On Local Computation of the Electromagnetic Force Field in Deformable Bodies *

Abstract

We present a finite-element based method for the computation of force fields, using the language and concepts of differential geometry, in the familiar "eddy-currents" context (displacement currents ignored). The approach is Lagrangian (comoving mesh) and the degrees of freedom are magnetomotive forces along material lines which coincide with the edges of the mesh. The essential result is: the edge-element implementation of the h-formulation of the eddy-currents problem can serve without any modification when conductors are mobile and deformable, provided the assembly of finite-element matrices is done at each time step. A simple formula gives the virtual work of electromagnetic forces, hence a notion of "nodal forces" from which an interpolation of the force field can be derived if needed.