The Structure of Material Forces in Electromagnetic Materials

Material forces govern the behaviour and the evolution of a defect or of an inhomogeneity in a solid material. In elastic materials these forces are associated with the Eshelby tensor, as is known. In structured or micro-structured materials, an Eshelby–like stress can be assembled by following a simple rule. By appealing to this rule, one is able to propose an expression for the Eshelby tensor in electromagnetism. A variational procedure is hereby expounded, from which an expression for the classical electromagnetic stress tensor, whose form is otherwise controversial, stems straightforwardly. The electromagnetic Eshelby–like tensor is derived on this base.