Fracture mechanics of open-porous materials: A Voronoi-based approach

Kurzfassung

The fracture behavior of open-porous materials is governed by a complex interplay between microstructural architecture and crack propagation mechanisms, necessitating systematic investigation to ensure their reliable use in structural, biomedical, and thermal insulation applications. Quantifying fracture toughness and strain energy release rates is essential for optimizing mechanical stability under stress. This study presents a computational framework based on Laguerre-Voronoi tessellation to model the intricate cellular architecture of open-porous solids. Under tensile loading, the model reproduces the classical scaling relations proposed by Maiti, Gibson, and Ashby. The effective elastic modulus exhibits a nearly quadratic dependence on the solid fraction, while the normalized fracture behavior follows a square-root function of the solid fraction. The model prediction for the normalized fracture toughness shows good agreement with experimental data reported in the literature. This consistency confirms the capability of Voronoi-based microstructures to capture established power laws, while also revealing deviations associated with pronounced heterogeneity. Subsequently, the key microstructural parameters, including solid fraction, pore size and pore-wall thickness, as well as the macroscopic crack geometric features, such as crack depth-to-height ratio and crack orientation, are systematically varied to assess their influence on fracture resistance. The results reveal critical dependence of crack propagation and energy dissipation on microstructural features, demonstrating how porosity and pore size distribution can be tuned to tailor the mechanical response. These findings contribute to a deeper understanding of fracture mechanics in porous systems and underscore the need for microstructure-informed material design to enhance mechanical performance.