Keywords: infinite element, non-linear finite element, magnetostrictive materials, Maxwell stress tensor, coupling.

In recent years, many non-linear finite element methods (FEM) have been developed to simulate magnetostrictive materials due to their technological capability of coupling elastic and magnetic fields. From the point of view of the magnetic field simulation, most of the works use the scalar magnetic potential formulation [1] but a minority, the vector potential one [2]. The last formulation permits the simulation of an electric current (magnetic sources) domain, although three magnetic degrees of freedom per node (one in each space direction) are required and the CPU time increases. Furthermore, in the electromagnetic problem, although the domain of interest is bounded, the physical domain is infinite. From a numerical point of view this dichotomy introduces two limitations: (a) it is not possible to model an infinite domain with a finite method, and (b) the Dirichlet boundary conditions can not be applied, especially with the use of the magnetic vector potential formulations. In previous studies, these limitations were solved by modeling a portion of the infinite domain, increasing the mesh size and consequently the computational cost and even the numerical error when the problem is not truncated at the correct distance. A convenient way to solve both limitations is through the infinite finite element method (IFEM).

In this work, an IFEM has been developed to ensure the magnetic boundary conditions and to reduce the computing time. The IFEM has been combined with a magnetostrictive nonlinear three-dimensional FEM, based on the magnetic vector potential and developed by the authors in previous studies, where residual vectors and consistent tangent matrices were formulated and implemented in a standard eight-node isoparametric element with seven degrees of freedom (displacements, voltage, magnetic vector potential) per node.

In order to validate the IFEM, experimental results given in Reference [3] are simulated and it is concluded that: (i) it is necessary to conduct a thermo-magneto-elastic formulation to study the magnetostrictive behavior under high electric currents and (ii) the combined FEM-IFEM reduces the computation time. That is the main drawback of the vector potential formulation, although it is the only way to model all magnetic domains. Therefore, this formulation permits the study of the thermo-magneto-elastic behavior due to the Joule heating generated by the electric currents. In addition, this formulation is ideal for the study of eddy currents when dynamic problems are simulated.

1

K.S. Kannan, A. Dasgupta, "A nonlinear Galerkin finite-element theory for modeling magnetostrictive smart structures", Smart Mater. Struct., 6(3), 341-350, 1997. doi:10.1088/0964-1726/6/3/011

2

J.L. Pérez-Aparicio, H. Sosa, "A continuum three-dimensional, fully coupled, dynamic, non-linear finite element formulation for magnetostrictive materials", Smart Mater. Struct., 13(3), 493-502, 2004. doi:10.1088/0964-1726/13/3/007

3

M. Anjanappa, J. Bi, "A theoretical and experimental study of magnetostrictive mini-actuators", Smart Mater. Struct., 3(2), 83-91, 1994. doi:10.1088/0964-1726/3/2/001

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