Computational modelling of fracture in random two-phase materials

The analysis of crack propagation in heterogeneous materials remains a challenging task in computational mechanics, due to the complex interplay between material heterogeneity, microstructural features, and failure mechanisms. Traditional deterministic approaches often provide limited insight into the variability of fracture behavior observed in real materials, especially when randomness governs the crack initiation and propagation paths. In this work, an alternative computational framework is proposed to investigate fracture processes in random two-phase materials. The approach combines statistical characterization of the material response [1, 2] with advanced numerical modeling strategies, allowing an effective representation of microstructural variability at the macroscale. In particular, a homogenization-based strategy is employed to capture the overall mechanical behavior of the heterogeneous medium, while an advanced numerical formulation is adopted to simulate crack initiation, propagation, and interaction with the underlying microstructure. [3, 4, 5]. The proposed framework enables the consistent transfer of information across scales, linking stochastic microstructural features to the macroscopic structural response and allowing crack initiation and propagation within different material regions, including matrix, interphases, and inclusions. This allows for a more realistic prediction of fracture patterns and energy dissipation mechanisms. The methodology proves to be flexible and computationally efficient, making it suitable for parametric analyses and for the investigation of complex heterogeneous materials under different loading conditions.