This work addresses the multiscale modelling of thermo-electro-mechanically coupled material behaviour, with particular emphasis on the influence of microstructural features such as inclusions, pores and material interfaces. In the first part, a thermodynamically consistent cohesive zone model is developed for electrical conductors subjected to coupled thermo-electro-mechanical loading. Special attention is given to the deformation-induced interface damage processes on the thermal and electrical conductivity. The formulation is validated through an analytical example and demonstrated via a numerical case study involving a wire bonding problem. The second part of the thesis is motivated by non-destructive testing of metals using resistivity measurements. A thermo-electro-mechanically coupled multiscale formulation for electrical conductors in small-strain settings is presented and later extended to explicitly account for material interfaces at the microscale. The proposed framework is illustrated through a series of numerical examples, capturing key features such as size effects and the impact of mechanically induced interfacial degradation. Furthermore, the predictive capabilities of the multiscale model are highlighted, particularly in relation to electrically conductive materials with resistive grain boundaries. In response to long-standing discrepancies in grain boundary resistivity measurements, the thesis revisits the Andrews method and reinterprets it within the proposed multiscale modelling framework using homogenisation theory. This reinterpretation establishes a clear link between measurable macroscopic resistance and microscopic interface behaviour. The final part of the thesis provides a mathematical foundation for the multiscale approach to thermo-electrical homogenisation. Using Hill--Mandel-type homogenisation, asymptotic expansions, and two-scale convergence technique, it is shown that the macroscopic equations governing coupled thermo-electrical behaviour -- previously derived from physical arguments -- can also be rigorously obtained through mathematical homogenisation theory. Overall, the developments in this thesis provide a mathematically and physically consistent basis for the multiscale analysis of thermo-electro-mechanically coupled fields in electrical conductors.
Dilek Güzel (Wed,) studied this question.