Implicit models for magnetic coenergy have been proposed by Pera et al. to describe the anisotropic nonlinear material behavior of electrical steel sheets. This approach aims at predicting magnetic response for any direction of excitation by interpolating measured of B--H curves in the rolling and transverse directions. In an analogous manner, an implicit model for magnetic energy is proposed. We highlight some mathematical properties of these implicit models and discuss their numerical realization, outline the computation of magnetic material laws via implicit differentiation, and discuss the potential use for finite element analysis in the context of nonlinear magnetostatics.

翻译：Pera等人提出了一种磁共能的隐式模型，用于描述电工钢片的各向异性非线性材料行为。该方法旨在通过插值沿轧制方向和横向测量的B-H曲线，预测任意激励方向下的磁响应。与此类似，我们提出了一种磁能的隐式模型。我们强调了这些隐式模型的某些数学性质，讨论了其数值实现，概述了通过隐式微分计算磁性材料本构关系的方法，并探讨了在非线性静磁学背景下用于有限元分析的潜在应用。