Abstract
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.
Highlights
Computational multiscale formulations are well-established numerical tools to predict macroscopic material properties from the underlying heterogeneous microstructure
An electro-mechanically coupled computational multiscale formulation for electrical conductors is proposed in the present contribution that allows to study the influence of microscale deformation processes on the effective electrical properties at the macroscale
The set of partial differential equations governing the electro-mechanically coupled behaviour of electrical conductors in a finite strain setting was discussed, and appropriate scale bridging relations were proposed that are in accordance with wellestablished computational homogenisation procedures for mechanical problems, thermal problems, and electrical problems of dielectric solids
Summary
Computational multiscale formulations are well-established numerical tools to predict macroscopic material properties from the underlying heterogeneous microstructure. Multiscale methods contribute to an understanding of experimentally recorded data at the macroscale by relating the properties of single phases and interfaces at the microscale to the effective macroscale material response In this regard, an electro-mechanically coupled computational multiscale formulation for electrical conductors is proposed in the present contribution that allows to study the influence of microscale deformation processes on the effective electrical properties at the macroscale. An electro-mechanically coupled computational multiscale formulation for electrical conductors is proposed in the present contribution that allows to study the influence of microscale deformation processes on the effective electrical properties at the macroscale This contribution is motivated by experimental findings on material thin films [7].
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