TY - JOUR
T1 - Incorporation of a 3D Energy-Based Vector Hysteresis Model into the Finite Element Method using a Reduced Scalar Potential Formulation
AU - Domenig, Lukas Daniel
AU - Roppert, Klaus
AU - Kaltenbacher, Manfred
N1 - Publisher Copyright:
Authors
PY - 2024/6/1
Y1 - 2024/6/1
N2 - In this work, the reduced scalar potential is utilized to derive a finite element formulation capable of handling hysteretic nonlinear material laws. The Fréchet derivative is employed to deduce a quasi-Newton scheme in the weak form for solving the nonlinear partial differential equation that describes the magnetostatic field. Methods for evaluating the Jacobian are presented, and their performance is compared on a 3-D domain under uniaxial and rotational excitation. The numerical results demonstrate the necessity of a flexible approximation to overcome the non-uniqueness of the Jacobian at reversal points, which naturally occurs in hysteresis loops. Consequently, an exact or excessively localized evaluation would give rise to difficulties in states of material magnetization characterized by these reversal points.
AB - In this work, the reduced scalar potential is utilized to derive a finite element formulation capable of handling hysteretic nonlinear material laws. The Fréchet derivative is employed to deduce a quasi-Newton scheme in the weak form for solving the nonlinear partial differential equation that describes the magnetostatic field. Methods for evaluating the Jacobian are presented, and their performance is compared on a 3-D domain under uniaxial and rotational excitation. The numerical results demonstrate the necessity of a flexible approximation to overcome the non-uniqueness of the Jacobian at reversal points, which naturally occurs in hysteresis loops. Consequently, an exact or excessively localized evaluation would give rise to difficulties in states of material magnetization characterized by these reversal points.
KW - Energy-based vector hysteresis
KW - Finite element analysis
KW - finite element method
KW - Jacobian matrices
KW - line search
KW - Magnetic domains
KW - Magnetic hysteresis
KW - Mathematical models
KW - Newton method
KW - quasi-Newton scheme
KW - Vectors
KW - finite element method (FEM)
UR - http://www.scopus.com/inward/record.url?scp=85190169339&partnerID=8YFLogxK
U2 - 10.1109/TMAG.2024.3387354
DO - 10.1109/TMAG.2024.3387354
M3 - Article
AN - SCOPUS:85190169339
SN - 0018-9464
VL - 60
SP - 1
EP - 8
JO - IEEE Transactions on Magnetics
JF - IEEE Transactions on Magnetics
IS - 6
M1 - 7300708
ER -