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There is a growing trend in both academia and industry towards carrying out realistic multiphysics simulations that account for coupling among different fields such as stress-displacement, thermal, electromagnetism, etc. This paper describes some recent work to implement capabilities for solving electromagnetic field problems in the commercial finite element software package, Abaqus, which augment the well-established capabilities (in Abaqus) to solve stress-displacement, thermal, and coupled thermo-mechanical problems. The specific class of coupled problems described in this paper is known as eddy current problems. Eddy currents are generated in a metal workpiece when it is placed within a timevarying magnetic field. Joule heating arises when the energy dissipated by the eddy currents flowing through the workpiece is converted into thermal energy. This heating mechanism is usually referred to as induction heating. The time-varying magnetic field is usually generated by a coil that carries either a known amount of total current or an unknown amount of current under a known potential (voltage) difference. The electric and magnetic fields are governed by Maxwell s equations describing electromagnetic phenomena. The formulation is based on the low-frequency assumption, which neglects the displacement current term in Ampere s law. The time-harmonic eddy current analysis procedure is based on the assumption that a time-harmonic excitation with a certain frequency results in a timeharmonic electromagnetic response with the same frequency everywhere in the domain. The transient eddy current analysis does not make any such assumption.The eddy current analysis provides output, such as Joule heat dissipation or magnetic body force intensity, that can be transferred to drive a subsequent heat transfer, coupled temperature-displacement, or stress/displacement analysis. This allows for modeling the interactions of the electromagnetic fields with thermal and/or mechanical fields in a sequentially coupled manner. The electromagnetic elements use an element edge-based interpolation of the fields instead of the standard node-based interpolation. The paper presents the theoretical formulation, outlines some of the unique challenges associated with solving electromagnetic field problems, and shows a few examples utilizing the new capabilities.

RECENT ADVANCES TOWARDS SOLVING ELECTROMAGNETIC PROBLEMS IN COMMERCIAL FINITE ELEMENT SOFTWARE PACKAGE ABAQUS