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.
Highlights
Advances in material science and fabrication technologies enable the development of flexible electronic devices like wearable sensors [1,22] and foldable displays [3,15], which are in the focus of many engineering applications
Processes at different material length- and timescales are considered in finite element-based computational multiscale simulations with the evaluation of classic constitutive material models being replaced by finite element calculations of the underlying material microstructures
Summary Motivated by advances in flexible electronic technologies and by the desire to develop non-destructive testing methods, an electro-mechanical multiscale formulation for conductors is proposed in this contribution
Summary
Advances in material science and fabrication technologies enable the development of flexible electronic devices like wearable sensors [1,22] and foldable displays [3,15], which are in the focus of many engineering applications. Processes at different material length- and timescales are considered in finite element-based computational multiscale simulations with the evaluation of classic constitutive material models being replaced by finite element calculations of the underlying material microstructures The latter ones are represented by representative volume elements (RVEs) that take distinct microstructural features like grains and microcracks into account [9,27]. Changes in electrical conductivity due to mechanically induced microcracks motivate the present contribution Against this background, assume for a homogeneous, quasi-one-dimensional electrical problem for which the effective macroscopic electrical resistance is given by. Averaging theorems for kinematic quantities and for their energetic duals are elaborated, generalized Hill–Mandel conditions are derived and suitable boundary conditions are discussed Based on these developments, a finite element implementation of the proposed theory is presented in Sect. A study of representative boundary value problems in Sect. 5 eventually shows the applicability of the proposed formulation
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
