The Maxwell stress tensor for magnetoelastic materials

Abstract

The emergency states of the electromagnetic devices short-circuit currents get very high impulse intensity and are the source of the undesirable electrodynamics forces. Mechanical stresses in the wires may than cause the long-term plastic strains. Therefore in designing of the elements of the power grid (distribution stations and transformation stations) the technical protective norms are used in order to omit such mechanical effects [e.g. Poland – the Polish Norm is PN-EN 60865-1:2002(U)]. In our opinion the above problem demand the wider theoretical description from the mechanical point of view. In this paper, deformable continuous medium immersed in electromagnetic field is considered. Based on momentum balance, on the traditional way a stress tensor and a volume force were introduced. Every quantity consists of two parts: electromagnetic part and mechanical part. Electromagnetic stress tensor is called Maxwell stress tensor. In the case of linear material equations the electromagnetic volume force equals zero. In this paper, we show the analysis of the influence of primary magnetic field orientation on the property of Maxwell stress tensor for linear magnetoelasticity and static magnetoelasticity. While doing research on eigenvalues of this tensor, it was established that the primary magnetic field always generates three-dimensional state of stress, no matter what the orientation was. In order to introduce reduced stresses, classical failure criteria were used: Tresca’s–Guest’s criterion and Huber–von Mises criterion. Having tested the eigenvalues of Maxwell stress tensor in linear magnetoelasticity, we received results that put the usefulness of this approximation into question. The approximation of static magnetoelasticity seems more reliable.