Incremental permeability modeling in 3MA hybrid prototype

This study presents a comprehensive 2D transient finite element method (FEM) for modeling incremental permeability in a hybrid 3MA prototype used for non-destructive testing (NDT) of ferromagnetic materials. A dynamic vector Jiles–Atherton (JA) hysteresis model is implemented to capture the nonlinear and hysteretic magnetic behavior of both the specimen and the ferrite yoke, specifically addressing the vector nature of magnetic fields in complex L- and T-shaped yoke–specimen junctions. Classical eddy current effects are incorporated through material electrical conductivity, while the FEM input parameters are identified via an Artificial Bee Colony (ABC) optimization algorithm. The model is validated against experimental measurements for two steel grades 22MnB5 and FeSi, demonstrating excellent agreement for 22MnB5 (relative error < 3%) and good qualitative agreement for FeSi, with residual deviations attributed to unmodeled excess losses. The results confirm the necessity of 2D vector hysteresis models over 1D scalar alternatives for accurate flux distribution prediction in complex geometries, and provide a validated simulation framework for advancing quantitative 3MA based NDT systems.