Phase-field modeling of fracture for ferromagnetic materials through Maxwell's equation

authored by
Nima Noii, Mehran Ghasabeh, Peter Wriggers
Abstract

Electro-active materials are classified as electrostrictive and piezoelectric materials. They deform under the action of an external electric field. Piezoelectric material, as a special class of active materials, can produce an internal electric field when subjected to mechanical stress or strain. In return, there is the converse piezoelectric response, which expresses the induction of the mechanical deformation in the material when it is subjected to the application of the electric field. This work presents a variational-based computational modeling approach for failure prediction of ferromagnetic materials. In order to solve this problem, a coupling between magnetostriction and mechanics is modeled, then the fracture mechanism in ferromagnetic materials is investigated. Furthermore, the failure mechanics of ferromagnetic materials under the magnetostrictive effects is studied based on a variational phase-field model of fracture. Phase-field fracture is numerically challenging since the energy functional may admit several local minima, imposing the global irreversibility of the fracture field and dependency of regularization parameters related discretization size. Here, the failure behavior of a magnetoelastic solid body is formulated based on the Helmholtz free energy function, in which the strain tensor, the magnetic induction vector, and the crack phase-field are introduced as state variables. This coupled formulation leads to a continuity equation for the magnetic vector potential through well-known Maxwell's equations. Hence, the energetic crack driving force is governed by the coupled magneto-mechanical effects under the magneto-static state. Several numerical results substantiate our developments.

Organisation(s)
Institute of Continuum Mechanics
PhoenixD: Photonics, Optics, and Engineering - Innovation Across Disciplines
External Organisation(s)
German Institute of Rubber Technology (DIK e.V.)
TU Bergakademie Freiberg - University of Resources
Type
Article
Journal
Engineering fracture mechanics
Volume
303
No. of pages
31
ISSN
0013-7944
Publication date
05.06.2024
Publication status
Published
Peer reviewed
Yes
ASJC Scopus subject areas
Materials Science(all), Mechanics of Materials, Mechanical Engineering
Electronic version(s)
https://doi.org/10.48550/arXiv.2404.07346 (Access: Open)
https://doi.org/10.1016/j.engfracmech.2024.110078 (Access: Closed)
 

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