# Electromagnetic analysis procedures

 Abaqus/Standard offers several analysis procedures to model piezoelectric, electrical conduction, and electromagnetic phenomena. The distinct electrical phenomena modeled by these procedures is described first, followed by a brief overview of each procedure. The following topics are discussed: Electrostatic, electrical conduction, magnetostatic, and electromagnetic analyses

## Electrostatic, electrical conduction, magnetostatic, and electromagnetic analyses

Piezoelectric effect is the electromechanical interaction exhibited by some materials. This coupled electrostatic-structural response is modeled using piezoelectric analysis in Abaqus/Standard. In this procedure the electric potential is a degree of freedom and its conjugate is the electric charge.

Coupled thermal-electrical conduction, with or without structural coupling, is modeled using electrical procedures. In these procedures the electric potential is a degree of freedom and its conjugate is the electric current. While transient effects are ignored in electrical conduction, thus making it steady state, thermal fields can be modeled either as transient or steady state.

Magnetostatic analysis is used to compute the magnetic fields due to direct currents. It solves the magnetostatic approximation to Maxwell's equations. The magnetic vector potential is a degree of freedom in a magnetostatic analysis, and its conjugate is the surface current.

Electromagnetic analysis is used to model the full coupling between time-varying electric and magnetic fields by solving Maxwell's equations. In such an analysis the magnetic vector potential is a degree of freedom and its conjugate is the surface current.

### Electrostatic procedure

The following electrostatic analysis procedure is available in Abaqus/Standard:

Piezoelectric analysis

In a piezoelectric material an electric potential gradient causes straining, while stress causes an electric potential in the material (Piezoelectric analysis). This coupling is provided by defining the piezoelectric and dielectric coefficients of a material and can be used in natural frequency extraction, transient dynamic analysis, both linear and nonlinear static stress analysis, and steady-state dynamic analysis procedures. In all procedures, including nonlinear statics and dynamics, the piezoelectric behavior is always assumed to be linear.

The following electrical conduction analyses procedures are available in Abaqus/Standard:

Coupled thermal-electrical analysis

The electric potential and temperature fields can be solved simultaneously by performing a coupled thermal-electrical analysis (Coupled thermal-electrical analysis). In these problems the energy dissipated by an electrical current flowing through a conductor is converted into thermal energy, and the electrical conductivity can, in turn, be temperature dependent. Thermal loads can be applied, but deformation of the structure is not considered. Coupled thermal-electrical problems can be linear or nonlinear.

Fully coupled thermal-electrical-structural analysis

A coupled thermal-electrical-structural analysis is used to solve simultaneously for the stress/displacement, the electric potential, and the temperature fields. A coupled analysis is used when the thermal, electrical, and mechanical solutions affect each other strongly. An example of such a process is resistance spot welding, where two or more metal parts are joined by fusion at discrete points at the material interface. The fusion is caused by heat generated due to the current flow at the contact points, which depends on the pressure applied at these points.

These problems can be transient or steady state and linear or nonlinear. Cavity radiation effects cannot be included in a fully coupled thermal-electrical-structural analysis. See Fully coupled thermal-electrical-structural analysis for more details.

### Magnetostatic procedure

The following magnetostatic analysis procedure is available in Abaqus/Standard:

Magnetostatic analysis

A magnetostatic analysis is used to solve for the magnetic vector potential, from which the magnetic field is computed in the entire domain. For example, the magnetic field due to the flow of direct current can be modeled. The procedure supports linear as well as nonlinear magnetic material properties. See Magnetostatic analysis for more details.

### Electromagnetic procedures

Electromagnetic analyses are used to solve for the magnetic vector potential, from which both electric and magnetic fields are computed in the entire domain. The following electromagnetic analysis procedures are available in Abaqus/Standard:

Time-harmonic eddy current analysis

This procedure assumes time-harmonic excitation and response. It supports linear electrical conductivity and linear magnetic material behavior. For example, eddy currents induced in a workpiece that is in the vicinity of a source of excitation (such as a coil carrying alternating current) can be modeled. See Time-harmonic analysis for more details.

Transient eddy current analysis

This procedure assumes general time variation of the excitation and response. It supports linear electrical conductivity and both linear and nonlinear magnetic material behavior. For example, eddy currents induced in a workpiece that is in the vicinity of a source of excitation (such as a coil carrying time-varying current) can be modeled. See Transient analysis for more details.