Work

On dissipative effects in thermo-electrically coupled systems: Hill–Mandel-type homogenisation, asymptotic expansions and two-scale convergence

Year: 2025

Type: article

Abstract: Accurately predicting the macroscopic behaviour of heterogeneous materials, particularly in thermo-electrically coupled systems, remains a challenging problem in materials science and engineering. Against this background, this study presents a comprehensive framework for the homogenisation of electrical conductors subject to strongly coupled thermo-electrical processes in (quasi-)stationary settings, with particular focus lying on Joule heating and temperature-dependent electrical conductivities. The proposed methodology combines analytical homogenisation, asymptotic expansions and Hill–Mandel-type multiscale techniques. In doing so, both, a natural physical interpretation and a rigorous mathematical justification of the governing set of effective macroscopic field equations are provided. Representative boundary value problems in two- and three dimensional settings are eventually studied to validate the effectiveness of these methods in capturing the complex behaviour of heterogeneous thermo-electric materials.

Source: Journal of the Mechanics and Physics of Solids

DOI: 10.1016/j.jmps.2025.106427

Authors: D. Güzel, D. Wiedemann, T. Kaiser, A. Menzel

Language: English

Topic: Advanced Mathematical Modeling in Engineering

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $4,220

Funder: Deutsche Forschungsgemeinschaft

Award: TRR 188: Schädigungskontrollierte Umformprozesse