A New Take on Sharp Cracks in Brittle Dielectrics: Where Electric Dipole Layers Meet Concentrated Line Forces

ABSTRACT In this work, novel electrostatic aspects of sharp cracks in brittle dielectrics are discussed using the example of an impermeable Griffith crack in an infinite linear isotropic dielectric plate. On the one hand, electrostatic force densities stemming from the Maxwell stress tensor according to Lorentz are derived mathematically, where the involvement of the characteristic square root singularity of the electric field at the crack fronts in the occurrence of concentrated line forces is examined. On the other hand, their physical interpretation is addressed, where the absence of any free or bound charges on a macroscopic level in the vicinity of the crack fronts complicates the matter. Introduction of the concept of electric dipole layers, usually absent in standard formulations of macroscopic electrostatics, finally sheds light on the issue, and a striking parallel is drawn to conducting sheets of zero thickness.