A direct FE2 method for concurrent multilevel modeling of a coupled thermoelectric problem – Joule heating effect – in multiscale materials and structures

Coupled thermoelectric problem significantly affects the performance of electric devices, while there seems to be no method for concurrent multiscale modeling of such problems, which significantly limits the development of advanced electric devices consisting of multiscale structures. To this end, a Direct FE ² (D-FE ²) method is proposed for concurrent multiscale modeling of a typical type of coupled thermoelectric problems, i.e., Joule heating effect, in heterogeneous materials and structures. To enforce energy equilibrium and realize information transfer between the macro- and meso‑scales, the Hill-Mandel homogenization condition was generalized to account for both thermal and electric energy, while periodic boundary conditions derived from kinematic constraints were prescribed to both electric potential and temperature to link meso‑scale RVEs to macro-elements in the D-FE ² model. The proposed D-FE ² method can be easily implemented using the available feature “Multiple Points Constraint (MPC)” in many commercial FE software. A series of numerical examples including steady-state analysis and transient analysis of fiber composites, porous materials and lattice structures validate the favorable accuracy and efficiency of the proposed D-FE ² method in modeling the Joule heating phenomenon in multiscale materials and structures. This also implies the promising potential of the proposed D-FE ² method in modeling and design of large-scale electric devices with multiscale structures.