Fundamentals of electro-mechanically coupled cohesive zone formulations for electrical conductors

Motivated by the influence of (micro-)cracks on the effective electrical properties of material systems and components, this contribution deals with fundamental developments on electro-mechanically coupled cohesive zone formulations for electrical conductors. For the quasi-stationary problems considered, Maxwell’s equations of electromagnetism reduce to the continuity equation for the electric current and to Faraday’s law of induction, for which non-standard jump conditions at the interface are derived. In addition, electrical interface contributions to the balance equation of energy are discussed and the restrictions posed by the dissipation inequality are studied. Together with well-established cohesive zone formulations for purely mechanical problems, the present developments provide the basis to study the influence of mechanically-induced interface damage processes on effective electrical properties of conductors. This is further illustrated by a study of representative boundary value problems based on a multi-field finite element implementation.