Material Description

Abstract

In the last two chapters the governing equations of field matter interaction were chiefly based on the spatial or Eulerian description. Only very briefly the material or Lagrangean formulation was given. Such a formulation is of advantage in describing the deformation of solids, because the boundary conditions for solids are usually prescribed on the undeformed body, which is generally the body in its reference configuration. As a consequence, any theory describing deformable solids in the electromagnetic fields should from the outset be given in the material description. This is not done in general; on the contrary, in almost all theories the spatial description is applied. The Lagrangean formulation is introduced only afterwards, and if so, only by introducing some approximations, e.g. linearizations. These linearization procedures, although being straightforward are nevertheless quite cumbersome. They become an almost trivial matter when the material description of the governing field equations is used from the outset.