A finite deformation electro-mechanically coupled computational multiscale formulation for electrical conductors

Motivated by the influence of deformation-induced microcracks on the effective electrical properties at the macroscale, an electro-mechanically coupled computational multiscale formulation for electrical conductors is proposed. The formulation accounts for finite deformation processes and is a direct extension of the fundamental theoretical developments presented by Kaiser and Menzel (Arch Appl Mech 91:1509–1526, 2021) who assume a geometrically linearised setting. More specifically speaking, averaging theorems for the electric field quantities are proposed and boundary conditions that a priori fulfil the extended Hill–Mandel condition of the electro-mechanically coupled problem are discussed. A study of representative boundary value problems in two- and three-dimensional settings eventually shows the applicability of the proposed formulation and reveals the severe influence of microscale deformation processes on the effective electrical properties at the macroscale.