An overview on the state of the art in fracture mechanics of functionally graded granular (meta)materials

This review provides a structured and comprehensive overview of the current state of fracture mechanics for functionally graded granular (meta)materials. The conceptual framework that situates functionally graded materials (FGMs) within the wider class of metamaterials is first introduced, followed by a classification of relevant microstructural architectures and gradient types (compositional, porous and microstructural). Emphasis is placed on damage and fracture phenomena peculiar to graded systems—including Mode I/II/III, mixed-mode, impact, fatigue, thermal and creep fractures—and on how spatial variations of elastic and fracture properties modulate crack initiation, propagation and arrest. Physical and mathematical modeling approaches are critically examined, spanning classical first-gradient formulations, higher-order strain-gradient theories and micromorphic frameworks, and highlights recent advances in phase-field and multiscale numerical strategies that capture gradient-induced toughening and size effects. Experimental and numerical evidence consistently demonstrates that tailored gradient architectures can markedly enhance damage tolerance, produce rising R-curves and increase impact resistance, whereas gradient orientation and interface smoothness crucially determine crack paths and failure modes. In conclusion, outstanding challenges are identified (rigorous multiscale coupling, standardized in-situ characterization, and design rules compatible with additive manufacturing) and a roadmap is proposed for integrating modeling, fabrication and testing to translate graded metamaterial concepts into reliable structural applications.