Thermo-Mechanically Coupled FE–FFT Homogenization of Porous Materials
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High-performance porous materials are increasingly used in lightweight structures and multifunctional components subjected to combined mechanical and thermal loading. Their macroscopic thermo-mechanical response is governed by complex interactions between pore morphology, material heterogeneity, and spatial variations in the microstructure. Reliable predictions therefore require multiscale simulation approaches that consistently account for coupled thermal and mechanical effects while remaining computationally efficient. This contribution presents a thermo-mechanically coupled FE–FFT multiscale simulation framework for the analysis of porous materials with functionally graded microstructures. At the macroscale, a finite element formulation based on the open-source FE environment Ferrite.jl [1] is employed, while the microscale response is captured through FFT-based homogenization of representative volume elements (RVEs). Thermal and mechanical field variables are consistently coupled on both scales, enabling the computation of effective stresses, heat fluxes, and thermally induced eigenstresses. The two-scale coupling is realized using the open-source coupling library preCICE [2], which allows for modular solver integration and efficient parallel execution. At the microscale, porous RVEs with complex pore architectures and strong material contrasts are analyzed using the FFT-based solver FeelMath [3], capturing localized thermo-mechanical fields and nonlinear material behavior. The framework naturally accommodates spatially varying microstructures and graded porosity. Several numerical examples demonstrate the capabilities of the proposed approach and highlight the influence of pore architecture and thermal loading on the effective thermo-mechanical response of porous materials. [1] Carlsson, K. et al., Ferrite.jl: A flexible and performant finite element toolkit in Julia, 2024, https://github.com/Ferrite-FEM/Ferrite.jl [2] Chourdakis, G. et al., preCICE v2: A sustainable and user-friendly coupling library, Open Research Europe, Vol. 2:51, 2022, https://doi.org/10.12688/openreseurope.14445.2 [3] M. Kabel and H. Andrae. Fast numerical computation of precise bounds of effective elastic moduli. Berichte des Fraunhofer ITWM, 224, 2013.
