Comparison of Analytical and FFT‐Based Predictions of Effective Stiffness in Isotropic and Anisotropic Closed‐Cell Materials

ABSTRACT This work investigates the elastic behavior of isotropic and anisotropic closed‐cell porous materials using analytical and Fast‐Fourier‐Transform (FFT)‐based numerical approaches. The study focuses on understanding how microstructural features, such as pore shape, orientation, and solid volume fraction, influence the macroscopic stiffness of the material. Analytical expressions based on extended Gibson–Ashby‐type models are used to predict the directional effective stiffness under varying anisotropy ratios and porosities. These predictions are compared with results obtained from FFT‐based homogenization of 3D microstructures. The analysis highlights significant deviations between analytical and numerical results in highly anisotropic or low‐density regimes, with the analytical models often overestimating the stiffness. The findings underline the limitations of classical analytical formulations for complex microstructures and demonstrate the accuracy and efficiency of FFT‐based homogenization in capturing anisotropy‐induced mechanical effects.