowing the model with Cauchy–Stefan–Boltzmann boundary conditions). Having verified the well-posedness of the problem, a Galerkin-FEM approach is implemented to recover the temperature maps, obtained by modeling the laser heat sources with formulations depending on the laser sliding speed. The results achieved show good adherence to the experimental evidence, opening up interesting future scenarios for technology transfer.

Eddy-current inspection of anisotropic composites, such as aeronautical CFRP, demands models that ensure mathematical rigor, tensorial consistency, and clear energetic interpretation. This work presents a novel unified variational framework with a multiplicative tensor perturbation for the time-harmonic eddy-current problem in anisotropic media with defective regions. The formulation is posed in the natural spaces $H(\mathrm{curl};\Omega )\times H^1\left({\Omega }_c\right)$, and the well-posedness is established via the Lax–Milgram theorem under physically consistent assumptions on permeability and conductivity. The sesquilinear form admits a Hermitian decomposition that separates dissipative and reactive contributions, revealing the energetic structure of the weak formulation. Defects are modeled through multiplicative modifications of the baseline anisotropic conductivity tensor. This congruence-based approach preserves symmetry and positive definiteness, ensuring non-negative Joule losses and structural stability, allowing a modular representation of subsurface delamination, fiber breakage, conductive inclusions, and distributed porosity within a single tensorial framework. A central result of the present formulation is the reconstruction of the complex power functional from the evaluation of the weak form at the solution, showing that the active dissipated power and the magnetic reactive power arise directly from the same integral terms. Through the complex Poynting theorem, the quadratic form is linked to the internal complex power, establishing a direct connection between the variational formulation and measurable quantities such as probe impedance variations. Simulations of realistic layered CFRP configurations, including single- and multi-defect scenarios, confirm that, compared with additive perturbations, the multiplicative model provides enhanced energetic contrast, particularly in strongly anisotropic and interacting defect conditions. Agreement with experimental measurements, supported by a quantitative comparison of dissipated power variations obtained from controlled EC experiments, corroborates the physical relevance and robustness of the proposed complex power functional.