Configurational Forces and Gauge Conditions in Electromagnetic Bodies

Material inhomogeneities, defective materials or fractured solids address the notion of configurational force. In electromagnetic deformable bodies this force also depends upon the electromagnetic potentials, which unfortunately are not uniquely defined. In electrostatics the problem of uniqueness is scarcely relevant, as only the scalar potential plays a role. Thus, dielectrics are adequately described in this context, even in the presence of a crack-line. In electrodynamics also the vector potential plays a prominent role and the lack of uniqueness of the electromagnetic potentials cannot be disregarded. The problem of solving this indeterminacy for the quantities of interest appeals to additional conditions, the gauge conditions. Gauge transformations, which leave invariant the Maxwell equations and the balance of momentum in material form, are here examined. In configurational mechanics of electromagnetic solids, a possible gauge dependent quantity is the material momentum, which seems to be related to some extent to supercurrents in deformable superconductors.