An FFT-based framework for predicting corrosion-driven damage in fractal porous media

Abstract: Understanding fracture in cementitious materials caused by the deposition and growth of corrosion products requires scale-bridging approaches due to the large length-scale difference between the micro-pores, where deposition occurs, and the structure, where deterioration manifests. Cementitious materials bear a highly heterogeneous micro-structure owing to the fractal nature of micro-pores. Simultaneously, a corrosion-driven fracture is a multi-physics problem involving ionic diffusion, chemical reactions, and stress development. This multi-scale and multi-physical character makes scale-bridging studies computationally costly, often leading to the use of simplified fractal porous media, which has important consequences for the quantitative interpretation of the results. Recent advances in homogenization approaches using Fast-Fourier-Transform (FFT) based methods have raised interest due to their ease of implementation and low computational cost. This paper presents an FFT-based framework for solving corrosion-driven fractures within fractal porous media. We demonstrate the effectiveness of the Fourier-based spectral method in resolving the multiple corrosion-driven mechanisms such as ionic diffusion, stress development, and damage within a fractal porous microstructure. Based on the presented methodology, we analyze the impact of simplifying fractal porous media with simple Euclidean geometry on corrosion-driven fracture. Our results demonstrate the importance of preserving both the porosity and fractal nature of pores for precise and reliable modeling of corrosion-driven failure mechanisms.