An electro-mechanically coupled computational multiscale formulation for electrical conductors

Abstract

Motivated by experimental findings on deformation induced microcracks in thin metal films and by their influence on the effective macroscopic electrical conductivity, a computational multiscale formulation for electrical conductors is proposed in this contribution. In particular, averaging theorems for kinematic quantities and for their energetic duals are discussed, an extended version of the Hill–Mandel energy equivalence condition is proposed and suitable boundary conditions for the microscale problem are elaborated. The implementation of the proposed framework in a two-scale finite element environment is shown and representative boundary value problems are studied in two- and three-dimensional settings.