Stress characterisation from the magneto-mechanical effect: a methodology based on numerical simulation

This paper presents a simulation-based framework for quantitative stress characterisation in ferromagnetic materials using the magneto-mechanical effect. The approach is demonstrated on a two-dimensional (2D) uniform in-plane stress configuration. Considering a specific magnetic excitation apparatus, finite element simulations incorporating magneto-mechanical coupling are used to generate the forward dataset of magnetic measurements. This dataset is fitted by a third-order polynomial analytical model that renders the inversion problem explicit and mathematically tractable. A two-stage inversion strategy is introduced to determine both the stress orientation and magnitude from magnetic induction measurements acquired along different directions. We show that the accuracy of stress reconstruction depends strongly on the stress configuration and on the chosen measurement directions. By combining multiple measurements and analysing the overlap area of admissible solutions, the uncertainty can be progressively reduced. The centroid of admissibility area provides a reliable estimate even when the uncertainty remains high. The proposed approach offers a general, calibration-free, and progressively refinable pathway for non-destructive magnetic stress characterisation. The reliability of the approach depends fundamentally on two elements: the accuracy of the forward magneto-mechanical model with properly identified material parameters, and the quality of the magnetic measurement system.