Structured Neural Network Models for Anisotropic Magnetic Constitutive Laws

High-performance electrical steel used for iron cores of power transformers and generators exhibits complex material behavior. While modeling and simulation of isotropic nonlinear response is well understood, the incorporation of magnetic anisotropy remains challenging. This work proposes to utilize a structured neural network architecture to systematically describe the anisotropic nonlinear anhysteretic magnetic material response of electrical steel sheets. By constructing a convex and smooth co-energy density with dedicated behavior at infinity, we can ensure thermodynamic consistency and correct physical behavior and further guarantee basic mathematical properties which provide well-posedness of corresponding magnetic field problems and efficient numerical solvers. Numerical tests demonstrate the capability of the proposed method to describe strongly anisotropic behavior as well as its robust convergence in finite-element simulations.