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Article
Publication date: 25 July 2019

Stephan Willerich and Hans-Georg Herzog

The use of gradient-based methods in finite element schemes can be prevented by undefined derivatives, which are encountered when modeling hysteresis in constitutive…

Abstract

Purpose

The use of gradient-based methods in finite element schemes can be prevented by undefined derivatives, which are encountered when modeling hysteresis in constitutive material laws. This paper aims to present a method to deal with this problem.

Design/methodology/approach

Non-smooth Newton methods provide a generalized framework for the treatment of minimization problems with undefined derivatives. Within this paper, a magnetostatic finite element formulation that includes hysteresis is presented. The non-linear equations are solved using a non-smooth Newton method.

Findings

The non-smooth Newton method shows promising convergence behavior when applied to a model problem. The numbers of iterations for magnetization curves with and without hysteresis are within the same range.

Originality/value

Mathematical tools like Clarke's generalized Jacobian are applied to magnetostatic field problems with hysteresis. The relation between the non-smooth Newton method and other methods for solving non-linear systems with hysteresis like the M(B)-iteration is established.

Details

COMPEL - The international journal for computation and mathematics in electrical and electronic engineering , vol. 38 no. 5
Type: Research Article
ISSN: 0332-1649

Keywords

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