A FEM-BEM coupling strategy for the modeling of magnetoelectric effects in composite structures

Urdaneta-Calzadilla, A; Galopin, Nicolas; Niyonzima, Innocent; Chadebec, Olivier; Bannwarth, Bertrand; Meunier, Gérard

doi:10.1016/j.enganabound.2023.02.034

Cited by 4 publications

(5 citation statements)

References 73 publications

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“…The electrical and mechanical problems are limited to the active domain Ω m [4]. Indeed, because of the high permittivity of piezoelectric materials and since the electrodes are in direct contact with the piezoelectric materials, the electric displacement field is canalyzed inside the materials.…”

Section: Formulations and Resolution Methodsmentioning

confidence: 99%

“…This is associated with poor conditioning of the global system which results from the difference in the scale of the physics involved (MPa vs Fm −1 vs mH −1 ). A coupled multiphysics solution can be obtained from the iterative resolution of single-physics problems [4].…”

Section: Solving the Discretized Me Problemmentioning

confidence: 99%

“…It involved solving for (B, S) in H = 3 H0 µr+2 , with µ r = B/µ 0 H, both supposed scalar and uniform because of the considered spherical geometry, with H 0 oriented along the (z) direction, together with solving for (B, S) in T zz = T 0 . Figure 1 shows the L 2 error of the formulation compared to the analytical solution [4]. They show the h-convergence of the formulation for H 0 = 200 kAm −1 and T 0 = 10 MPa.…”

Section: Formulationmentioning

confidence: 99%

“…This can be avoided by setting up a coupling between the Boundary Element Method (BEM) and the FEM for the magnetic part, and the FEM for the electric and mechanical parts. The coupling between FEM and BEM has proved to be a powerful tool for reducing computational time and allocated memory for solving multi-physics problems, and enabling the use of a single mesh for all the problems concerned (see e.g., [4] by the authors). It should be noted, however, that this previous work was limited to a linearized approach to magneto-mechanical effects, which severely limited the validity of the model.…”

Section: Introductionmentioning

confidence: 99%

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FEM-BEM Modeling of Nonlinear Magnetoelectric Effects in Heterogeneous Composite Structures

Urdaneta-Calzadilla,

Galopin,

Niyonzima

et al. 2024

IEEE Trans. Magn.

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This paper proposes a multiphysics multi-method model for 3D nonlinear magnetoelectric effects in heterogeneous composite structures made of the association of piezoelectric and magnetostrictive materials. Through the coupling of the Finite Element Method with the Boundary Element Method, only the active material is explicitly considered, and thus a single mesh is used for the resolution of all the physics. A mixed formulation combining the vector potential in the volume and a scalar potential in the free space is used to model magnetic phenomena. Non-linear constitutive laws for the magnetostrictive phase are derived from partial derivatives of a scalar invariant's formulation of the Helmholtz free energy, while linear relations are used to describe piezoelectric behavior. The coupled problem is solved by iteratively solving single-physics problems, and the full algorithm is used to model a rotating coilless ME device which can operate as an energy harvester or as an actuator.

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Section: Formulations and Resolution Methodsmentioning

confidence: 99%

Section: Solving the Discretized Me Problemmentioning

confidence: 99%

Section: Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

FEM-BEM Modeling of Nonlinear Magnetoelectric Effects in Heterogeneous Composite Structures

Urdaneta-Calzadilla,

Galopin,

Niyonzima

et al. 2024

IEEE Trans. Magn.

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“…The main interest in this approach based on MMM is to avoid the need to mesh the air. Note that, there exist some other numerical modelization approaches like FEM-BEM (Calzadilla, 2023; Wautischer et al , 2022), volume integral methods (VIM) (Trowbridge, 1996; Le-Van et al , 2015; Han et al , 1994) or FEM-MMP (Smajic et al , 2015) which also does not need to mesh the air. In this work, we choose to work with MMM because it is one of the most popular numerical methods in electrical engineering and it focuses on the optimization unknowns.…”

Section: Introductionmentioning

confidence: 99%

Topological optimization in 3D-magnetostatics: development of adjoint methods using the equations of magnetic moments

Michel,

Messine,

Poirier

2024

COMPEL

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Purpose The purpose of this paper is mainly to develop the adjoint method within the method of magnetic moment (MMM) and thus, to provide an efficient new way to solve topology optimization problems in magnetostatic to design 3D-magnetic circuits. Design/methodology/approach First, the MMM is recalled and the optimization design problem is reformulated as a partial derivative equation-constrained optimization problem where the constraint is the Maxwell equation in magnetostatic. From the Karush–Khun–Tucker optimality conditions, a new problem is derived which depends on a Lagrangian parameter. This problem is called the adjoint problem and the Lagrangian parameter is called the adjoint parameter. Thus, solving the direct and the adjoint problems, the values of the objective function as well as its gradient can be efficiently obtained. To obtain a topology optimization code, a semi isotropic material with penalization (SIMP) relaxed-penalization approach associated with an optimization based on gradient descent steps has been developed and used. Findings In this paper, the authors provide theoretical results which make it possible to compute the gradient via the continuous adjoint of the MMMs. A code was developed and it was validated by comparing it with a finite difference method. Thus, a topology optimization code associating this adjoint based gradient computations and SIMP penalization technique was developed and its efficiency was shown by solving a 3D design problem in magnetostatic. Research limitations/implications This research is limited to the design of systems in magnetostatic using the linearity of the materials. The simple examples, the authors provided, are just done to validate our theoretical results and some extensions of our topology optimization code have to be done to solve more interesting design cases. Originality/value The problem of design is a 3D magnetic circuit. The 2D optimization problems are well known and several methods of resolution have been introduced, but rare are the problems using the adjoint method in 3D. Moreover, the association with the MMMs has never been treated yet. The authors show in this paper that this association could provide gains in CPU time.

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Multiphysics modeling of magnetoelectric composite disks by a 2D axisymmetric finite element approach

Karimi,

Talleb

2024

Finite Elements in Analysis and Design

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A FEM-BEM coupling strategy for the modeling of magnetoelectric effects in composite structures

Cited by 4 publications

References 73 publications

FEM-BEM Modeling of Nonlinear Magnetoelectric Effects in Heterogeneous Composite Structures

FEM-BEM Modeling of Nonlinear Magnetoelectric Effects in Heterogeneous Composite Structures

Topological optimization in 3D-magnetostatics: development of adjoint methods using the equations of magnetic moments

Multiphysics modeling of magnetoelectric composite disks by a 2D axisymmetric finite element approach

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