An extended finite element method formulation for modeling multi-phase boundary interactions in steady state heat conduction problems

Abstract

The present paper proposes an XFEM formulation for heat transfer analysis of multi-phase materials with explicit treatment of boundary interactions. The existence of interfacial resistance at the boundaries of the material phases produces discontinuities in the temperature field and a standard finite element treatment would require complex domain discretizations and additional surface elements to capture the jumps of the temperature values. To overcome this problem, the proposed method captures these jumps by enriching the temperature field around the phase boundaries with appropriate discontinuous functions. Specifically, a new XFEM enrichment scheme is developed to address the issue of multiple-phase junctions, that is, areas where multiple boundaries with different properties intersect. This approach offers the advantage of bypassing the need for complex meshes required by the standard FE method and thus it significantly simplifies the analysis procedure. The elaborated methodology is first validated with existing results from the literature on heat conduction in polycrystalline materials. Then, a detailed model for heat conduction analysis of polymers reinforced with carbon-nanotubes is introduced, which takes into account the role of the interfacial resistance between different material phases. Even though the proposed method is demonstrated in heat conduction problems, it can be straightforwardly extended to other similar problem types, such us electrical conduction or equivalent mechanical properties.