## Details

Originalsprache | Englisch |
---|---|

Aufsatznummer | 110078 |

Seitenumfang | 31 |

Fachzeitschrift | Engineering fracture mechanics |

Jahrgang | 303 |

Frühes Online-Datum | 17 Apr. 2024 |

Publikationsstatus | Veröffentlicht - 5 Juni 2024 |

## 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.

## ASJC Scopus Sachgebiete

**Werkstoffwissenschaften (insg.)**- Ingenieurwesen (insg.)
**Werkstoffmechanik**- Ingenieurwesen (insg.)
**Maschinenbau**

## Zitieren

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**Phase-field modeling of fracture for ferromagnetic materials through Maxwell's equation.**/ Noii, Nima; Ghasabeh, Mehran; Wriggers, Peter.

in: Engineering fracture mechanics, Jahrgang 303, 110078, 05.06.2024.

Publikation: Beitrag in Fachzeitschrift › Artikel › Forschung › Peer-Review

*Engineering fracture mechanics*,

*303*, Artikel 110078. https://doi.org/10.48550/arXiv.2404.07346, https://doi.org/10.1016/j.engfracmech.2024.110078

}

TY - JOUR

T1 - Phase-field modeling of fracture for ferromagnetic materials through Maxwell's equation

AU - Noii, Nima

AU - Ghasabeh, Mehran

AU - Wriggers, Peter

N1 - Funding Information: N. Noii founded by the Priority Program DFG-SPP 2020 within its second funding phase. P. Wriggers were funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany\u2019s Excellence Strategy within the Cluster of Excellence PhoenixD, EXC 2122 (project number: 390833453 ).

PY - 2024/6/5

Y1 - 2024/6/5

N2 - 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.

AB - 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.

KW - Electric field

KW - Ferromagnetic

KW - Magnetic field

KW - Magnetic vector potential

KW - Magnetization

KW - Magnetomechanical

KW - Magnetostriction

KW - Maxwell's equation

KW - Phase-field fracture

UR - http://www.scopus.com/inward/record.url?scp=85190789697&partnerID=8YFLogxK

U2 - 10.48550/arXiv.2404.07346

DO - 10.48550/arXiv.2404.07346

M3 - Article

AN - SCOPUS:85190789697

VL - 303

JO - Engineering fracture mechanics

JF - Engineering fracture mechanics

SN - 0013-7944

M1 - 110078

ER -